Tiago de Paula Peixoto

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Tiago de Paula Peixoto

Professor of Complex Systems and Network Science

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Year

Ordered community detection in directed networks

2025

Tiago P. Peixoto
Physical Review E 106 (2), 024305
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Authors:	Tiago P. Peixoto
Publication date:	05/05/2025
Journal:	Physical Review E
Volume:	106
Issue:	2
Pages:	024305
Description:	We develop a method to infer community structure in directed networks where the groups are ordered in a latent one-dimensional hierarchy that determines the preferred edge direction. Our nonparametric Bayesian approach is based on a modification of the stochastic block model (SBM), which can take advantage of rank alignment and coherence to produce parsimonious descriptions of networks that combine ordered hierarchies with arbitrary mixing patterns between groups. Since our model also includes directed degree correction, we can use it to distinguish nonlocal hierarchical structure from local in- and out-degree imbalance—thus, removing a source of conflation present in most ranking methods. We also demonstrate how we can reliably compare with the results obtained with the unordered SBM variant to determine whether a hierarchical ordering is statistically warranted in the first place. We illustrate the …
Cited by:	17
Resources:	[PDF] from arxiv.org

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The Netzschleuder network catalogue and repository

2025

Tiago P Peixoto
https://networks.skewed.de
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Authors:	Tiago P Peixoto
Publication date:	05/05/2025
Journal:	https://networks.skewed.de
Cited by:	88

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Network Reconstruction and Community Detection from Dynamics

2025

Tiago P. Peixoto
Physical Review Letters 123, 128301
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Authors:	Tiago P. Peixoto
Publication date:	05/05/2025
Journal:	Physical Review Letters
Volume:	123
Pages:	128301
Publisher:	American Physical Society
Description:	We present a scalable nonparametric Bayesian method to perform network reconstruction from observed functional behavior that at the same time infers the communities present in the network. We show that the joint reconstruction with community detection has a synergistic effect, where the edge correlations used to inform the existence of communities are also inherently used to improve the accuracy of the reconstruction which, in turn, can better inform the uncovering of communities. We illustrate the use of our method with observations arising from epidemic models and the Ising model, both on synthetic and empirical networks, as well as on data containing only functional information.
Cited by:	165
Resources:	[PDF] from aps.org

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Modelling sequences and temporal networks with dynamic community structures

2025

Tiago P. Peixoto, Martin Rosvall
Nature Communications 8, 582
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Authors:	Tiago P. Peixoto, Martin Rosvall
Publication date:	05/05/2025
Journal:	Nature Communications
Volume:	8
Pages:	582
Publisher:	Nature
Description:	In evolving complex systems such as air traffic and social organisations, collective effects emerge from their many components’ dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and links that change over time, they remain highly complex. It is therefore often necessary to use methods that extract the temporal networks’ large-scale dynamic community structure. However, such methods are subject to overfitting or suffer from effects of arbitrary, a priori-imposed timescales, which should instead be extracted from data. Here we simultaneously address both problems and develop a principled data-driven method that determines relevant timescales and identifies patterns of dynamics that take place on networks, as well as shape the networks themselves. We base our method on an arbitrary-order Markov chain model with community structure, and develop a …
Cited by:	160
Resources:	[HTML] from nature.com Full View

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Multiple Transitions and Disease Localization in Multilayer Networks

2025

Guilherme Ferraz De Arruda, Emanuele Cozzo, P Tiago, Francisco A Rodrigues, Yamir Moreno
Final Draft. Submitt. Publ, 1-18
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Authors:	Guilherme Ferraz De Arruda, Emanuele Cozzo, P Tiago, Francisco A Rodrigues, Yamir Moreno
Publication date:	05/05/2025
Journal:	Final Draft. Submitt. Publ
Pages:	1-18
Description:	We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the SIS and SIR dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasi-stationary state (QS) method we numerically show the existence of disease localization and the emergence of two or more phase transitions, which are characterized analytically and numerically through the inverse participation ratio. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems opening new possibilities for the study of spreading processes. Finally, our findings show the importance of considering the multilayer nature of many real systems, as this interdependency usually gives raise to new phenomenology.
Cited by:	1
Resources:	[PDF] from researchgate.net

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The graph-tool Python library

2025

Tiago P. Peixoto
figshare
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Authors:	Tiago P. Peixoto
Publication date:	05/05/2025
Journal:	figshare
Description:	Graph-tool is an efficient Python module for manipulation and statistical analysis of graphs (aka networks). Contrary to most other python modules with similar functionality, the core data structures and algorithms are implemented in C++, making extensive use of template metaprogramming, based heavily on the Boost Graph Library. This confers it a level of performance that is comparable (both in memory usage and computation time) to that of a pure C/C++ library.
Cited by:	578

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Polymer confinement effects in aligned carbon nanotubes arrays

2025

Pitamber Mahanandia, Jörg J Schneider, Marina Khaneft, Bernd Stühn, Tiago P Peixoto, Ba…
Physical Chemistry Chemical Physics 12 (17), 4407-4417
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Authors:	Pitamber Mahanandia, Jörg J Schneider, Marina Khaneft, Bernd Stühn, Tiago P Peixoto, Barbara Drossel
Publication date:	05/05/2025
Journal:	Physical Chemistry Chemical Physics
Volume:	12
Issue:	17
Pages:	4407-4417
Publisher:	Royal Society of Chemistry
Description:	We present experimental and theoretical studies on the infiltration of polymers (polystyrene (PS), polymethylmethacrylate (PMMA)) into the free interstices of 3D aligned carbon nanotube arrays. The 3D aligned CNT structures were prepared by a template assisted non catalytic CVD approach. The infiltrated CNT/polymer composites were characterized by microscopic techniques such as infra-red and Raman spectroscopy. Small angle X-ray scattering (SAXS) has been employed to study the structural evolution and polymer confinement after the polymers are infiltrated in the aligned arrays of CNTs. A theoretical model has been used to understand and predict possible confinement effects of these polymers within the aligned CNT arrays, using self-consistent field theory (SCFT) and Monte-Carlo simulations based on the bond-fluctuation model.
Cited by:	18
Resources:	[PDF] from google.com

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Criticalidade auto-organizada no modelo Olami-Feder-Christensen de terremotos: dinâmica dos epicentros

2025

Tiago de Paula Peixoto
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Authors:	Tiago de Paula Peixoto
Publication date:	05/05/2025
Description:	Nesse trabalho será estudada a dinâmica de epicentros do modelo Olami-Feder-Christensen (OFC). Para isso, serão usados conceitos e ferramentas de redes comple-xas. Será analisado, em particular, o grafo de epicentros consecutivos do modelo, onde dois eventos subseqüentes são representados por uma aresta direcionada, cuja origem e vértice incidido representam os respectivos sítios no reticulado. A topologia desse grafo, que possui invariância de escala e correlação entre os graus, revela uma dinâmica característica, com atratores temporários, e quase-periodicidade. Essa dinâmica é comparada com a de terremotos reais, e as limitações do modelo são avaliadas. Em particular, foi constatado que a dinâmica governada por atratores temporários se encontra presente em terremotos reais, porém difere em pontos centrais da observada no modelo OFC. Além da análise da dinâmica dos epicentros, será feito um estudo sistemático de dois comportamentos não-triviais do modelo, o que foi necessário para a análise da dinâmica de epicentros: A identificação e caracterização de um" efeito de borda" no modelo, e uma separação de escalas de eventos de diferentes tamanhos, que considera também as suas distribuições espaciais. Esses resultados têm uma relevância importante o estudo do modelo de modo geral. Em particular, será retomada a análise da criticalidade do modelo, à luz dessescritérios
Cited by:	1

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Uncertainty quantification and posterior sampling for network reconstruction

2025

Tiago P Peixoto
arXiv preprint arXiv:2503.07736
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Authors:	Tiago P Peixoto
Publication date:	03/10/2025
Journal:	arXiv preprint arXiv:2503.07736
Description:	Network reconstruction is the task of inferring the unseen interactions between elements of a system, based only on their behavior or dynamics. This inverse problem is in general ill-posed, and admits many solutions for the same observation. Nevertheless, the vast majority of statistical methods proposed for this task -- formulated as the inference of a graphical generative model -- can only produce a ``point estimate,'' i.e. a single network considered the most likely. In general, this can give only a limited characterization of the reconstruction, since uncertainties and competing answers cannot be conveyed, even if their probabilities are comparable, while being structurally different. In this work we present an efficient MCMC algorithm for sampling from posterior distributions of reconstructed networks, which is able to reveal the full population of answers for a given reconstruction problem, weighted according to their plausibilities. Our algorithm is general, since it does not rely on specific properties of particular generative models, and is specially suited for the inference of large and sparse networks, since in this case an iteration can be performed in time for a network of nodes, instead of , as would be the case for a more naive approach. We demonstrate the suitability of our method in providing uncertainties and consensus of solutions (which provably increases the reconstruction accuracy) in a variety of synthetic and empirical cases.
Resources:	[PDF] from arxiv.org

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Network Reconstruction via the Minimum Description Length Principle

2025

Tiago P Peixoto
Physical Review X 15 (1), 011065
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Authors:	Tiago P Peixoto
Publication date:	01/01/2025
Journal:	Physical Review X
Volume:	15
Issue:	1
Pages:	011065
Publisher:	American Physical Society
Cited by:	8

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Recommendations for sharing network data and materials

2024

Zachary P Neal, Zack W Almquist, James Bagrow, Aaron Clauset, Jana Diesner, Emmanuel La…
Network Science 12 (4), 404-417
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Authors:	Zachary P Neal, Zack W Almquist, James Bagrow, Aaron Clauset, Jana Diesner, Emmanuel Lazega, Juniper Lovato, James Moody, Tiago P Peixoto, Zachary Steinert-Threlkeld, Andreia Sofia Teixeira
Publication date:	12/01/2024
Journal:	Network Science
Volume:	12
Issue:	4
Pages:	404-417
Publisher:	Cambridge University Press
Description:	One of the goals of open science is to promote the transparency and accessibility of research. Sharing data and materials used in network research is critical to these goals. In this paper, we present recommendations for whether, what, when, and where network data and materials should be shared. We recommend that network data and materials should be shared, but access to or use of shared data and materials may be restricted if necessary to avoid harm or comply with regulations. Researchers should share the network data and materials necessary to reproduce reported results via a publicly accessible repository when an associated manuscript is published. To ensure the adoption of these recommendations, network journals should require sharing, and network associations and academic institutions should reward sharing.
Cited by:	1
Resources:	[PDF] from cambridge.org

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Scalable network reconstruction in subquadratic time

2024

Tiago P Peixoto
arXiv preprint arXiv:2401.01404
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Authors:	Tiago P Peixoto
Publication date:	01/02/2024
Journal:	arXiv preprint arXiv:2401.01404
Description:	Network reconstruction consists in determining the unobserved pairwise couplings between nodes given only observational data on the resulting behavior that is conditioned on those couplings -- typically a time-series or independent samples from a graphical model. A major obstacle to the scalability of algorithms proposed for this problem is a seemingly unavoidable quadratic complexity of , corresponding to the requirement of each possible pairwise coupling being contemplated at least once, despite the fact that most networks of interest are sparse, with a number of non-zero couplings that is only . Here we present a general algorithm applicable to a broad range of reconstruction problems that significantly outperforms this quadratic baseline. Our algorithm relies on a stochastic second neighbor search (Dong et al., 2011) that produces the best edge candidates with high probability, thus bypassing an exhaustive quadratic search. If we rely on the conjecture that the second-neighbor search finishes in log-linear time (Baron & Darling, 2020; 2022), we demonstrate theoretically that our algorithm finishes in subquadratic time, with a data-dependent complexity loosely upper bounded by , but with a more typical log-linear complexity of . In practice, we show that our algorithm achieves a performance that is many orders of magnitude faster than the quadratic baseline -- in a manner consistent with our theoretical analysis -- allows for easy parallelization, and thus enables the reconstruction of networks with hundreds of thousands and even millions of nodes and edges.
Cited by:	2
Resources:	[PDF] from arxiv.org

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Modelling temporal networks with Markov chains, community structures and change points

2023

Tiago P Peixoto, Martin Rosvall
Temporal network theory, 65-82
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Authors:	Tiago P Peixoto, Martin Rosvall
Publication date:	11/21/2023
Journal:	Temporal network theory
Pages:	65-82
Publisher:	Springer International Publishing
Description:	While temporal networks contain crucial information about the evolving systems they represent, only recently have researchers showed how to incorporate higher-order Markov chains, community structure and abrupt transitions to describe them. However, each approach can only capture one aspect of temporal networks, which often are multifaceted with dynamics taking place concurrently at small and large structural scales and also at short and long timescales. Therefore, these approaches must be combined for more realistic descriptions of empirical systems. Here we present two data-driven approaches developed to capture multiple aspects of temporal network dynamics. Both approaches capture short timescales and small structural scales with Markov chains. Whereas one approach also captures large structural scales with communities, the other instead captures long timescales with change points. Using a …
Cited by:	9
Resources:	[PDF] from google.com

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Implicit models, latent compression, intrinsic biases, and cheap lunches in community detection

2023

Tiago P. Peixoto, Alec Kirkley
Phys. Rev. E 108, 024309
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Authors:	Tiago P. Peixoto, Alec Kirkley
Publication date:	09/01/2023
Journal:	Phys. Rev. E
Volume:	108
Pages:	024309
Description:	The task of community detection, which aims to partition a network into clusters of nodes to summarize its large-scale structure, has spawned the development of many competing algorithms with varying objectives. Some community detection methods are inferential, explicitly deriving the clustering objective through a probabilistic generative model, while other methods are descriptive, dividing a network according to an objective motivated by a particular application, making it challenging to compare these methods on the same scale. Here we present a solution to this problem that associates any community detection objective, inferential or descriptive, with its corresponding implicit network generative model. This allows us to compute the description length of a network and its partition under arbitrary objectives, providing a principled measure to compare the performance of different algorithms without the need for "ground truth" labels. Our approach also gives access to instances of the community detection problem that are optimal to any given algorithm, and in this way reveals intrinsic biases in popular descriptive methods, explaining their tendency to overfit. Using our framework, we compare a number of community detection methods on artificial networks, and on a corpus of over 500 structurally diverse empirical networks. We find that more expressive community detection methods exhibit consistently superior compression performance on structured data instances, without having degraded performance on a minority of situations where more specialized algorithms perform optimally. Our results undermine the implications of the "no free lunch" …
Cited by:	15
Resources:	[PDF] from arxiv.org

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Descriptive vs. inferential community detection in networks: Pitfalls, myths and half-truths

2023

Tiago P Peixoto
Elements in the Structure and Dynamics of Complex Networks
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Authors:	Tiago P Peixoto
Publication date:	07/01/2023
Journal:	Elements in the Structure and Dynamics of Complex Networks
Publisher:	Cambridge University Press
Description:	Community detection is one of the most important methodological fields of network science, and one which has attracted a significant amount of attention over the past decades. This area deals with the automated division of a network into fundamental building blocks, with the objective of providing a summary of its large-scale structure. Despite its importance and widespread adoption, there is a noticeable gap between what is arguably the state-of-the-art and the methods which are actually used in practice in a variety of fields. The Elements attempts to address this discrepancy by dividing existing methods according to whether they have a'descriptive'or an'inferential'goal. While descriptive methods find patterns in networks based on context-dependent notions of community structure, inferential methods articulate a precise generative model, and attempt to fit it to data. In this way, they are able to provide insights into …
Cited by:	91
Resources:	[PDF] from arxiv.org

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Social network modeling and applications, a tutorial

2023

Lisette Espín-Noboa, Tiago Peixoto, Fariba Karimi
arXiv preprint arXiv:2306.11004
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Authors:	Lisette Espín-Noboa, Tiago Peixoto, Fariba Karimi
Publication date:	06/19/2023
Journal:	arXiv preprint arXiv:2306.11004
Description:	Social networks have been widely studied over the last century from multiple disciplines to understand societal issues such as inequality in employment rates, managerial performance, and epidemic spread. Today, these and many more issues can be studied at global scale thanks to the digital footprints that we generate when browsing the Web or using social media platforms. Unfortunately, scientists often struggle to access to such data primarily because it is proprietary, and even when it is shared with privacy guarantees, such data is either no representative or too big. In this tutorial, we will discuss recent advances and future directions in network modeling. In particular, we focus on how to exploit synthetic networks to study real-world problems such as data privacy, spreading dynamics, algorithmic bias, and ranking inequalities. We start by reviewing different types of generative models for social networks including node-attributed and scale-free networks. Then, we showcase how to perform a network selection analysis to characterize the mechanisms of edge formation of any given real-world network.
Cited by:	1
Resources:	[PDF] from arxiv.org

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Tutorials at the web conference 2023

2023

Valeria Fionda, Olaf Hartig, Reyhaneh Abdolazimi, Sihem Amer-Yahia, Hongzhi Chen, Xiao …
Companion Proceedings of the ACM Web Conference 2023, 648-658
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Authors:	Valeria Fionda, Olaf Hartig, Reyhaneh Abdolazimi, Sihem Amer-Yahia, Hongzhi Chen, Xiao Chen, Peng Cui, Jeffrey Dalton, Xin Luna Dong, Lisette Espin-Noboa, Wenqi Fan, Manuela Fritz, Quan Gan, Jingtong Gao, Xiaojie Guo, Torsten Hahmann, Jiawei Han, Soyeon Han, Estevam Hruschka, Liang Hu, Jiaxin Huang, Utkarshani Jaimini, Olivier Jeunen, Yushan Jiang, Fariba Karimi, George Karypis, Krishnaram Kenthapadi, Himabindu Lakkaraju, Hady W Lauw, Thai Le, Trung-Hoang Le, Dongwon Lee, Geon Lee, Liat Levontin, Cheng-Te Li, Haoyang Li, Ying Li, Jay Chiehen Liao, Qidong Liu, Usha Lokala, Ben London, Siqu Long, Hande Kücük Mcginty, Yu Meng, Seungwhan Moon, Usman Naseem, Pradeep Natarajan, Behrooz Omidvar-Tehrani, Zijie Pan, Devesh Parekh, Jian Pei, Tiago Peixoto, Steven Pemberton, Josiah Poon, Filip Radlinski, Federico Rossetto, Kaushik Roy, Aghiles Salah, Mehrnoosh Sameki, Amit Sheth, Cogan Shimizu, Kijung Shin, Dongjin Song, Julia Stoyanovich, Dacheng Tao, Johanne Trippas, Quoc Truong, Yu-Che Tsai, Adaku Uchendu, Bram Van Den Akker, Lin Wang, Minjie Wang, Shoujin Wang, Xin Wang, Ingmar Weber, Henry Weld, Lingfei Wu, Da Xu, Ethan Yifan Xu, Shuyuan Xu, Bo Yang, Ke Yang, Elad Yom-Tov, Jaemin Yoo, Zhou Yu, Reza Zafarani, Hamed Zamani, Meike Zehlike, Qi Zhang, Xikun Zhang, Yongfeng Zhang, Yu Zhang, Zheng Zhang, Liang Zhao, Xiangyu Zhao, Wenwu Zhu
Publication date:	04/30/2023
Journal:	Companion Proceedings of the ACM Web Conference 2023
Pages:	648-658
Description:	This paper summarizes the content of the 28 tutorials that have been given at The Web Conference 2023.
Cited by:	7
Resources:	[PDF] from acm.org

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Statistical inference links data and theory in network science

2022

Leto Peel, Tiago P Peixoto, Manlio De Domenico
Nature Communications 13 (1), 6794
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Authors:	Leto Peel, Tiago P Peixoto, Manlio De Domenico
Publication date:	11/10/2022
Journal:	Nature Communications
Volume:	13
Issue:	1
Pages:	6794
Publisher:	Nature Publishing Group UK
Description:	The number of network science applications across many different fields has been rapidly increasing. Surprisingly, the development of theory and domain-specific applications often occur in isolation, risking an effective disconnect between theoretical and methodological advances and the way network science is employed in practice. Here we address this risk constructively, discussing good practices to guarantee more successful applications and reproducible results. We endorse designing statistically grounded methodologies to address challenges in network science. This approach allows one to explain observational data in terms of generative models, naturally deal with intrinsic uncertainties, and strengthen the link between theory and applications.
Cited by:	106
Resources:	[HTML] from nature.com Full View

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Systematic assessment of the quality of fit of the stochastic block model for empirical networks

2022

Felipe Vaca-Ramírez, Tiago P Peixoto
Physical Review E 105 (5), 054311
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Authors:	Felipe Vaca-Ramírez, Tiago P Peixoto
Publication date:	05/18/2022
Journal:	Physical Review E
Volume:	105
Issue:	5
Pages:	054311
Publisher:	American Physical Society
Description:	We perform a systematic analysis of the quality of fit of the stochastic block model (SBM) for 275 empirical networks spanning a wide range of domains and orders of size magnitude. We employ posterior predictive model checking as a criterion to assess the quality of fit, which involves comparing networks generated by the inferred model with the empirical network, according to a set of network descriptors. We observe that the SBM is capable of providing an accurate description for the majority of networks considered, but falls short of saturating all modeling requirements. In particular, networks possessing a large diameter and slow-mixing random walks tend to be badly described by the SBM. However, contrary to what is often assumed, networks with a high abundance of triangles can be well described by the SBM in many cases. We demonstrate that simple network descriptors can be used to evaluate whether or …
Cited by:	13
Resources:	[PDF] from arxiv.org

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Disentangling homophily, community structure, and triadic closure in networks

2022

Tiago P Peixoto
Physical Review X 12 (1), 011004
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Authors:	Tiago P Peixoto
Publication date:	01/06/2022
Journal:	Physical Review X
Volume:	12
Issue:	1
Pages:	011004
Publisher:	American Physical Society
Description:	Network homophily, the tendency of similar nodes to be connected, and transitivity, the tendency of two nodes to be connected if they share a common neighbor, are conflated properties in network analysis since one mechanism can drive the other. Here, we present a generative model and corresponding inference procedure that are capable of distinguishing between both mechanisms. Our approach is based on a variation of the stochastic block model (SBM) with the addition of triadic closure edges, and its inference can identify the most plausible mechanism responsible for the existence of every edge in the network, in addition to the underlying community structure itself. We show how the method can evade the detection of spurious communities caused solely by the formation of triangles in the network and how it can improve the performance of edge prediction when compared to the pure version of the SBM …
Cited by:	57
Resources:	[PDF] from aps.org

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Multilayer networks for text analysis with multiple data types

2021

Charles C Hyland, Yuanming Tao, Lamiae Azizi, Martin Gerlach, Tiago P Peixoto, Eduardo …
EPJ Data Science 10 (1), 33
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Authors:	Charles C Hyland, Yuanming Tao, Lamiae Azizi, Martin Gerlach, Tiago P Peixoto, Eduardo G Altmann
Publication date:	12/01/2021
Journal:	EPJ Data Science
Volume:	10
Issue:	1
Pages:	33
Publisher:	Springer Berlin Heidelberg
Description:	We are interested in the widespread problem of clustering documents and finding topics in large collections of written documents in the presence of metadata and hyperlinks. To tackle the challenge of accounting for these different types of datasets, we propose a novel framework based on Multilayer Networks and Stochastic Block Models. The main innovation of our approach over other techniques is that it applies the same non-parametric probabilistic framework to the different sources of datasets simultaneously. The key difference to other multilayer complex networks is the strong unbalance between the layers, with the average degree of different node types scaling differently with system size. We show that the latter observation is due to generic properties of text, such as Heaps’ law, and strongly affects the inference of communities. We present and discuss the performance of our method in different datasets …
Cited by:	23
Resources:	[PDF] from springer.com Full View

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The physics of higher-order interactions in complex systems

2021

Federico Battiston, Enrico Amico, Alain Barrat, Ginestra Bianconi, Guilherme Ferraz de …
Nature Physics 17 (10), 1093-1098
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Authors:	Federico Battiston, Enrico Amico, Alain Barrat, Ginestra Bianconi, Guilherme Ferraz de Arruda, Benedetta Franceschiello, Iacopo Iacopini, Sonia Kéfi, Vito Latora, Yamir Moreno, Micah M Murray, Tiago P Peixoto, Francesco Vaccarino, Giovanni Petri
Publication date:	10/01/2021
Journal:	Nature Physics
Volume:	17
Issue:	10
Pages:	1093-1098
Publisher:	Nature Publishing Group UK
Description:	Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.
Cited by:	745
Resources:	[PDF] from arxiv.org

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Hypergraph reconstruction from network data

2021

Jean-Gabriel Young, Giovanni Petri, Tiago P Peixoto
Communications Physics 4 (1), 135
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Authors:	Jean-Gabriel Young, Giovanni Petri, Tiago P Peixoto
Publication date:	06/15/2021
Journal:	Communications Physics
Volume:	4
Issue:	1
Pages:	135
Publisher:	Nature Publishing Group UK
Description:	Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the fundamental interactions involve more than two entities at the same time. Pairwise representations nonetheless remain ubiquitous, because higher-order interactions are often not recorded explicitly in network data. Here, we introduce a Bayesian approach to reconstruct latent higher-order interactions from ordinary pairwise network data. Our method is based on the principle of parsimony and only includes higher-order structures when there is sufficient statistical evidence for them. We demonstrate its applicability to a wide range of datasets, both synthetic and empirical.
Cited by:	123
Resources:	[HTML] from nature.com Full View

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Revealing consensus and dissensus between network partitions

2021

Tiago P Peixoto
Physical Review X 11 (2), 021003
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Authors:	Tiago P Peixoto
Publication date:	04/05/2021
Journal:	Physical Review X
Volume:	11
Issue:	2
Pages:	021003
Publisher:	American Physical Society
Description:	Community detection methods attempt to divide a network into groups of nodes that share similar properties, thus revealing its large-scale structure. A major challenge when employing such methods is that they are often degenerate, typically yielding a complex landscape of competing answers. As an attempt to extract understanding from a population of alternative solutions, many methods exist to establish a consensus among them in the form of a single partition “point estimate” that summarizes the whole distribution. Here, we show that it is, in general, not possible to obtain a consistent answer from such point estimates when the underlying distribution is too heterogeneous. As an alternative, we provide a comprehensive set of methods designed to characterize and summarize complex populations of partitions in a manner that captures not only the existing consensus but also the dissensus between elements of …
Cited by:	65
Resources:	[PDF] from aps.org

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Statistical inference of assortative community structures

2020

Lizhi Zhang, Tiago P Peixoto
Physical Review Research 2 (4), 043271
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Authors:	Lizhi Zhang, Tiago P Peixoto
Publication date:	11/23/2020
Journal:	Physical Review Research
Volume:	2
Issue:	4
Pages:	043271
Publisher:	American Physical Society
Description:	We develop a principled methodology to infer assortative communities in networks based on a nonparametric Bayesian formulation of the planted partition model. We show that this approach succeeds in finding statistically significant assortative modules in networks, unlike alternatives such as modularity maximization, which systematically overfits both in artificial as well as in empirical examples. In addition, we show that our method is not subject to an appreciable resolution limit, and can uncover an arbitrarily large number of communities, as long as there is statistical evidence for them. Our formulation is amenable to model selection procedures, which allow us to compare it to more general approaches based on the stochastic block model, and in this way reveal whether assortativity is in fact the dominating large-scale mixing pattern. We perform this comparison with several empirical networks and identify …
Cited by:	81
Resources:	[PDF] from aps.org

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Null models for multioptimized large-scale network structures

2020

Sebastian Morel-Balbi, Tiago P Peixoto
Physical Review E 102 (3), 032306
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Authors:	Sebastian Morel-Balbi, Tiago P Peixoto
Publication date:	06/22/2020
Journal:	Physical Review E
Volume:	102
Issue:	3
Pages:	032306
Publisher:	American Physical Society
Description:	We study the emerging large-scale structures in networks subject to selective pressures that simultaneously drive toward higher modularity and robustness against random failures. We construct maximum-entropy null models that isolate the effects of the joint optimization on the network structure from any kind of evolutionary dynamics. Our analysis reveals a rich phase diagram of optimized structures, composed of many combinations of modular, core-periphery, and bipartite patterns. Furthermore, we observe parameter regions where the simultaneous optimization can be either synergistic or antagonistic, with the improvement of one criterion directly aiding or hindering the other, respectively. Our results show how interactions between different selective pressures can be pivotal in determining the emerging network structure, and that these interactions can be captured by simple network models.
Cited by:	3
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Merge-split Markov chain Monte Carlo for community detection

2020

Tiago P Peixoto
Phys. Rev. E 102, 012305
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Authors:	Tiago P Peixoto
Publication date:	03/16/2020
Journal:	Phys. Rev. E
Volume:	102
Pages:	012305
Description:	We present a Markov chain Monte Carlo scheme based on merges and splits of groups that is capable of efficiently sampling from the posterior distribution of network partitions, defined according to the stochastic block model (SBM). We demonstrate how schemes based on the move of single nodes between groups systematically fail at correctly sampling from the posterior distribution even on small networks, and how our merge-split approach behaves significantly better, and improves the mixing time of the Markov chain by several orders of magnitude in typical cases. We also show how the scheme can be straightforwardly extended to nested versions of the SBM, yielding asymptotically exact samples of hierarchical network partitions.
Cited by:	57
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Latent Poisson models for networks with heterogeneous density

2020

Tiago P Peixoto
Phys. Rev. E 102, 012309
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Authors:	Tiago P Peixoto
Publication date:	02/18/2020
Journal:	Phys. Rev. E
Volume:	102
Pages:	012309
Description:	Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense, for example, with a few nodes connecting to a large fraction of the rest of the network, or with small groups of nodes with a large probability of connections between them. Here we show how latent Poisson models that generate hidden multigraphs can be effective at capturing this density heterogeneity, while being more tractable mathematically than some of the alternatives that model simple graphs directly. We show how these latent multigraphs can be reconstructed from data on simple graphs, and how this allows us to disentangle disassortative degree-degree correlations from the constraints of imposed degree sequences, and to improve the identification of community …
Cited by:	11
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Bayesian stochastic blockmodeling

2019

Tiago P Peixoto
Advances in network clustering and blockmodeling, 289-332
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Authors:	Tiago P Peixoto
Publication date:	11/23/2019
Journal:	Advances in network clustering and blockmodeling
Pages:	289-332
Publisher:	John Wiley & Sons, Ltd
Description:	This chapter describes the basic variants of the stochastic blockmodel (SBM), and a consistent Bayesian formulation that allows readers to infer them from data. The focus is on developing a framework to extract the large‐scale structure of networks while avoiding both overfitting and underfitting, and doing so in a manner that is analytically tractable and computationally efficient. The Bayesian inference approach provides a methodologically correct answer to the very central question in network analysis of whether patterns of large‐scale structure can in fact be supported by statistical evidence. Besides this practical aspect, it also opens a window into the fundamental limits of network analysis itself, giving readers a theoretical underpinning we can use to understand more about the nature of network systems. The chapter shows how inferring the SBM can be used to predict missing and spurious links and also sheds …
Cited by:	322
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Reconstructing networks with unknown and heterogeneous errors

2018

Tiago P. Peixoto
Physical Review X 8, 041011
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Authors:	Tiago P. Peixoto
Publication date:	10/01/2018
Journal:	Physical Review X
Volume:	8
Pages:	041011
Publisher:	American Physical Society
Description:	The vast majority of network data sets contain errors and omissions, although this fact is rarely incorporated in traditional network analysis. Recently, an increasing effort has been made to fill this methodological gap by developing network-reconstruction approaches based on Bayesian inference. These approaches, however, rely on assumptions of uniform error rates and on direct estimations of the existence of each edge via repeated measurements, something that is currently unavailable for the majority of network data. Here, we develop a Bayesian reconstruction approach that lifts these limitations by allowing for not only heterogeneous errors, but also for single edge measurements without direct error estimates. Our approach works by coupling the inference approach with structured generative network models, which enable the correlations between edges to be used as reliable uncertainty estimates. Although …
Cited by:	120
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Change points, memory and epidemic spreading in temporal networks

2018

Tiago P. Peixoto, Laetitia Gauvin
Scientific Reports 8, 15511
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Authors:	Tiago P. Peixoto, Laetitia Gauvin
Publication date:	09/01/2018
Journal:	Scientific Reports
Volume:	8
Pages:	15511
Publisher:	Nature
Description:	Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks attempt to capture only a single characteristic time scale in isolation — typically associated with the short-time memory of a Markov chain or with long-time abrupt changes caused by external or systemic events. Here we propose a unified approach to model both aspects simultaneously, detecting short and long-time behaviors of temporal networks. We do so by developing an arbitrary-order mixed Markov model with change points, and using a nonparametric Bayesian formulation that allows the Markov order and the position of change points to be determined from data without overfitting. In addition, we evaluate the quality of the multiscale model in its capacity to reproduce the …
Cited by:	35
Resources:	[HTML] from nature.com

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A network approach to topic models

2018

Martin Gerlach, Tiago P Peixoto, Eduardo G Altmann
Science advances 4 (7), eaaq1360
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Authors:	Martin Gerlach, Tiago P Peixoto, Eduardo G Altmann
Publication date:	07/18/2018
Journal:	Science advances
Volume:	4
Issue:	7
Pages:	eaaq1360
Publisher:	American Association for the Advancement of Science
Description:	One of the main computational and scientific challenges in the modern age is to extract useful information from unstructured texts. Topic models are one popular machine-learning approach that infers the latent topical structure of a collection of documents. Despite their success—particularly of the most widely used variant called latent Dirichlet allocation (LDA)—and numerous applications in sociology, history, and linguistics, topic models are known to suffer from severe conceptual and practical problems, for example, a lack of justification for the Bayesian priors, discrepancies with statistical properties of real texts, and the inability to properly choose the number of topics. We obtain a fresh view of the problem of identifying topical structures by relating it to the problem of finding communities in complex networks. We achieve this by representing text corpora as bipartite networks of documents and words. By adapting …
Cited by:	317
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Consistencies and inconsistencies between model selection and link prediction in networks

2018

Toni Vallès-Català, Tiago P Peixoto, Marta Sales-Pardo, Roger Guimerà
Physical Review E 97 (6), 062316
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Authors:	Toni Vallès-Català, Tiago P Peixoto, Marta Sales-Pardo, Roger Guimerà
Publication date:	06/28/2018
Journal:	Physical Review E
Volume:	97
Issue:	6
Pages:	062316
Publisher:	American Physical Society
Description:	A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand, discounting statistical fluctuations. This problem can be approached using two principled criteria that at first may seem equivalent: selecting the most plausible model in terms of its posterior probability; or selecting the model with the highest predictive performance in terms of identifying missing links. Here we show that while these two approaches yield consistent results in most cases, there are also notable instances where they do not, that is, where the most plausible model is not the most predictive. We show that in the latter case the improvement of predictive performance can in fact lead to overfitting both in artificial and empirical settings. Furthermore, we show that, in …
Cited by:	65
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Nonparametric weighted stochastic block models

2018

Tiago P Peixoto
Physical Review E 97 (1), 012306
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Authors:	Tiago P Peixoto
Publication date:	01/16/2018
Journal:	Physical Review E
Volume:	97
Issue:	1
Pages:	012306
Publisher:	American Physical Society
Description:	We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the model, which are instead inferred from data. We give a comprehensive treatment of different kinds of edge weights (i.e., continuous or discrete, signed or unsigned, bounded or unbounded), as well as arbitrary weight transformations, and describe an unsupervised model selection approach to choose the best network description. We illustrate the application of our method to a variety of empirical weighted networks, such as global migrations, voting patterns in congress, and neural connections in the human brain.
Cited by:	135
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On the consistency between model selection and link prediction in networks

2017

Toni Vallès-Català, Tiago P Peixoto, Roger Guimerà, Marta Sales-Pardo
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Authors:	Toni Vallès-Català, Tiago P Peixoto, Roger Guimerà, Marta Sales-Pardo
Publication date:	05/22/2017
Description:	A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand, discounting statistical fluctuations. This problem can be approached using two principled criteria that at first may seem equivalent: selecting the most plausible model in terms of its posterior probability; or selecting the model with the highest predictive performance in terms of identifying missing links. Here we show that while these two approaches yield consistent results in most of cases, there are also notable instances where they do not, that is, where the most plausible model is not the most predictive. We show that in the latter case the improvement of predictive performance can in fact lead to overfitting both in artificial and empirical settings. Furthermore, we show that, in general, the predictive performance is higher when we average over collections of models that are individually less plausible, than when we consider only the single most plausible model.
Cited by:	12
Resources:	[PDF] from bath.ac.uk

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Disease localization in multilayer networks

2017

Guilherme Ferraz de Arruda, Emanuele Cozzo, Tiago P Peixoto, Francisco A Rodrigues, Yam…
Physical Review X 7 (1), 011014
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Authors:	Guilherme Ferraz de Arruda, Emanuele Cozzo, Tiago P Peixoto, Francisco A Rodrigues, Yamir Moreno
Publication date:	02/02/2017
Journal:	Physical Review X
Volume:	7
Issue:	1
Pages:	011014
Publisher:	American Physical Society
Description:	We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptible-infected-recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe …
Cited by:	116
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Publisher’s Note: Nonparametric Bayesian inference of the microcanonical stochastic block model [Phys. Rev. E 95, 012317 (2017)]

2017

Tiago P Peixoto
Physical Review E 95 (1), 019904
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Authors:	Tiago P Peixoto
Publication date:	01/26/2017
Journal:	Physical Review E
Volume:	95
Issue:	1
Pages:	019904
Publisher:	American Physical Society
Description:	This paper was published online on 17 January 2017 with an error in the text of the abstract. The first line of the abstract should read as “A principled approach to characterize the hidden structure of networks is to formulate generative....” The paper has been corrected as of 20 January 2017. The text is correct in the printed version of the journal.
Cited by:	1

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Nonparametric Bayesian inference of the microcanonical stochastic block model

2017

Tiago P Peixoto
Physical Review E 95 (1), 012317
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Authors:	Tiago P Peixoto
Publication date:	01/17/2017
Journal:	Physical Review E
Volume:	95
Issue:	1
Pages:	012317
Publisher:	American Physical Society
Description:	A principled approach to characterize the hidden structure of networks is to formulate generative models and then infer their parameters from data. When the desired structure is composed of modules or “communities,” a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints, i.e., the generated networks are not allowed to violate the patterns imposed by the model. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: (1) deeper Bayesian …
Cited by:	221
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Network structure, metadata, and the prediction of missing nodes and annotations

2016

Darko Hric, Tiago P Peixoto, Santo Fortunato
Physical Review X 6 (3), 031038
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Authors:	Darko Hric, Tiago P Peixoto, Santo Fortunato
Publication date:	09/12/2016
Journal:	Physical Review X
Volume:	6
Issue:	3
Pages:	031038
Publisher:	American Physical Society
Description:	The empirical validation of community detection methods is often based on available annotations on the nodes that serve as putative indicators of the large-scale network structure. Most often, the suitability of the annotations as topological descriptors itself is not assessed, and without this it is not possible to ultimately distinguish between actual shortcomings of the community detection algorithms, on one hand, and the incompleteness, inaccuracy, or structured nature of the data annotations themselves, on the other. In this work, we present a principled method to access both aspects simultaneously. We construct a joint generative model for the data and metadata, and a nonparametric Bayesian framework to infer its parameters from annotated data sets. We assess the quality of the metadata not according to their direct alignment with the network communities, but rather in their capacity to predict the placement of …
Cited by:	127
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Sampling motif-constrained ensembles of networks

2015

Rico Fischer, Jorge C Leitao, Tiago P Peixoto, Eduardo G Altmann
Physical review letters 115 (18), 188701
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Authors:	Rico Fischer, Jorge C Leitao, Tiago P Peixoto, Eduardo G Altmann
Publication date:	10/29/2015
Journal:	Physical review letters
Volume:	115
Issue:	18
Pages:	188701
Publisher:	American Physical Society
Description:	The statistical significance of network properties is conditioned on null models which satisfy specified properties but that are otherwise random. Exponential random graph models are a principled theoretical framework to generate such constrained ensembles, but which often fail in practice, either due to model inconsistency or due to the impossibility to sample networks from them. These problems affect the important case of networks with prescribed clustering coefficient or number of small connected subgraphs (motifs). In this Letter we use the Wang-Landau method to obtain a multicanonical sampling that overcomes both these problems. We sample, in polynomial time, networks with arbitrary degree sequences from ensembles with imposed motifs counts. Applying this method to social networks, we investigate the relation between transitivity and homophily, and we quantify the correlation between different types …
Cited by:	26
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Generalized communities in networks

2015

Mark EJ Newman, Tiago P Peixoto
Physical review letters 115 (8), 088701
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Authors:	Mark EJ Newman, Tiago P Peixoto
Publication date:	08/20/2015
Journal:	Physical review letters
Volume:	115
Issue:	8
Pages:	088701
Publisher:	American Physical Society
Description:	A substantial volume of research is devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here, we describe a broad extension of community structure that encompasses traditional communities but includes a wide range of generalized structural patterns as well. We describe a principled method for detecting this generalized structure in empirical network data and demonstrate with real-world examples how it can be used to learn new things about the shape and meaning of networks.
Cited by:	91
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Maximum-entropy large-scale structures of Boolean networks optimized for criticality

2015

Marco Möller, Tiago P Peixoto
New Journal of Physics 17 (4), 043021
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Authors:	Marco Möller, Tiago P Peixoto
Publication date:	04/14/2015
Journal:	New Journal of Physics
Volume:	17
Issue:	4
Pages:	043021
Publisher:	IOP Publishing
Description:	We construct statistical ensembles of modular Boolean networks that are constrained to lie at the critical line between frozen and chaotic dynamic regimes. The ensembles are maximally random given the imposed constraints, and thus represent null models of critical networks. By varying the network density and the entropic cost associated with biased Boolean functions, the ensembles undergo several phase transitions. The observed structures range from fully random to several ordered ones, including a prominent core–periphery-like structure, and an'attenuated'two-group structure, where the network is divided in two groups of nodes, and one of them has Boolean functions with very low sensitivity. This shows that such simple large-scale structures are the most likely to occur when optimizing for criticality, in the absence of any other constraint or competing optimization criteria.
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Model selection and hypothesis testing for large-scale network models with overlapping groups

2015

Tiago P Peixoto
Physical Review X 5 (1), 011033
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Authors:	Tiago P Peixoto
Publication date:	03/25/2015
Journal:	Physical Review X
Volume:	5
Issue:	1
Pages:	011033
Publisher:	American Physical Society
Description:	The effort to understand network systems in increasing detail has resulted in a diversity of methods designed to extract their large-scale structure from data. Unfortunately, many of these methods yield diverging descriptions of the same network, making both the comparison and understanding of their results a difficult challenge. A possible solution to this outstanding issue is to shift the focus away from ad hoc methods and move towards more principled approaches based on statistical inference of generative models. As a result, we face instead the more well-defined task of selecting between competing generative processes, which can be done under a unified probabilistic framework. Here, we consider the comparison between a variety of generative models including features such as degree correction, where nodes with arbitrary degrees can belong to the same group, and community overlap, where nodes are …
Cited by:	149
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Limits and trade-offs of topological network robustness

2014

Christopher Priester, Sebastian Schmitt, Tiago P Peixoto
PloS one 9 (9), e108215
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Authors:	Christopher Priester, Sebastian Schmitt, Tiago P Peixoto
Publication date:	09/24/2014
Journal:	PloS one
Volume:	9
Issue:	9
Pages:	e108215
Publisher:	Public Library of Science
Description:	We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale structures. We present results from numerical two-objective optimization simulations for networks with various fixed mean degree and number of blocks. The results provide strong evidence that three different blocks are sufficient to realize the best trade-off between the two measures of robustness, i.e. to obtain the complete front of Pareto-optimal networks. For all values of the mean degree, a characteristic three block structure emerges over large parts of the Pareto-optimal front. This structure can be often characterized as a core-periphery structure, composed of a group of core nodes with high degree connected among themselves and to a periphery of low-degree nodes, in addition to a third group of nodes which is disconnected from the periphery, and weakly connected to the core. Only at both extremes of the Pareto-optimal front, corresponding to maximal robustness against random and targeted node removal, a two-block core-periphery structure or a one-block fully random network are found, respectively.
Cited by:	12
Resources:	[HTML] from plos.org Full Text Finder

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Hierarchical block structures and high-resolution model selection in large networks

2014

Tiago P Peixoto
Physical Review X 4 (1), 011047
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Authors:	Tiago P Peixoto
Publication date:	03/24/2014
Journal:	Physical Review X
Volume:	4
Issue:	1
Pages:	011047
Publisher:	American Physical Society
Description:	Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks suffer from serious problems, such as being oblivious to the statistical evidence supporting the discovered patterns, which results in the inability to separate actual structure from noise. In addition to this, one also observes a resolution limit on the size of communities, where smaller but well-defined clusters are not detectable when the network becomes large. This phenomenon occurs for the very popular approach of modularity optimization, which lacks built-in statistical validation, but also for more principled methods based on statistical inference and model selection, which do incorporate statistical validation in a formally correct way. Here, we construct a nested generative model …
Cited by:	536
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Efficient Monte Carlo and greedy heuristic for the inference of stochastic block models

2014

Tiago P Peixoto
Physical Review E 89 (1), 012804
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Authors:	Tiago P Peixoto
Publication date:	01/13/2014
Journal:	Physical Review E
Volume:	89
Issue:	1
Pages:	012804
Publisher:	American Physical Society
Description:	We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to getting trapped in metastable states, or as a greedy agglomerative heuristic, with an almost linear complexity, where is the number of nodes in the network, independent of the number of blocks being inferred. We show that the heuristic is capable of delivering results which are indistinguishable from the more exact and numerically expensive MCMC method in many artificial and empirical networks, despite being much faster. The method is entirely unbiased towards any specific mixing pattern, and in particular it does not favor assortative community structures.
Cited by:	304
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Spontaneous centralization of control in a network of company ownerships

2013

Sebastian M Krause, Tiago P Peixoto, Stefan Bornholdt
PloS One 8 (12), e80303
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Authors:	Sebastian M Krause, Tiago P Peixoto, Stefan Bornholdt
Publication date:	12/06/2013
Journal:	PloS One
Volume:	8
Issue:	12
Pages:	e80303
Publisher:	Public Library of Science
Description:	We introduce a model for the adaptive evolution of a network of company ownerships. In a recent work it has been shown that the empirical global network of corporate control is marked by a central, tightly connected “core” made of a small number of large companies which control a significant part of the global economy. Here we show how a simple, adaptive “rich get richer” dynamics can account for this characteristic, which incorporates the increased buying power of more influential companies, and in turn results in even higher control. We conclude that this kind of centralized structure can emerge without it being an explicit goal of these companies, or as a result of a well-organized strategy.
Cited by:	7
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Eigenvalue spectra of modular networks

2013

Tiago P Peixoto
Physical review letters 111 (9), 098701
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Authors:	Tiago P Peixoto
Publication date:	08/26/2013
Journal:	Physical review letters
Volume:	111
Issue:	9
Pages:	098701
Publisher:	American Physical Society
Description:	A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often, such spectral features are theoretically obtained by considering only local node properties, such as degree distributions. Many networks, however, possess large-scale modular structures that can drastically influence their spectral characteristics and which are neglected in such simplified descriptions. Here, we obtain in a unified fashion the spectrum of a large family of operators, including the adjacency, Laplacian, and normalized Laplacian matrices, for networks with generic modular structure, in the limit of large degrees. We focus on the conditions necessary for the merging of the isolated eigenvalues with the continuous band of the spectrum, after which the planted modular structure can no …
Cited by:	67
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Parsimonious module inference in large networks

2013

Tiago P Peixoto
Physical review letters 110 (14), 148701
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Authors:	Tiago P Peixoto
Publication date:	04/05/2013
Journal:	Physical review letters
Volume:	110
Issue:	14
Pages:	148701
Publisher:	American Physical Society
Cited by:	270

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Reliable dynamics in Boolean and continuous networks

2012

Eva Ackermann, Tiago P Peixoto, Barbara Drossel
New Journal of Physics 14 (12), 123029
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Authors:	Eva Ackermann, Tiago P Peixoto, Barbara Drossel
Publication date:	12/18/2012
Journal:	New Journal of Physics
Volume:	14
Issue:	12
Pages:	123029
Publisher:	IOP Publishing
Description:	We investigate the dynamical behavior of a model of robust gene regulatory networks which possess' entirely reliable'trajectories. In a Boolean representation, these trajectories are characterized by being insensitive to the order in which the nodes are updated, ie they always go through the same sequence of states. The Boolean model for gene activity is compared with a continuous description in terms of differential equations for the concentrations of mRNA and proteins. We found that entirely reliable Boolean trajectories can be reproduced perfectly in the continuous model when realistic Hill coefficients are used. We investigate to what extent this high correspondence between Boolean and continuous trajectories depends on the extent of reliability of the Boolean trajectories, and we identify simple criteria that enable the faithful reproduction of the Boolean dynamics in the continuous description.
Cited by:	5
Resources:	[PDF] from iop.org Full View

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Evolution of robust network topologies: Emergence of central backbones

2012

Tiago P Peixoto, Stefan Bornholdt
Physical review letters 109 (11), 118703
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Authors:	Tiago P Peixoto, Stefan Bornholdt
Publication date:	09/13/2012
Journal:	Physical review letters
Volume:	109
Issue:	11
Pages:	118703
Publisher:	American Physical Society
Description:	We model the robustness against random failure or an intentional attack of networks with an arbitrary large-scale structure. We construct a block-based model which incorporates—in a general fashion—both connectivity and interdependence links, as well as arbitrary degree distributions and block correlations. By optimizing the percolation properties of this general class of networks, we identify a simple core-periphery structure as the topology most robust against random failure. In such networks, a distinct and small “core” of nodes with higher degree is responsible for most of the connectivity, functioning as a central “backbone” of the system. This centralized topology remains the optimal structure when other constraints are imposed, such as a given fraction of interdependence links and fixed degree distributions. This distinguishes simple centralized topologies as the most likely to emerge, when robustness against …
Cited by:	97
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No need for conspiracy: Self-organized cartel formation in a modified trust game

2012

Tiago P Peixoto, Stefan Bornholdt
Physical review letters 108 (21), 218702
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Authors:	Tiago P Peixoto, Stefan Bornholdt
Publication date:	05/22/2012
Journal:	Physical review letters
Volume:	108
Issue:	21
Pages:	218702
Publisher:	American Physical Society
Description:	We investigate the dynamics of a trust game on a mixed population, where individuals with the role of buyers are forced to play against a predetermined number of sellers whom they choose dynamically. Agents with the role of sellers are also allowed to adapt the level of value for money of their products, based on payoff. The dynamics undergoes a transition at a specific value of the strategy update rate, above which an emergent cartel organization is observed, where sellers have similar values of below-optimal value for money. This cartel organization is not due to an explicit collusion among agents; instead, it arises spontaneously from the maximization of the individual payoffs. This dynamics is marked by large fluctuations and a high degree of unpredictability for most of the parameter space and serves as a plausible qualitative explanation for observed elevated levels and fluctuations of certain commodity prices.
Cited by:	9
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Entropy of stochastic blockmodel ensembles

2012

Tiago P Peixoto
Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 85 (5), 056122
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Authors:	Tiago P Peixoto
Publication date:	05/01/2012
Journal:	Physical Review E—Statistical, Nonlinear, and Soft Matter Physics
Volume:	85
Issue:	5
Pages:	056122
Publisher:	American Physical Society
Description:	Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we derive expressions for the entropy of stochastic blockmodel ensembles. We consider several ensemble variants, including the traditional model as well as the newly introduced degree-corrected version [Karrer , Phys. Rev. E 83, 016107 (2011)PLEEE81539-375510.1103/PhysRevE.83.016107], which imposes a degree sequence on the vertices, in addition to the block structure. The imposed degree sequence is implemented both as “soft” constraints, where only the expected degrees are imposed, and as “hard” constraints, where they are required to be the same on all samples of the ensemble. We also consider generalizations to multigraphs and directed graphs. We illustrate one …
Cited by:	168
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Emergence of robustness against noise: A structural phase transition in evolved models of gene regulatory networks

2012

Tiago P Peixoto
Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 85 (4), 041908
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Authors:	Tiago P Peixoto
Publication date:	04/01/2012
Journal:	Physical Review E—Statistical, Nonlinear, and Soft Matter Physics
Volume:	85
Issue:	4
Pages:	041908
Publisher:	American Physical Society
Description:	We investigate the evolution of Boolean networks subject to a selective pressure which favors robustness against noise, as a model of evolved genetic regulatory systems. By mapping the evolutionary process into a statistical ensemble and minimizing its associated free energy, we find the structural properties which emerge as the selective pressure is increased and identify a phase transition from a random topology to a “segregated-core” structure, where a smaller and more densely connected subset of the nodes is responsible for most of the regulation in the network. This segregated structure is very similar qualitatively to what is found in gene regulatory networks, where only a much smaller subset of genes—those responsible for transcription factors—is responsible for global regulation. We obtain the full phase diagram of the evolutionary process as a function of selective pressure and the average number of …
Cited by:	25
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The behavior of noise-resilient Boolean networks with diverse topologies

2012

Tiago P Peixoto
Journal of Statistical Mechanics: Theory and Experiment 2012 (01), P01006
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Authors:	Tiago P Peixoto
Publication date:	01/10/2012
Journal:	Journal of Statistical Mechanics: Theory and Experiment
Volume:	2012
Issue:	01
Pages:	P01006
Publisher:	IOP Publishing
Description:	The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the dynamics always undergoes a phase transition from a non-ergodic regime, where a memory of its past states is preserved, to an ergodic regime, where no such memory exists and every microstate is equally probable. Both the average error on the network and the critical value of noise where the transition occurs are investigated analytically, and compared to numerical simulations. The results for'partially dense'networks, comprising relatively few, but dynamically important nodes, which have a number of inputs that greatly exceeds the average for the entire network, give very general upper bounds on the maximum resilience against noise attainable on globally sparse systems.
Cited by:	5
Resources:	[PDF] from arxiv.org

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Density profile and polymer configurations for a polymer melt in a regular array of nanotubes

2011

Tiago P Peixoto, Barbara Drossel
New Journal of Physics 13 (7), 073030
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Authors:	Tiago P Peixoto, Barbara Drossel
Publication date:	07/22/2011
Journal:	New Journal of Physics
Volume:	13
Issue:	7
Pages:	073030
Publisher:	IOP Publishing
Description:	By using two generic polymer models, namely self-consistent field theory and bond-fluctuation Monte-Carlo simulations, we investigate numerically the properties of a polymer melt in a hexagonal array of nanotubes as a function of the polymer length, the interaction with the nanotubes and the compressibility or average density. The combined effect of the attractive interaction with the nanotube walls, the entropy decrease due to the impenetrability of the walls and the hexagonal arrangement of the nanotubes with varying gap size in between them leads to a wide array of possible density profiles and polymer configurations as a function of the model parameters. Even in the case of the Monte-Carlo simulations, where the contact interaction affects only the first layer of monomers, the effect of the wall can nevertheless be felt throughout the entire melt at intermediate temperatures.
Cited by:	1
Resources:	[PDF] from iop.org

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Trust transitivity in social networks

2011

Oliver Richters, Tiago P Peixoto
PloS one 6 (4), e18384
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Authors:	Oliver Richters, Tiago P Peixoto
Publication date:	04/05/2011
Journal:	PloS one
Volume:	6
Issue:	4
Pages:	e18384
Publisher:	Public Library of Science
Description:	Non-centralized recommendation-based decision making is a central feature of several social and technological processes, such as market dynamics, peer-to-peer file-sharing and the web of trust of digital certification. We investigate the properties of trust propagation on networks, based on a simple metric of trust transitivity. We investigate analytically the percolation properties of trust transitivity in random networks with arbitrary in/out-degree distributions, and compare with numerical realizations. We find that the existence of a non-zero fraction of absolute trust (i.e. entirely confident trust) is a requirement for the viability of global trust propagation in large systems: The average pair-wise trust is marked by a discontinuous transition at a specific fraction of absolute trust, below which it vanishes. Furthermore, we perform an extensive analysis of the Pretty Good Privacy (PGP) web of trust, in view of the concepts introduced. We compare different scenarios of trust distribution: community- and authority-centered. We find that these scenarios lead to sharply different patterns of trust propagation, due to the segregation of authority hubs and densely-connected communities. While the authority-centered scenario is more efficient, and leads to higher average trust values, it favours weakly-connected “fringe” nodes, which are directly trusted by authorities. The community-centered scheme, on the other hand, favours nodes with intermediate in/out …
Cited by:	92
Resources:	[HTML] from plos.org

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Boolean networks with robust and reliable trajectories

2010

Christoph Schmal, Tiago P Peixoto, Barbara Drossel
New Journal of Physics 12 (11), 113054
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Authors:	Christoph Schmal, Tiago P Peixoto, Barbara Drossel
Publication date:	11/30/2010
Journal:	New Journal of Physics
Volume:	12
Issue:	11
Pages:	113054
Publisher:	IOP Publishing
Description:	We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule and which is also robust against noise. Robustness is quantified as the probability that the dynamics return to the reliable trajectory after a perturbation of the state of a single node. In order to achieve high robustness, we navigate through the space of possible update functions by using an evolutionary algorithm. We constrain the networks to those having the minimum number of connections required to obtain the reliable trajectory. Surprisingly, we find that robustness always reaches values close to 100% during the evolutionary optimization process. The set of update functions can be evolved such that it differs only slightly from that of networks that were not optimized with respect to robustness. The state space of the optimized networks is dominated by the …
Cited by:	20
Resources:	[PDF] from iop.org

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The phase diagram of random Boolean networks with nested canalizing functions

2010

Tiago P Peixoto
The European Physical Journal B 78, 187-192
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Authors:	Tiago P Peixoto
Publication date:	11/01/2010
Journal:	The European Physical Journal B
Volume:	78
Pages:	187-192
Publisher:	Springer-Verlag
Description:	We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number b t of nodes with value one, and the network sensitivity λ, and compare with numerical simulations of quenched networks. We find that, contrary to what was reported by Kauffman et al. [Proc. Natl. Acad. Sci. 101, 17102 (2004)], these networks have a rich phase diagram, were both the “chaotic" and frozen phases are present, as well as an oscillatory regime of the value of b t . We argue that the presence of only the frozen phase in the work of Kauffman et al. was due simply to the specific parametrization used, and is not an inherent feature of this class of functions. However, these networks are significantly more stable than the variant where all possible Boolean functions are …
Cited by:	25
Resources:	[PDF] from arxiv.org

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Spatiotemporal correlations of aftershock sequences

2010

Tiago P Peixoto, Katharina Doblhoff‐Dier, Jörn Davidsen
Journal of Geophysical Research: Solid Earth 115 (B10)
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Authors:	Tiago P Peixoto, Katharina Doblhoff‐Dier, Jörn Davidsen
Publication date:	10/01/2010
Journal:	Journal of Geophysical Research: Solid Earth
Volume:	115
Issue:	B10
Description:	Aftershock sequences are of particular interest in seismic research because they may condition seismic activity in a given region over long time spans. Although they are typically identified with periods of enhanced seismic activity after a large earthquake as characterized by the Omori law, our knowledge of the spatiotemporal correlations between events in an aftershock sequence is limited. Here, we study the spatiotemporal correlations of two aftershock sequences form California (Parkfield and Hector Mine) using the recently introduced concept of “recurrent” events. We find that both sequences have very similar properties and that most of them are captured by the space‐time epidemic‐type aftershock sequence (ETAS) model if one takes into account catalog incompleteness. However, the stochastic ETAS model does not capture those spatiotemporal correlations that give rise to the observed distribution of …
Cited by:	19
Resources:	[PDF] from wiley.com Full View

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Network of recurrent events: an application to aftershock sequences and the ETAS model of seismicity

2010

J Davidsen, T Peixoto
EGU General Assembly Conference Abstracts, 14797
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Authors:	J Davidsen, T Peixoto
Publication date:	05/01/2010
Journal:	EGU General Assembly Conference Abstracts
Pages:	14797
Description:	Many striking features of geophysical processes can be portrayed as patterns or clusters of localized events including, but not limited to, solar flares and earthquakes. A generic attribute in all these cases is that one event can trigger or somehow induce another one to occur-or possibly numerous further events. Studying the spatiotemporal clustering of such localized events is often the only way to gain insight into the underlying microscopic dynamics that causes the triggering. A recently introduced approach (Geophys. Res. Lett. 33, L11304 (2006)) allows one to quantify non-trivial spatiotemporal clustering and to infer the causal structure of activity patterns based on the view that any suitable definition of clustering should be purely contextual and depend only on the actual history of events. The approach utilizes the notion of space-time records and maps the activity pattern onto a network. Here, we apply this method …

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Redundancy and error resilience in Boolean networks

2010

Tiago P Peixoto
Physical review letters 104 (4), 048701
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Authors:	Tiago P Peixoto
Publication date:	01/25/2010
Journal:	Physical review letters
Volume:	104
Issue:	4
Pages:	048701
Publisher:	American Physical Society
Description:	We consider the effect of noise in sparse Boolean networks with redundant functions. We show that they always exhibit a nonzero error level, and the dynamics undergoes a phase transition from nonergodicity to ergodicity, as a function of noise, after which the system is no longer capable of preserving a memory of its initial state. We obtain upper bounds on the critical value of noise for networks of different sparsity.
Cited by:	27
Resources:	[PDF] from arxiv.org

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Boolean networks with reliable dynamics

2009

Tiago P Peixoto, Barbara Drossel
Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 80 (5), 056102
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Authors:	Tiago P Peixoto, Barbara Drossel
Publication date:	11/01/2009
Journal:	Physical Review E—Statistical, Nonlinear, and Soft Matter Physics
Volume:	80
Issue:	5
Pages:	056102
Publisher:	American Physical Society
Description:	We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states, which is independent of the order in which the nodes are updated. We explored numerically the topology, the update functions, and the state space structure of these networks, which we constructed using a minimum number of links and the simplest update functions. We found that the clustering coefficient is larger than in random networks and that the probability distribution of three-node motifs is similar to that found in gene regulation networks. Among the update functions, only a subset of all possible functions occurs, and they can be classified according to their probability. More homogeneous functions occur more often, leading to a dominance of canalyzing functions. Finally, we studied the entire state space of the networks. We observed that with …
Cited by:	14
Resources:	[PDF] from arxiv.org

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Spatiotemporal clustering of aftershock sequences

2009

J Davidsen, T de Paula Peixoto, K Doblhoff
AGU Spring Meeting Abstracts 2009, NG23A-07
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Authors:	J Davidsen, T de Paula Peixoto, K Doblhoff
Publication date:	05/01/2009
Journal:	AGU Spring Meeting Abstracts
Volume:	2009
Pages:	NG23A-07
Description:	Describing and modeling the spatiotemporal organization of seismicity and understanding the underlying physical mechanisms of earthquake triggering have been proven challenging. This is especially true for aftershock sequences. To share new light on this issue, we follow a recently proposed method to characterize spatiotemporal clustering of seismicity by networks of recurrent events [Geophys. Res. Lett. 33, L1304, 2006] and compare the properties of aftershock sequences like Parkfield to synthetic catalogs generated by the epidemic type aftershock sequence (ETAS) model.

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Noise in random boolean networks

2009

Tiago P Peixoto, Barbara Drossel
Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 79 (3), 036108
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Authors:	Tiago P Peixoto, Barbara Drossel
Publication date:	03/01/2009
Journal:	Physical Review E—Statistical, Nonlinear, and Soft Matter Physics
Volume:	79
Issue:	3
Pages:	036108
Publisher:	American Physical Society
Description:	We investigate the effect of noise on random Boolean networks. Noise is implemented as a probability that a node does not obey its deterministic update rule. We define two order parameters, the long-time average of the Hamming distance between a network with and without noise, and the average frozenness, which is a measure of the extent to which a node prefers one of the two Boolean states. We evaluate both order parameters as function of the noise strength, and of the number of inputs per node finding a smooth transition from deterministic to fully stochastic dynamics for networks with , and a first-order transition at for . Most of the results obtained by computer simulation are also derived analytically. The average Hamming distance can be evaluated using the annealed approximation. In order to obtain the distribution of frozenness as function of the noise strength, more sophisticated self …
Cited by:	31
Resources:	[PDF] from arxiv.org

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Spatiotemporal clustering: A comparison between earthquake catalogs and models of seismicity

2008

J Davidsen, T de Paula Peixoto
AGU Fall Meeting Abstracts 2008, NG33B-03
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Authors:	J Davidsen, T de Paula Peixoto
Publication date:	12/01/2008
Journal:	AGU Fall Meeting Abstracts
Volume:	2008
Pages:	NG33B-03
Description:	Describing and modeling the spatiotemporal organization of seismicity and understanding the underlying physical mechanisms of earthquake triggering have been proven challenging. To share new light on this issue, we follow a recently proposed method to characterize spatiotemporal clustering of seismicity by networks of recurrent events [Geophys. Res. Lett. 33, L1304, 2006] and compare the properties of earthquake catalogs to that of synthetic catalogs generated by different models of seismicity. In particular, we discuss the spatiotemporal clustering generated by the epidemic type aftershock sequence (ETAS) model and compare it to the clustering found in aftershock sequences like Parkfield.

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Network of recurrent events for the Olami-Feder-Christensen model

2008

Tiago P Peixoto, Jörn Davidsen
Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 77 (6), 066107
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Authors:	Tiago P Peixoto, Jörn Davidsen
Publication date:	06/01/2008
Journal:	Physical Review E—Statistical, Nonlinear, and Soft Matter Physics
Volume:	77
Issue:	6
Pages:	066107
Publisher:	American Physical Society
Description:	We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder, and Christensen (OFC) to mimic earthquakes and investigate to what extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicity. Following a recently proposed method to characterize such clustering by networks of recurrent events [J. Davidsen, P. Grassberger, and M. Paczuski, Geophys. Res. Lett. 33, L11304 (2006)], we find that for synthetic catalogs generated by the OFC model these networks have many nontrivial statistical properties. This includes characteristic degree distributions, very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs, indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.
Cited by:	20
Resources:	[PDF] from arxiv.org

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Network of epicenters of the Olami-Feder-Christensen model of earthquakes

2006

Tiago P Peixoto, Carmen PC Prado
Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 74 (1), 016126
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Authors:	Tiago P Peixoto, Carmen PC Prado
Publication date:	07/01/2006
Journal:	Physical Review E—Statistical, Nonlinear, and Soft Matter Physics
Volume:	74
Issue:	1
Pages:	016126
Publisher:	American Physical Society
Description:	We study the dynamics of the Olami-Feder-Christensen (OFC) model of earthquakes, focusing on the behavior of sequences of epicenters regarded as a growing complex network. Besides making a detailed and quantitative study of the effects of the borders (the occurrence of epicenters is dominated by a strong border effect which does not scale with system size), we examine the degree distribution and the degree correlation of the graph. We detect sharp differences between the conservative and nonconservative regimes of the model. Removing border effects, the conservative regime exhibits a Poisson-like degree statistics and is uncorrelated, while the nonconservative has a broad power-law-like distribution of degrees (if the smallest events are ignored), which reproduces the observed behavior of real earthquakes. In this regime the graph has also an unusually strong degree correlation among the vertices …
Cited by:	27
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Statistics of epicenters in the Olami–Feder–Christensen model in two and three dimensions

2004

Tiago P Peixoto, Carmen PC Prado
Physica A: Statistical Mechanics and its Applications 342 (1-2), 171-177
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Authors:	Tiago P Peixoto, Carmen PC Prado
Publication date:	10/15/2004
Journal:	Physica A: Statistical Mechanics and its Applications
Volume:	342
Issue:	1-2
Pages:	171-177
Publisher:	North-Holland
Description:	Recently, Abe and Suzuki pointed out that epicenters of earthquakes could be connected in order to generate a graph, with properties of a scale-free network. We have shown that the Olami–Feder–Christensen (OFC) model for the dynamics of earthquakes, defined both in square and cubic lattices, is able to reproduce this new behavior. The distribution of distances between successive earthquakes is also presented. Our results indicate the robustness of the OFC model to describe earthquake dynamics. Surprisingly, we found that only the non-conservative version of the OFC model generates a network with scale-free properties. The conservative version, instead, behaves like a random graph. The distribution of distances in 3-D and the distribution of connectivities in a 2-D lattice confirm the differences observed between the conservative and non-conservative regime.
Cited by:	12

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Distribution of epicenters in the Olami-Feder-Christensen model

2004

Tiago P Peixoto, Carmen PC Prado
Physical Review E 69 (2), 025101
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Authors:	Tiago P Peixoto, Carmen PC Prado
Publication date:	02/25/2004
Journal:	Physical Review E
Volume:	69
Issue:	2
Pages:	025101
Publisher:	American Physical Society
Description:	We show that the well established Olami-Feder-Christensen (OFC) model for the dynamics of earthquakes is able to reproduce a striking property of real earthquake data. Recently, it has been pointed out by Abe and Suzuki that the epicenters of earthquakes could be connected in order to generate a graph, with properties of a scale-free network of the Barabási-Albert type. However, only the nonconservative version of the Olami-Feder-Christensen model is able to reproduce this behavior. The conservative version, instead, behaves like a random graph. Besides indicating the robustness of the model to describe earthquake dynamics, those findings reinforce that conservative and nonconservative versions of the OFC model are qualitatively different. Also, we propose a completely different dynamical mechanism that, even without an explicit rule of preferential attachment, generates a scale-free network. The …
Cited by:	37
Resources:	[PDF] from arxiv.org

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The graph-tool python library, figshare 10.6084/m9. figshare. 1164194 (2014)

TP Peixoto
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Authors:	TP Peixoto
Cited by:	7

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Network structure, metadata and the prediction of missing nodes

Darko Hric, Tiago P Peixoto, Santo Fortunato
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Authors:	Darko Hric, Tiago P Peixoto, Santo Fortunato
Description:	The empirical validation of community detection methods is often based on available annotations on the nodes that serve as putative indicators of the large-scale network structure. Most often, the suitability of the annotations as topological descriptors itself is not assessed, and without this it is not possible to ultimately distinguish between actual shortcomings of the community detection algorithms on one hand, and the incompleteness, inaccuracy or structured nature of the data annotations themselves on the other. In this work we present a principled method to access both aspects simultaneously. We construct a joint generative model for the data and metadata, and a non-parametric Bayesian framework to infer its parameters from annotated datasets. We assess the quality of the metadata not according to its direct alignment with the network communities, but rather in its capacity to predict the placement of edges in the network. We also show how this feature can be used to predict the connections to missing nodes when only the metadata is available. By investigating a wide range of datasets, we show that while there are seldom exact agreements between metadata tokens and the inferred data groups, the metadata is often informative of the network structure nevertheless, and can improve the prediction of missing nodes. This shows that the method uncovers meaningful patterns in both the data and metadata, without requiring or expecting a perfect agreement between the two.
Resources:	[PDF] from researchgate.net

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Tiago de Paula Peixoto

Publications