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Determining the best algorithm to detect community structures in networks: application to power systems

Environment Systems and Decisions 2022年第2期42卷 251-264页

作者： Rocco, Claudio M. Barker, Kash Moronta, Jose Facultad de Ingeniería Universidad Central de Venezuela Caracas Venezuela School of Industrial and Systems Engineering University of Oklahoma 202 W. Boyd St. Rm. 124 Norman 73019 OK United States Departamento de Tecnología Industrial Universidad Simón Bolívar Caracas Venezuela

A common feature of many networks is the presence of communities, or groups of relatively densely connected nodes with sparse connections between groups. An understanding of community structures could enable the network design for improved system performance. For electric power systems, most work in the detection of community structures (i) selects a specific algorithm to perform the detection of communities (or compares a proposed algorithm against algorithms), and (ii) focuses on topological information about the networks. The objective of this article is to provide a framework to improve the selection of appropriate community detection algorithms for a family of networks with similar structures. We propose an approach to determine the most effective community detection algorithm for a set of networks and compare which algorithms provide the most similar partitions across these networks. To illustrate the comparison of various community detection algorithms, 16 electric power systems are analyzed. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

关键词： community detection algorithms Multi-criteria decision analysis Power systems Rank aggregation Sensitivity analysis TOPSIS

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Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model

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Physical Review E 2024年第6期109卷 064309-064309页

作者： Zhana Kuncheva Ognyan Kounchev Data Science and Engineering Optima Partners London UK WC1X 8HN Bulgarian Academy of Sciences Sofia 1113 Bulgaria

We study the behavior of the eigenvectors associated with the smallest eigenvalues of the Laplacian matrix of temporal networks. We consider the multilayer representation of temporal networks, i.e., a set of networks linked through ordinal interconnected layers. We analyze the Laplacian matrix, known as supra-Laplacian, constructed through the supraadjacency matrix associated with the multilayer formulation of temporal networks, using a constant block Jacobi model which has closed-form solution. To do this, we assume that the interlayer weights are perturbations of the Kronecker sum of the separate adjacency matrices forming the temporal network. Thus we investigate the properties of the eigenvectors associated with the smallest eigenvalues (close to zero) of the supra-Laplacian matrix. Using arguments of perturbation theory, we show that these eigenvectors can be approximated by linear combinations of the zero eigenvectors of the individual time layers. This finding is crucial in reconsidering and generalizing the role of the Fielder vector in supra-Laplacian matrices.

关键词： Clustering community structure Network evolution Erdos-Renyi graph Interconnected & interdependent networks Multilayer & multiplex networks Weighted networks Block models community detection algorithms Diffusion & random walks

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community Analysis of a Crisis Response Network

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SOCIAL SCIENCE COMPUTER REVIEW 2021年第3期39卷 371-390页

作者： Kim, Yushim Kim, Jihong Oh, Seong Soo Kim, Sang-Wook Ku, Minyoung Cha, Jaehyuk Arizona State Univ Sch Publ Affairs Phoenix AZ USA Hanyang Univ Dept Comp Sci & Engn Seoul South Korea Hanyang Univ 222 Wangshimni Ro Seoul 04763 South Korea Hanyang Univ Dept Comp & Software Seoul South Korea John Jay Coll New York NY USA

This article distinguishes between clique family subgroups and communities in a crisis response network. Then, we examine the way organizations interacted to achieve a common goal by employing community analysis of an epidemic response network in Korea in 2015. The results indicate that the network split into two groups: core response communities in one group and supportive functional communities in the other. The core response communities include organizations across government jurisdictions, sectors, and geographic locations. Other communities are confined geographically, homogenous functionally, or both. We also find that whenever intergovernmental relations were present in communities, the member connectivity was low, even if intersectoral relations appeared together within them.

关键词： epidemic response network community detection algorithms network analysis emergency management

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Network homophily via tail inequalities

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Physical Review E 2023年第5期108卷 054130-054130页

作者： Nicola Apollonio Paolo G. Franciosa Daniele Santoni Istituto per le Applicazioni del Calcolo “Mauro Picone” Consiglio Nazionale delle Ricerche Via dei Taurini 19 00185 Rome Italy Dipartimento di Scienze Statistiche Università di Roma “La Sapienza” Piazzale Aldo Moro 5 00185 Rome Italy Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti ” Consiglio Nazionale delle Ricerche Via dei Taurini 19 00185 Rome Italy

Homophily is the principle whereby “similarity breeds connections.” We give a quantitative formulation of this principle within networks. Given a network and a labeled partition of its vertices, the vector indexed by each class of the partition, whose entries are the number of edges of the subgraphs induced by the corresponding classes, is viewed as the observed outcome of the random vector described by picking labeled partitions at random among labeled partitions whose classes have the same cardinalities as the given one. This is the recently introduced random coloring model for network homophily. In this perspective, the value of any homophily score Θ, namely, a nondecreasing real-valued function in the sizes of subgraphs induced by the classes of the partition, evaluated at the observed outcome, can be thought of as the observed value of a random variable. Consequently, according to the score Θ, the input network is homophillic at the significance level α whenever the one-sided tail probability of observing a value of Θ at least as extreme as the observed one is smaller than α. Since, as we show, even approximating α is an NP-hard problem, we resort to classical tails inequality to bound α from above. These upper bounds, obtained by specializing Θ, yield a class of quantifiers of network homophily. Computing the upper bounds requires the knowledge of the covariance matrix of the random vector, which was not previously known within the random coloring model. In this paper we close this gap. Interestingly, the matrix depends on the input partition only through the cardinalities of its classes and depends on the network only through its degrees. Furthermore all the covariances have the same sign, and this sign is a graph invariant. Plugging this structure into the bounds yields a meaningful, easy to compute class of indices for measuring network homophily. As demonstrated in real-world network applications, these indices are effective and reliable, and may lead to d

关键词： Assortativity Combinatorics community detection algorithms Computational complexity Data analysis

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Generative model for reciprocity and community detection in networks

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Physical Review Research 2021年第2期3卷 023209-023209页

作者： Hadiseh Safdari Martina Contisciani Caterina De Bacco Max Planck Institute for Intelligent Systems Cyber Valley Tuebingen 72076 Germany

We present a probabilistic generative model and efficient algorithm to model reciprocity in directed networks. Unlike other methods that address this problem such as exponential random graphs, it assigns latent variables as community memberships to nodes and a reciprocity parameter to the whole network rather than fitting order statistics. It formalizes the assumption that a directed interaction is more likely to occur if an individual has already observed an interaction towards her. It provides a natural framework for relaxing the common assumption in network generative models of conditional independence between edges, and it can be used to perform inference tasks such as predicting the existence of an edge given the observation of an edge in the reverse direction. Inference is performed using an efficient expectation-maximization algorithm that exploits the sparsity of the network, leading to an efficient and scalable implementation. We illustrate these findings by analyzing synthetic and real data, including social networks, academic citations, and the Erasmus student exchange program. Our method outperforms others in both predicting edges and generating networks that reflect the reciprocity values observed in real data, while at the same time inferring an underlying community structure. We provide an open-source implementation of the code online.

关键词： community structure Patterns in complex systems Topological tools Directed networks Social networks community detection algorithms

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Colloquium: Multiscale modeling of brain network organization

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Reviews of Modern Physics 2022年第3期94卷 031002-031002页

作者： Charley Presigny Fabrizio De Vico Fallani Sorbonne Université Institut du Cerveau—Paris Brain Institute—ICM CNRS Inria Inserm AP-HP Hôpital de la Pitié Salpêtrière F-75013 Paris France

A complete understanding of the brain requires an integrated description of the numerous scales and levels of neural organization. This means studying the interplay of genes and synapses, but also the relation between the structure and dynamics of the whole brain, which ultimately leads to different types of behavior, from perception to action, while asleep or awake. Yet multiscale brain modeling is challenging, in part because of the difficulty to simultaneously access information from multiple scales and levels. While some insight has been gained on the role of specific microcircuits on the generation of macroscale brain activity, a comprehensive characterization of how changes occurring at one scale or level can have an impact on other ones remains poorly understood. Recent efforts to address this gap include the development of new frameworks originating mostly from network science and complex systems theory. These theoretical contributions provide a powerful framework to analyze and model interconnected systems exhibiting interactions within and between different layers of information. Recent advances for the characterization of the multiscale brain organization in terms of structure-function, oscillation frequencies, and temporal evolution are presented. Efforts are reviewed on the multilayer network properties underlying the physics of higher-order organization of neuronal assemblies, as well as on the identification of multimodal network-based biomarkers of brain pathologies such as Alzheimer’s disease. This Colloquium concludes with a perspective discussion of how recent results from multilayer network theory, involving generative modeling, controllability, and machine learning, could be adopted to address new questions in modern physics and neuroscience.

关键词： Network phase transitions Random walks Brain network Coupled oscillators Multilayer & multiplex networks community detection algorithms Neuroimaging Neuronal network models

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Large deviations of semisupervised learning in the stochastic block model

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Physical Review E 2022年第3期105卷 034108-034108页

作者： Hugo Cui Luca Saglietti Lenka Zdeborová SPOC Laboratory Physics Department École Polytechnique Fédérale de Lausanne 1015 Lausanne Switzerland

In semisupervised community detection, the membership of a set of revealed nodes is known in addition to the graph structure and can be leveraged to achieve better inference accuracies. While previous works investigated the case where the revealed nodes are selected at random, this paper focuses on correlated subsets leading to atypically high accuracies. In the framework of the dense stochastic block model, we employ statistical physics methods to derive a large deviation analysis of the number of these rare subsets, as characterized by their free energy. We find theoretical evidence of a nonmonotonic relationship between reconstruction accuracy and the free energy associated to the posterior measure of the inference problem. We further discuss possible implications for active learning applications in community detection.

关键词： Disordered systems community detection algorithms

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Role extraction for digraphs via neighborhood pattern similarity

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Physical Review E 2022年第5期106卷 054301-054301页

作者： Giovanni Barbarino Vanni Noferini Paul Van Dooren Université catholique de Louvain Department of Mathematical Engineering Av. Lemaitre 4 B-1348 Louvain-la-Neuve Belgium

We analyze the recovery of different roles in a network modeled by a directed graph, based on the so-called Neighborhood Pattern Similarity approach. Our analysis uses results from random matrix theory to show that, when assuming that the graph is generated as a particular stochastic block model with Bernoulli probability distributions for the different blocks, then the recovery is asymptotically correct when the graph has a sufficiently large dimension. Under these assumptions there is a sufficient gap between the dominant and dominated eigenvalues of the similarity matrix, which guarantees the asymptotic correct identification of the number of different roles. We also comment on the connections with the literature on stochastic block models, including the case of probabilities of order log(n)/n where n is the graph size. We provide numerical experiments to assess the effectiveness of the method when applied to practical networks of finite size.

关键词： Clustering community structure Block models community detection algorithms

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Exploiting homophily to characterize communities in online social networks

Exploiting homophily to characterize communities in online s...

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Concurrency and Computation: Practice and Experience

作者： De Salve, Andrea Guidi, Barbara Michienzi, Andrea Consiglio Nazionale delle Ricerche Institute of Applied Sciences and Intelligent Systems Lecce Italy Dipartimento di Informatica Universitã di Pisa Pisa Italy

Online social networks (OSNs) have become one of the most popular platforms where people communicate by sharing contents and personal information. The interactions performed by the users allow to identify the homophily between users and reveal the presence of several communities that could depend on several factors: such as the type of relationships (eg, colleagues and school mates) or to users' preferences (eg, users' interests or hobbies). A very important issue in this scenario is the necessary to characterize such communities by using known real properties or attributes about their members. In this article, we propose an approach that identifies the communities of users by exploiting several community detection algorithms. Afterward, for each user, we exploit decision trees to find a model that describes and distinguishes community affiliations based on known attributes of the members. The evaluation of our approach is derived from a real dataset which consists of the profile information, relationships, and interactions of 95 716 Facebook users. The experimental results show that the proposed approach is able to correctly recognize which attributes of the members properly characterize their corresponding community while ensuring a high level of accuracy (about 85%). © 2020 John Wiley & Sons Ltd.

关键词： Social networking (online) Decision trees community detection algorithms Homophily On line social networks Online social networks (OSNs) Personal information Popular platform Real properties Users' interests

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Merge-split Markov chain Monte Carlo for community detection

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Physical Review E 2020年第1期102卷 012305-012305页

作者： Tiago P. Peixoto Department of Network and Data Science Central European University H-1051 Budapest Hungary ISI Foundation Via Chisola 5 10126 Torino Italy and Department of Mathematical Sciences University of Bath Claverton Down Bath BA2 7AY United Kingdom

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.

关键词： community structure Stochastic inference Block models community detection algorithms Monte Carlo methods

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