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Local topological moves determine global diffusion properties of hyperbolic higher-order networks

Physical Review E 2021年第5期104卷 054302-054302页

作者： Ana P. Millán Reza Ghorbanchian Nicolò Defenu Federico Battiston Ginestra Bianconi Amsterdam UMC Vrije Universiteit Amsterdam Department of Clinical Neurophysiology and MEG Center Amsterdam Neuroscience De Boelelaan 1117 Amsterdam The Netherlands School of Mathematical Sciences Queen Mary University of London Mile End Road E1 4NS London United Kingdom Institute for Theoretical Physics ETH Zürich Wolfgang-Pauli-Str. 27 8093 Zurich Switzerland Department of Network and Data Science Central European University 1100 Vienna Austria The Alan Turing Institute British Library 96 Euston Road NW1 2DB London United Kingdom

From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the role that network topology and geometry has on the emerging dynamical properties of higher-order networks is yet to be clarified. In this perspective, the spectral dimension plays a key role since it determines the effective dimension for diffusion processes on a network. Despite its relevance, a theoretical understanding of which mechanisms lead to a finite spectral dimension, and how this can be controlled, still represents a challenge and is the object of intense research. Here, we introduce two nonequilibrium models of hyperbolic higher-order networks and we characterize their network topology and geometry by investigating the intertwined appearance of small-world behavior, δ-hyperbolicity, and community structure. We show that different topological moves, determining the nonequilibrium growth of the higher-order hyperbolic network models, induce tuneable values of the spectral dimension, showing a rich phenomenology which is not displayed in random graph ensembles. In particular, we observe that, if the topological moves used to construct the higher-order network increase the area/volume ratio, then the spectral dimension continuously decreases, while the opposite effect is observed if the topological moves decrease the area/volume ratio. Our work reveals a new link between the geometry of a network and its diffusion properties, contributing to a better understanding of the complex interplay between network structure and dynamics.

关键词： Growth processes Network diffusion Network evolution Network structure Random walks Topological tools Scale free & inhomogeneous networks Small-world networks Stochastic networks Surface growth Triangular network community detection algorithms Evolving network models Monte Carlo methods Network Models Preferential attachment models Small-world model

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Detecting brain network communities: Considering the role of information flow and its different temporal scales

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NEUROIMAGE 2021年 225卷 117431-117431页

作者： Sanchez-Rodriguez, Lazaro M. Iturria-Medina, Yasser Mouches, Pauline Sotero, Roberto C. Univ Calgary Dept Radiol 3330 Hosp Dr NW Calgary AB T2N 4N1 Canada Univ Calgary Hotchkiss Brain Inst 3330 Hosp Dr NW Calgary AB T2N 4N1 Canada McGill Univ Montreal Neurol Inst Dept Neurol & Neurosurg Montreal PQ Canada McGill Univ McConnel Brain Imaging Ctr Montreal Neurol Inst Montreal PQ Canada McGill Univ Ludmer Ctr Neuroinformat & Mental Hlth Montreal PQ Canada Univ Calgary Biomed Engn Grad Program Calgary AB Canada

The identification of community structure in graphs continues to attract great interest in several fields. Network neuroscience is particularly concerned with this problem considering the key roles communities play in brain processes and functionality. Most methods used for community detection in brain graphs are based on the maximization of a parameter-dependent modularity function that often obscures the physical meaning and hierarchical organization of the partitions of network nodes. In this work, we present a new method able to detect communities at different scales in a natural, unrestricted way. First, to obtain an estimation of the information flow in the network we release random walkers to freely move over it. The activity of the walkers is separated into oscillatory modes by using empirical mode decomposition. After grouping nodes by their co-occurrence at each time scale, k-modes clustering returns the desired partitions. Our algorithm was first tested on benchmark graphs with favorable performance. Next, it was applied to real and simulated anatomical and/or functional connectomes in the macaque and human brains. We found a clear hierarchical repertoire of community structures in both the anatomical and the functional networks. The observed partitions range from the evident division in two hemispheres -in which all processes are managed globally- to specialized communities seemingly shaped by physical proximity and shared function. Additionally, the spatial scales of a network's community structure (characterized by a measure we term within-communities path length) appear inversely proportional to the oscillatory modes' average frequencies. The proportionality constant may constitute a network-specific propagation velocity for the information flow. Our results stimulate the research of hierarchical community organization in terms of temporal scales of information flow in the brain network.

关键词： community detection algorithms Brain networks Random walkers Empirical mode decomposition k-modes clustering

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Relational flexibility of network elements based on inconsistent community detection

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Physical Review E 2019年第2期100卷 022311-022311页

作者： Heetae Kim (김희태) Sang Hoon Lee (이상훈) Department of Industrial Engineering Universidad de Talca Curicó 3341717 Chile Asia Pacific Center for Theoretical Physics Pohang 37673 Korea Department of Liberal Arts Gyeongnam National University of Science and Technology Jinju 52725 Korea

community identification of network components enables us to understand the mesoscale clustering structure of networks. A number of algorithms have been developed to determine the most likely community structures in networks. Such a probabilistic or stochastic nature of this problem can naturally involve the ambiguity in resultant community structures. More specifically, stochastic algorithms can result in different community structures for each realization in principle. In this study, instead of trying to “solve” this community degeneracy problem, we turn the tables by taking the degeneracy as a chance to quantify how strong companionship each node has with other nodes. For that purpose, we define the concept of companionship inconsistency that indicates how inconsistently a node is identified as a member of a community regarding the other nodes. Analyzing model and real networks, we show that companionship inconsistency discloses unique characteristics of nodes, thus we suggest it as a new type of node centrality. In social networks, for example, companionship inconsistency can classify outsider nodes without firm community membership and promiscuous nodes with multiple connections to several communities. In infrastructure networks such as power grids, it can diagnose how the connection structure is evenly balanced in terms of power transmission. Companionship inconsistency, therefore, abstracts individual nodes' intrinsic property on its relationship to a higher-order organization of the network.

关键词： community structure Network structure community detection algorithms

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Hierarchical clustering of bipartite data sets based on the statistical significance of coincidences

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Physical Review E 2020年第4期102卷 042304-042304页

作者： Ignacio Tamarit María Pereda José A. Cuesta Grupo Interdisciplinar de Sistemas Complejos (GISC) Departamento de Matemáticas de la Universidad Carlos III de Madrid Leganés Spain Unidad Mixta Interdisciplinar de Comportamiento y Complejidad Social (UMICCS) Madrid Spain Grupo de Investigación Ingeniería de Organización y Logística (IOL) Escuela Técnica Superior de Ingenieros Industriales Universidad Politécnica de Madrid Madrid Spain Instituto de Biocomputación y Física de Sistemas Complejos (BIFI) Universidad de Zaragoza Zaragoza Spain UC3M-Santander Big Data Institute (IBiDat) Getafe Spain

When some ‘entities’ are related by the ‘features’ they share they are amenable to a bipartite network representation. Plant-pollinator ecological communities, co-authorship of scientific papers, customers and purchases, or answers in a poll, are but a few examples. Analyzing clustering of such entities in the network is a useful tool with applications in many fields, like internet technology, recommender systems, or detection of diseases. The algorithms most widely applied to find clusters in bipartite networks are variants of modularity optimization. Here, we provide a hierarchical clustering algorithm based on a dissimilarity between entities that quantifies the probability that the features shared by two entities are due to mere chance. The algorithm performance is O(n2) when applied to a set of n entities, and its outcome is a dendrogram exhibiting the connections of those entities. Through the introduction of a ‘susceptibility’ measure we can provide an ‘optimal’ choice for the clustering as well as quantify its quality. The dendrogram reveals further useful structural information though—like the existence of subclusters within clusters or of nodes that do not fit in any cluster. We illustrate the algorithm by applying it first to a set of synthetic networks, and then to a selection of examples. We also illustrate how to transform our algorithm into a valid alternative for one-mode networks as well, and show that it performs at least as well as the standard, modularity-based algorithms—with a higher numerical performance. We provide an implementation of the algorithm in python freely accessible from GitHub.

关键词： community structure Bipartite graphs Real world networks community detection algorithms Data analysis

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Item and domain network structures of the Resilience Scale for Adults in 675 university students

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EPIDEMIOLOGY AND PSYCHIATRIC SCIENCES 2020年 29卷 e33-e33页

作者： Briganti, G. Linkowski, P. Univ Libre Bruxelles Sch Publ Hlth Dept Clin Epidemiol & Biostat Route Lennik 808 B-1070 Brussels Belgium Ecole Super Sante Dept Pathophysiol Pl Chateau 3 CH-1014 Lausanne Switzerland

Aims. The Resilience Scale for Adults (RSA) is a questionnaire that measures protective factors of mental health. The aim of this paper is to perform a network analysis of the RSA in a dataset composed of 675 French-speaking Belgian university students, to identify potential targets for intervention to improve protective factors in individuals. Methods. We estimated a network structure for the 33-item questionnaire and for the six domains of resilience: perception of self, planned future, social competence, structured style, family cohesion and social competence. Node predictability (shared variance with surrounding nodes in the network) was used to assess the connectivity of items. An exploratory graph analysis (EGA) was performed to detect communities in the network: the number of communities detected being different than the original number of factors proposed in the scale, we estimated a new network with the resulting structure and verified the validity of the new construct which was proposed. We provide the anonymised dataset and code in external online materials (10.17632/64db36w8kf.2) to ensure complete reproducibility of the results. Results. The network composed of items from the RSA is overall positively connected with strongest connections arising among items from the same domain. The domain network reports several connections, both positive and negative. The EGA reported the existence of four communities that we propose as an additional network structure. Node predictability estimates show that connectedness varies among the items and domains of the RSA. Conclusions. Network analysis is a useful tool to explore resilience and identify targets for clinical intervention. In this study, the four domains acting as components of the additional four-domain network structure may be potential targets to improve an individual's resilience. Further studies may endeavour to replicate our findings in different samples.

关键词： Behaviour community detection algorithms psychometrics

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Fragility of spectral clustering for networks with an overlapping structure

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Physical Review Research 2020年第4期2卷 043101-043101页

作者： Chihiro Noguchi Tatsuro Kawamoto Artificial Intelligence Research Center National Institute of Advanced Industrial Science and Technology 2-3-26 Aomi Koto-ku Tokyo Japan

Overlapping communities are commonly observed in real-world networks. This is a motivation to develop overlapping community detection methods, because methods for nonoverlapping communities may not perform well. However, deterioration mechanism of the detection methods used for nonoverlapping communities have rarely been investigated theoretically. Here, we analyze accuracy of spectral clustering, which does not consider overlapping structures, by using the replica method from statistical physics. Our analysis on an overlapping stochastic block model reveals how the structural information is lost from the leading eigenvector because of the overlapping structure.

关键词： Clustering community structure Random graphs Block models community detection algorithms Overlapping communities Replica methods Replica theory

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On the community Discovery Methods for Complex Networks: A Case Study

On the Community Discovery Methods for Complex Networks: A C...

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Federated Conference on Computer Science and Information Systems (FedCSIS)

作者： Kirubel W. Afrassa Genco Cosgun Ulku F. Gursoy Enes M. Yildiz Mehmet S. Aktas Computer Engineering Dept. Yildiz Technical University Istanbul Turkey R&D Center Intellica Business Intelligence Consultancy Istanbul Turkey

ISBN: (数字)9788395541674

ISBN: (纸本)9781728141473

The inherent knowledge discovery problem regarding networks that represent complex real world phenomenon is a popular research topic. Specifically, in social network analysis (SNA), several community discovery techniques with various approaches have been put forward to distinguish closely related entities. Identifying the relevant techniques to utilize based on the context of the application is a key difficulty researchers face. In this study we propose a methodology for classifying these techniques, visualize a prototype, and analyze the performance and quality of selected approaches over a real world call detail record (CDR) data set.

关键词： community discovery community detection algorithms visualization CDR CONCEPTUAL DESIGN REPORT RUNX1T1 gene RECORDABLE COMPACT DISC AKR1C4 gene Visualization detection algorithms complex networks Communities Case studies

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Efficient detection of Overlapping Communities Using Asymmetric Triangle Cuts

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2018年第11期30卷 2093-2105页

作者： Rezvani, Mojtaba Liang, Weifa Liu, Chengfei Yu, Jeffrey Xu Australian Natl Univ Res Sch Comp Sci Canberra ACT 2601 Australia Swinburne Univ Technol Dept Comp Sci & Software Engn Hawthorn Vic 3122 Australia Chinese Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Hong Kong Peoples R China

Real social networks contain many communities, where members within each community are densely connected with each other, while they are sparsely connected with the members outside of the community. Since each member can join multiple communities simultaneously, communities in social networks are usually overlapping with each other. How to efficiently and effectively identify overlapping communities in a large social network becomes a fundamental problem in the big data era. Most existing studies on community finding focused on non-overlapping communities based on several well-known community fitness metrics. However, recent investigations have shown that these fitness metrics may suffer free rider and separation effects where the overlapping region of two communities always belongs to the denser one, rather to both of them. In this paper, we study the overlapping community detection problem in social networks that not only takes the quality of the found overlapping communities but also incorporate both free rider and separation effects on the found communities into consideration. Specifically, in this paper, we first propose a novel community fitness metric - triangle based fitness metric, for overlapping community detection that can minimize the free rider and separation effects on found overlapping communities, and show that the problem is NP-hard. We then propose an efficient yet scalable algorithm for the problem that can deliver a feasible solution. We finally validate the effectiveness of the proposed fitness metric and evaluate the performance of the proposed algorithm, through conducting extensive experiments on real-world datasets with over 100 million vertices and edges. Experimental results demonstrate that the proposed algorithm is very promising.

关键词： Overlapping community detection fitness metrics for overlapping communities social networks community detection algorithms

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Comparative analysis on the selection of number of clusters in community detection

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Physical Review E 2018年第2期97卷 022315-022315页

作者： Tatsuro Kawamoto Yoshiyuki Kabashima Artificial Intelligence Research Center National Institute of Advanced Industrial Science and Technology 2-3-26 Aomi Koto-ku Tokyo Japan Department of Mathematical and Computing Science Tokyo Institute of Technology W8-45 2-12-1 Ookayma Meguro-ku Tokyo Japan

We conduct a comparative analysis on various estimates of the number of clusters in community detection. An exhaustive comparison requires testing of all possible combinations of frameworks, algorithms, and assessment criteria. In this paper we focus on the framework based on a stochastic block model, and investigate the performance of greedy algorithms, statistical inference, and spectral methods. For the assessment criteria, we consider modularity, map equation, Bethe free energy, prediction errors, and isolated eigenvalues. From the analysis, the tendency of overfit and underfit that the assessment criteria and algorithms have becomes apparent. In addition, we propose that the alluvial diagram is a suitable tool to visualize statistical inference results and can be useful to determine the number of clusters.

关键词： community structure Bayesian methods Block models community detection algorithms

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An upper approximation based community detection algorithm for complex networks

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DECISION SUPPORT SYSTEMS 2017年 96卷 103-118页

作者： Kumar, Pradeep Gupta, Samtat Bhasker, Bharat Indian Inst Management Lucknow IT & Syst Dept Lucknow Uttar Pradesh India

The emergence of multifarious complex networks has attracted researchers and practitioners from various disciplines. Discovering cohesive subgroups or communities in complex networks is essential to understand the dynamics of real-world systems. Researchers have made persistent efforts to investigate and infer community patterns in complex networks. However, real-world networks exhibit various characteristics wherein existing communities are not only disjoint but are also overlapping and nested. The existing literature on community detection consists of limited methods to discover co-occurring disjoint, overlapping and nested communities. In this work, we propose a novel rough set based algorithm capable of uncovering true community structure in networks, be it disjoint overlapping or nested. Initial sets of granules are constructed using neighborhood connectivity around the nodes and represented as rough sets. Subsequently, we iteratively obtain the constrained connectedness upper approximation of these sets. To constrain the sets and merge them during each iteration, we utilize the concept of relative connectedness among the nodes. We illustrate the proposed algorithm on a toy network and evaluate it on fourteen real-world benchmark networks. Experimental results show that the proposed algorithm reveals more accurate communities and significantly outperforms state-of-the-art techniques. (C) 2017 Elsevier B.V. All rights reserved.

关键词： community structure Complex networks community detection algorithms Overlapping communities Neighborhood model Rough sets

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