Network Community Detection : a Review and Visual Survey
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Detecting Statistically Significant Communities
1 Detecting Statistically Significant Communities Zengyou He, Hao Liang, Zheng Chen, Can Zhao, Yan Liu Abstract—Community detection is a key data analysis problem across different fields. During the past decades, numerous algorithms have been proposed to address this issue. However, most work on community detection does not address the issue of statistical significance. Although some research efforts have been made towards mining statistically significant communities, deriving an analytical solution of p-value for one community under the configuration model is still a challenging mission that remains unsolved. The configuration model is a widely used random graph model in community detection, in which the degree of each node is preserved in the generated random networks. To partially fulfill this void, we present a tight upper bound on the p-value of a single community under the configuration model, which can be used for quantifying the statistical significance of each community analytically. Meanwhile, we present a local search method to detect statistically significant communities in an iterative manner. Experimental results demonstrate that our method is comparable with the competing methods on detecting statistically significant communities. Index Terms—Community Detection, Random Graphs, Configuration Model, Statistical Significance. F 1 INTRODUCTION ETWORKS are widely used for modeling the structure function that is able to always achieve the best performance N of complex systems in many fields, such as biology, in all possible scenarios. engineering, and social science. Within the networks, some However, most of these objective functions (metrics) do vertices with similar properties will form communities that not address the issue of statistical significance of commu- have more internal connections and less external links. -
Centrality in Modular Networks
Ghalmane et al. EPJ Data Science (2019)8:15 https://doi.org/10.1140/epjds/s13688-019-0195-7 REGULAR ARTICLE OpenAccess Centrality in modular networks Zakariya Ghalmane1,3, Mohammed El Hassouni1, Chantal Cherifi2 and Hocine Cherifi3* *Correspondence: hocine.cherifi@u-bourgogne.fr Abstract 3LE2I, UMR6306 CNRS, University of Burgundy, Dijon, France Identifying influential nodes in a network is a fundamental issue due to its wide Full list of author information is applications, such as accelerating information diffusion or halting virus spreading. available at the end of the article Many measures based on the network topology have emerged over the years to identify influential nodes such as Betweenness, Closeness, and Eigenvalue centrality. However, although most real-world networks are made of groups of tightly connected nodes which are sparsely connected with the rest of the network in a so-called modular structure, few measures exploit this property. Recent works have shown that it has a significant effect on the dynamics of networks. In a modular network, a node has two types of influence: a local influence (on the nodes of its community) through its intra-community links and a global influence (on the nodes in other communities) through its inter-community links. Depending on the strength of the community structure, these two components are more or less influential. Based on this idea, we propose to extend all the standard centrality measures defined for networks with no community structure to modular networks. The so-called “Modular centrality” is a two-dimensional vector. Its first component quantifies the local influence of a node in its community while the second component quantifies its global influence on the other communities of the network. -
Incorporating Network Structure with Node Contents for Community Detection on Large Networks Using Deep Learning
Neurocomputing 297 (2018) 71–81 Contents lists available at ScienceDirect Neurocomputing journal homepage: www.elsevier.com/locate/neucom Incorporating network structure with node contents for community detection on large networks using deep learning ∗ Jinxin Cao a, Di Jin a, , Liang Yang c, Jianwu Dang a,b a School of Computer Science and Technology, Tianjin University, Tianjin 300350, China b School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan c School of Computer Science and Engineering, Hebei University of Technology, Tianjin 300401, China a r t i c l e i n f o a b s t r a c t Article history: Community detection is an important task in social network analysis. In community detection, in gen- Received 3 June 2017 eral, there exist two types of the models that utilize either network topology or node contents. Some Revised 19 December 2017 studies endeavor to incorporate these two types of models under the framework of spectral clustering Accepted 28 January 2018 for a better community detection. However, it was not successful to obtain a big achievement since they Available online 2 February 2018 used a simple way for the combination. To reach a better community detection, it requires to realize a Communicated by Prof. FangXiang Wu seamless combination of these two methods. For this purpose, we re-examine the properties of the mod- ularity maximization and normalized-cut models and fund out a certain approach to realize a seamless Keywords: Community detection combination of these two models. These two models seek for a low-rank embedding to represent of the Deep learning community structure and reconstruct the network topology and node contents, respectively. -
Aaron Clauset
Aaron Clauset Contact Department of Computer Science voice: 303{492{6643 Information University of Colorado at Boulder fax: 303{492{2844 430 UCB email: [email protected] Boulder CO, 80309-0430 USA web: www.santafe.edu/∼aaronc Research Network science (methods, theories, applications); Data science, statistical inference, machine learn- Interests ing; Models and simulations; Collective dynamics and complex systems; Rare events, power laws and forecasting; Computational social science; Computational biology and biological computation. Education Ph.D. Computer Science, University of New Mexico (with distinction) 2002 { 2006 B.S. Physics, Haverford College (with honors and concentration in Computer Science) 1997 { 2001 Academic Associate Professor, Computer Science Dept., University of Colorado, Boulder 2018 { present Positions Core Faculty, BioFrontiers Institute, University of Colorado, Boulder 2010 { present External Faculty, Santa Fe Institute 2012 { present Affiliated Faculty, Ecology & Evo. Biology Dept., University of Colorado, Boulder 2011 { present Affiliated Faculty, Applied Mathematics Dept., University of Colorado, Boulder 2012 { present Affiliated Faculty, Information Dept., University of Colorado, Boulder 2015 { present Assistant Professor, Computer Science Dept., University of Colorado, Boulder 2010 { 2018 Omidyar Fellow, Santa Fe Institute 2006 { 2010 Editorial Deputy Editor, Science Advances, AAAS 2017 { present Positions Associate Editor, Science Advances, AAAS 2014 { 2017 Associate Editor, Journal of Complex Networks, Oxford University Press 2012 { 2017 Honors & Top 20 Teachers, College of Engineering, U. Colorado, Boulder 2016 Awards Erd}os-R´enyi Prize in Network Science 2016 (Selected) NSF CAREER Award 2015 { 2020 Kavli Fellow 2014 Santa Fe Institute Public Lecture Series (http://bit.ly/I6t9gf) 2010 Graduation Speaker, U. New Mexico School of Engineering Convocation 2006 Outstanding Graduate Student Award, U. -
Review of Community Detection Over Social Media: Graph Prospective
(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 10, No. 2, 2019 Review of Community Detection over Social Media: Graph Prospective Pranita Jain1, Deepak Singh Tomar2 Department of Computer Science Maulana Azad National Institute of Technology Bhopal, India 462001 Abstract—Community over the social media is the group of globally distributed end users having similar attitude towards a particular topic or product. Community detection algorithm is used to identify the social atoms that are more densely interconnected relatively to the rest over the social media platform. Recently researchers focused on group-based algorithm and member-based algorithm for community detection over social media. This paper presents comprehensive overview of community detection technique based on recent research and subsequently explores graphical prospective of social media mining and social theory (Balance theory, status theory, correlation theory) over community detection. Along with that this paper presents a comparative analysis of three different state of art community detection algorithm available on I-Graph package on python i.e. walk trap, edge betweenness and fast greedy over six different social media data set. That yield intersecting facts about the capabilities and deficiency of community analysis methods. Fig 1. Social Media Network. Keywords—Community detection; social media; social media Aim of Community detection is to form group of mining; homophily; influence; confounding; social theory; homogenous nodes and figure out a strongly linked subgraphs community detection algorithm from heterogeneous network. In strongly linked sub- graphs (Community structure) nodes have more internal links than I. INTRODUCTION external. Detecting communities in heterogeneous networks is The Emergence of Social networking Site (SNS) like Face- same as, the graph partition problem in modern graph theory book, Twitter, LinkedIn, MySpace, etc. -
Closeness Centrality for Networks with Overlapping Community Structure
Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (AAAI-16) Closeness Centrality for Networks with Overlapping Community Structure Mateusz K. Tarkowski1 and Piotr Szczepanski´ 2 Talal Rahwan3 and Tomasz P. Michalak1,4 and Michael Wooldridge1 2Department of Computer Science, University of Oxford, United Kingdom 2 Warsaw University of Technology, Poland 3Masdar Institute of Science and Technology, United Arab Emirates 4Institute of Informatics, University of Warsaw, Poland Abstract One aspect of networks that has been largely ignored in the literature on centrality is the fact that certain real-life Certain real-life networks have a community structure in which communities overlap. For example, a typical bus net- networks have a predefined community structure. In public work includes bus stops (nodes), which belong to one or more transportation networks, for example, bus stops are typically bus lines (communities) that often overlap. Clearly, it is im- grouped by the bus lines (or routes) that visit them. In coau- portant to take this information into account when measur- thorship networks, the various venues where authors pub- ing the centrality of a bus stop—how important it is to the lish can be interpreted as communities (Szczepanski,´ Micha- functioning of the network. For example, if a certain stop be- lak, and Wooldridge 2014). In social networks, individuals comes inaccessible, the impact will depend in part on the bus grouped by similar interests can be thought of as members lines that visit it. However, existing centrality measures do not of a community. Clearly for such networks, it is desirable take such information into account. Our aim is to bridge this to have a centrality measure that accounts for the prede- gap. -
A Centrality Measure for Networks with Community Structure Based on a Generalization of the Owen Value
ECAI 2014 867 T. Schaub et al. (Eds.) © 2014 The Authors and IOS Press. This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License. doi:10.3233/978-1-61499-419-0-867 A Centrality Measure for Networks With Community Structure Based on a Generalization of the Owen Value Piotr L. Szczepanski´ 1 and Tomasz P. Michalak2 ,3 and Michael Wooldridge2 Abstract. There is currently much interest in the problem of mea- cated — approaches have been considered in the literature. Recently, suring the centrality of nodes in networks/graphs; such measures various methods for the analysis of cooperative games have been ad- have a range of applications, from social network analysis, to chem- vocated as measures of centrality [16, 10]. The key idea behind this istry and biology. In this paper we propose the first measure of node approach is to consider groups (or coalitions) of nodes instead of only centrality that takes into account the community structure of the un- considering individual nodes. By doing so this approach accounts for derlying network. Our measure builds upon the recent literature on potential synergies between groups of nodes that become visible only game-theoretic centralities, where solution concepts from coopera- if the value of nodes are analysed jointly [18]. Next, given all poten- tive game theory are used to reason about importance of nodes in the tial groups of nodes, game-theoretic solution concepts can be used to network. To allow for flexible modelling of community structures, reason about players (i.e., nodes) in such a coalitional game. -
Cristopher Moore
Cristopher Moore Santa Fe Institute Santa Fe, NM 87501 [email protected] August 23, 2021 1 Education Born March 12, 1968 in New Brunswick, New Jersey. Northwestern University, B.A. in Physics, Mathematics, and the Integrated Science Program, with departmental honors in all three departments, 1986. Cornell University, Ph.D. in Physics, 1991. Philip Holmes, advisor. Thesis: “Undecidability and Unpredictability in Dynamical Systems.” 2 Employment Professor, Santa Fe Institute 2012–present Professor, Computer Science Department with a joint appointment in the Department of Physics and Astronomy, University of New Mexico, Albuquerque 2008–2012 Associate Professor, University of New Mexico 2005–2008 Assistant Professor, University of New Mexico 2000–2005 Research Professor, Santa Fe Institute 1998–1999 City Councilor, District 2, Santa Fe 1994–2002 Postdoctoral Fellow, Santa Fe Institute 1992–1998 Lecturer, Cornell University Spring 1991 Graduate Intern, Niels Bohr Institute/NORDITA, Copenhagen Summers 1988 and 1989 Teaching Assistant, Cornell University Physics Department Fall 1986–Spring 1990 Computer programmer, Bio-Imaging Research, Lincolnshire, Illinois Summers 1984–1986 3 Other Appointments Visiting Researcher, Microsoft Research New England Fall 2019 Visiting Professor, Ecole´ Normale Sup´erieure October–November 2016 Visiting Professor, Northeastern University October–November 2015 Visiting Professor, University of Michigan, Ann Arbor September–October 2005 Visiting Professor, Ecole´ Normale Sup´erieure de Lyon June 2004 Visiting Professor, -
Structural Diversity and Homophily: a Study Across More Than One Hundred Big Networks
KDD 2017 Research Paper KDD’17, August 13–17, 2017, Halifax, NS, Canada Structural Diversity and Homophily: A Study Across More Than One Hundred Big Networks Yuxiao Dong∗ Reid A. Johnson Microso Research University of Notre Dame Redmond, WA 98052 Notre Dame, IN 46556 [email protected] [email protected] Jian Xu Nitesh V. Chawla University of Notre Dame University of Notre Dame Notre Dame, IN 46556 Notre Dame, IN 46556 [email protected] [email protected] ABSTRACT ACM Reference format: A widely recognized organizing principle of networks is structural Yuxiao Dong, Reid A. Johnson, Jian Xu, and Nitesh V. Chawla. 2017. Struc- tural Diversity and Homophily: A Study Across More an One Hundred homophily, which suggests that people with more common neigh- Big Networks. In Proceedings of KDD ’17, August 13–17, 2017, Halifax, NS, bors are more likely to connect with each other. However, what in- Canada., , 10 pages. uence the diverse structures embedded in common neighbors (e.g., DOI: hp://dx.doi.org/10.1145/3097983.3098116 and ) have on link formation is much less well-understood. To explore this problem, we begin by characterizing the structural diversity of common neighborhoods. Using a collection of 120 large- 1 INTRODUCTION scale networks, we demonstrate that the impact of the common neighborhood diversity on link existence can vary substantially Since the time of Aristotle, it has been observed that people “love across networks. We nd that its positive eect on Facebook and those who are like themselves” [2]. We now know this as the negative eect on LinkedIn suggest dierent underlying network- principle of homophily, which asserts that people’s propensity to ing needs in these networks. -
Curriculum Vitae of Danny Dorling
January 2021 1993 to 1996: British Academy Fellow, Department of Geography, Newcastle University 1991 to 1993: Joseph Rowntree Foundation Curriculum Vitae Fellow, Many Departments, Newcastle University 1987 to 1991: Part-Time Researcher/Teacher, Danny Dorling Geography Department, Newcastle University Telephone: +44(0)1865 275986 Other Posts [email protected] skype: danny.dorling 2020-2023 Advisory Board Member: ‘The political economies of school exclusion and their consequences’ (ESRC project ES/S015744/1). Current appointment: Halford Mackinder 2020-Assited with the ‘Time to Care’ Oxfam report. Professor of Geography, School of 2020- Judge for data visualisation competition Geography and the Environment, The Nuffield Trust, the British Medical Journal, the University of Oxford, South Parks Road, British Medical Association and NHS Digital. Oxford, OX1 3QY 2019- Judge for the annual Royal Geographical th school 6 form essay competition. 2019 – UNDP (United Nations Development Other Appointments Programme) Human Development Report reviewer. 2019 – Advisory Broad member: Sheffield Visiting Professor, Department of Sociology, University Nuffield project on an Atlas of Inequality. Goldsmiths, University of London, 2013-2016. 2019 – Advisory board member - Glasgow Centre for Population Health project on US mortality. Visiting Professor, School of Social and 2019- Editorial Board Member – Bristol University Community Medicine, University of Bristol, UK Press, Studies in Social Harm Book Series. 2018 – Member of the Bolton Station Community Adjunct Professor in the Department of Development Partnership. Geography, University of Canterbury, NZ 2018-2022 Director of the Graduate School, School of Geography and the Environment, Oxford. 2018 – Member of the USS review working group of the Council of the University of Oxford. -
A Preferential Attachment Paradox: How Preferential Attachment Combines with Growth to Produce Networks with Log-Normal In-Degree Distributions
A Preferential Attachment Paradox: How Preferential Attachment Combines with Growth to Produce Networks with Log-normal In-degree Distributions Paul Sheridan1,* and Taku Onodera2 1Hirosaki University, Department of Active Life Promotion Science, Hirosaki, 036-8562, Japan 2The University of Tokyo, Institute of Medical Science, Human Genome Center, Tokyo, 108-8639, Japan *[email protected] ABSTRACT Every network scientist knows that preferential attachment combines with growth to produce networks with power-law in-degree distributions. How, then, is it possible for the network of American Physical Society journal collection citations to enjoy a log-normal citation distribution when it was found to have grown in accordance with preferential attachment? This anomalous result, which we exalt as the preferential attachment paradox, has remained unexplained since the physicist Sidney Redner first made light of it over a decade ago. Here we propose a resolution. The chief source of the mischief, we contend, lies in Redner having relied on a measurement procedure bereft of the accuracy required to distinguish preferential attachment from another form of attachment that is consistent with a log-normal in-degree distribution. There was a high-accuracy measurement procedure in use at the time, but it would have have been difficult to use it to shed light on the paradox, due to the presence of a systematic error inducing design flaw. In recent years the design flaw had been recognised and corrected. We show that the bringing of the newly corrected measurement procedure to bear on the data leads to a resolution of the paradox. Introduction The physicist Sidney Redner reported a rather curious anomaly in a decade-old study on the citation statistics of the American Physical Society (APS) journal collection1. -
Community Extraction in Multilayer Networks with Heterogeneous Community Structure
Journal of Machine Learning Research 18 (2017) 1-49 Submitted 12/16; Revised 9/17; Published 11/17 Community Extraction in Multilayer Networks with Heterogeneous Community Structure James D. Wilson∗ [email protected] Department of Mathematics and Statistics University of San Francisco San Francisco, CA 94117-1080 John Palowitch∗ [email protected] Shankar Bhamidi [email protected] Andrew B. Nobel [email protected] Department of Statistics and Operations Research University of North Carolina at Chapel Hill Chapel Hill, NC 27599 Editor: Edo Airoldi Abstract Multilayer networks are a useful way to capture and model multiple, binary or weighted relationships among a fixed group of objects. While community detection has proven to be a useful exploratory technique for the analysis of single-layer networks, the develop- ment of community detection methods for multilayer networks is still in its infancy. We propose and investigate a procedure, called Multilayer Extraction, that identifies densely connected vertex-layer sets in multilayer networks. Multilayer Extraction makes use of a significance based score that quantifies the connectivity of an observed vertex-layer set through comparison with a fixed degree random graph model. Multilayer Extraction di- rectly handles networks with heterogeneous layers where community structure may be different from layer to layer. The procedure can capture overlapping communities, as well as background vertex-layer pairs that do not belong to any community. We estab- lish consistency of the vertex-layer set optimizer of our proposed multilayer score un- der the multilayer stochastic block model. We investigate the performance of Multi- layer Extraction on three applications and a test bed of simulations.