Mixing Patterns and Community Structure in Networks 3 Apply Those Methods to Particular Networks
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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. -
Analysis of Topological Characteristics of Huge Online Social Networking Services Yong-Yeol Ahn, Seungyeop Han, Haewoon Kwak, Young-Ho Eom, Sue Moon, Hawoong Jeong
1 Analysis of Topological Characteristics of Huge Online Social Networking Services Yong-Yeol Ahn, Seungyeop Han, Haewoon Kwak, Young-Ho Eom, Sue Moon, Hawoong Jeong Abstract— Social networking services are a fast-growing busi- the statistics severely and it is imperative to use large data sets ness in the Internet. However, it is unknown if online relationships in network structure analysis. and their growth patterns are the same as in real-life social It is only very recently that we have seen research results networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpace, and orkut, from large networks. Novel network structures from human each with more than 10 million users, respectively. We have societies and communication systems have been unveiled; just access to complete data of Cyworld’s ilchon (friend) relationships to name a few are the Internet and WWW [3] and the patents, and analyze its degree distribution, clustering property, degree Autonomous Systems (AS), and affiliation networks [4]. Even correlation, and evolution over time. We also use Cyworld data in the short history of the Internet, SNSs are a fairly new to evaluate the validity of snowball sampling method, which we use to crawl and obtain partial network topologies of MySpace phenomenon and their network structures are not yet studied and orkut. Cyworld, the oldest of the three, demonstrates a carefully. The social networks of SNSs are believed to reflect changing scaling behavior over time in degree distribution. The the real-life social relationships of people more accurately than latest Cyworld data’s degree distribution exhibits a multi-scaling any other online networks. -
Correlation in Complex Networks
Correlation in Complex Networks by George Tsering Cantwell A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in the University of Michigan 2020 Doctoral Committee: Professor Mark Newman, Chair Professor Charles Doering Assistant Professor Jordan Horowitz Assistant Professor Abigail Jacobs Associate Professor Xiaoming Mao George Tsering Cantwell [email protected] ORCID iD: 0000-0002-4205-3691 © George Tsering Cantwell 2020 ACKNOWLEDGMENTS First, I must thank Mark Newman for his support and mentor- ship throughout my time at the University of Michigan. Further thanks are due to all of the people who have worked with me on projects related to this thesis. In alphabetical order they are Eliz- abeth Bruch, Alec Kirkley, Yanchen Liu, Benjamin Maier, Gesine Reinert, Maria Riolo, Alice Schwarze, Carlos Serván, Jordan Sny- der, Guillaume St-Onge, and Jean-Gabriel Young. ii TABLE OF CONTENTS Acknowledgments .................................. ii List of Figures ..................................... v List of Tables ..................................... vi List of Appendices .................................. vii Abstract ........................................ viii Chapter 1 Introduction .................................... 1 1.1 Why study networks?...........................2 1.1.1 Example: Modeling the spread of disease...........3 1.2 Measures and metrics...........................8 1.3 Models of networks............................ 11 1.4 Inference................................. -
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. -
Happiness Is Assortative in Online Social Networks
Happiness Is Assortative in Johan Bollen*,** Online Social Networks Indiana University Bruno Goncalves**̧ Indiana University Guangchen Ruan** Indiana University Abstract Online social networking communities may exhibit highly Huina Mao** complex and adaptive collective behaviors. Since emotions play such Indiana University an important role in human decision making, how online networks Downloaded from http://direct.mit.edu/artl/article-pdf/17/3/237/1662787/artl_a_00034.pdf by guest on 25 September 2021 modulate human collective mood states has become a matter of considerable interest. In spite of the increasing societal importance of online social networks, it is unknown whether assortative mixing of psychological states takes place in situations where social ties are mediated solely by online networking services in the absence Keywords of physical contact. Here, we show that the general happiness, Social networks, mood, sentiment, or subjective well-being (SWB), of Twitter users, as measured from a assortativity, homophily 6-month record of their individual tweets, is indeed assortative across the Twitter social network. Our results imply that online social A version of this paper with color figures is networks may be equally subject to the social mechanisms that cause available online at http://dx.doi.org/10.1162/ assortative mixing in real social networks and that such assortative artl_a_00034. Subscription required. mixing takes place at the level of SWB. Given the increasing prevalence of online social networks, their propensity to connect users with similar levels of SWB may be an important factor in how positive and negative sentiments are maintained and spread through human society. Future research may focus on how event-specific mood states can propagate and influence user behavior in “real life.” 1 Introduction Bird flocking and fish schooling are typical and well-studied examples of how large communities of relatively simple individuals can exhibit highly complex and adaptive behaviors at the collective level. -
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. -
Dynamics of Dyads in Social Networks: Assortative, Relational, and Proximity Mechanisms
SO36CH05-Uzzi ARI 2 June 2010 23:8 Dynamics of Dyads in Social Networks: Assortative, Relational, and Proximity Mechanisms Mark T. Rivera,1 Sara B. Soderstrom,1 and Brian Uzzi1,2 1Department of Management and Organizations, Kellogg School of Management, Northwestern University, Evanston, Illinois 60208; email: [email protected], [email protected], [email protected] 2Northwestern University Institute on Complex Systems and Network Science (NICO), Evanston, Illinois 60208-4057 Annu. Rev. Sociol. 2010. 36:91–115 Key Words First published online as a Review in Advance on Annu. Rev. Sociol. 2010.36:91-115. Downloaded from arjournals.annualreviews.org embeddedness, homophily, complexity, organizations, network April 12, 2010 evolution by NORTHWESTERN UNIVERSITY - Evanston Campus on 07/13/10. For personal use only. The Annual Review of Sociology is online at soc.annualreviews.org Abstract This article’s doi: Embeddedness in social networks is increasingly seen as a root cause of 10.1146/annurev.soc.34.040507.134743 human achievement, social stratification, and actor behavior. In this arti- Copyright c 2010 by Annual Reviews. cle, we review sociological research that examines the processes through All rights reserved which dyadic ties form, persist, and dissolve. Three sociological mech- 0360-0572/10/0811-0091$20.00 anisms are overviewed: assortative mechanisms that draw attention to the role of actors’ attributes, relational mechanisms that emphasize the influence of existing relationships and network positions, and proximity mechanisms that focus on the social organization of interaction. 91 SO36CH05-Uzzi ARI 2 June 2010 23:8 INTRODUCTION This review examines journal articles that explain how social networks evolve over time. -
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. -
The Perceived Assortativity of Social Networks: Methodological Problems and Solutions
The perceived assortativity of social networks: Methodological problems and solutions David N. Fisher1, Matthew J. Silk2 and Daniel W. Franks3 Abstract Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections. Social networks are typically thought to be distinct from other networks in being assortative (possessing positive degree correlations); well-connected individuals associate with other well-connected individuals, and poorly-connected individuals associate with each other. We review the evidence for this in the literature and find that, while social networks are more assortative than non-social networks, only when they are built using group-based methods do they tend to be positively assortative. Non-social networks tend to be disassortative. We go on to show that connecting individuals due to shared membership of a group, a commonly used method, biases towards assortativity unless a large enough number of censuses of the network are taken. We present a number of solutions to overcoming this bias by drawing on advances in sociological and biological fields. Adoption of these methods across all fields can greatly enhance our understanding of social networks and networks in general. 1 1. Department of Integrative Biology, University of Guelph, Guelph, ON, N1G 2W1, Canada. Email: [email protected] (primary corresponding author) 2. Environment and Sustainability Institute, University of Exeter, Penryn Campus, Penryn, TR10 9FE, UK Email: [email protected] 3. Department of Biology & Department of Computer Science, University of York, York, YO10 5DD, UK Email: [email protected] Keywords: Assortativity; Degree assortativity; Degree correlation; Null models; Social networks Introduction Network theory is a useful tool that can help us explain a range of social, biological and technical phenomena (Pastor-Satorras et al 2001; Girvan and Newman 2002; Krause et al 2007).