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34
Comparing community structure identification
 Journal of Statistical Mechanics: Theory and Experiment
, 2005
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Statistical properties of community structure in large social and information networks
"... A large body of work has been devoted to identifying community structure in networks. A community is often though of as a set of nodes that has more connections between its members than to the remainder of the network. In this paper, we characterize as a function of size the statistical and structur ..."
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Cited by 134 (10 self)
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A large body of work has been devoted to identifying community structure in networks. A community is often though of as a set of nodes that has more connections between its members than to the remainder of the network. In this paper, we characterize as a function of size the statistical and structural properties of such sets of nodes. We define the network community profile plot, which characterizes the “best ” possible community—according to the conductance measure—over a wide range of size scales, and we study over 70 large sparse realworld networks taken from a wide range of application domains. Our results suggest a significantly more refined picture of community structure in large realworld networks than has been appreciated previously. Our most striking finding is that in nearly every network dataset we examined, we observe tight but almost trivial communities at very small scales, and at larger size scales, the best possible communities gradually “blend in ” with the rest of the network and thus become less “communitylike.” This behavior is not explained, even at a qualitative level, by any of the commonlyused network generation models. Moreover, this behavior is exactly the opposite of what one would expect based on experience with and intuition from expander graphs, from graphs that are wellembeddable in a lowdimensional structure, and from small social networks that have served as testbeds of community detection algorithms. We have found, however, that a generative model, in which new edges are added via an iterative “forest fire” burning process, is able to produce graphs exhibiting a network community structure similar to our observations.
Computing communities in large networks using random walks
 J. of Graph Alg. and App. bf
, 2004
"... Dense subgraphs of sparse graphs (communities), which appear in most realworld complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advan ..."
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Cited by 113 (2 self)
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Dense subgraphs of sparse graphs (communities), which appear in most realworld complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn 2) and space O(n 2) in the worst case, and in time O(n 2 log n) and space O(n 2) in most realworld cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.
Characterization of complex networks: A survey of measurements
 ADVANCES IN PHYSICS
, 2005
"... Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of mea ..."
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Cited by 102 (7 self)
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Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements organized into classes. Special attention is given to relating complex network analysis with the areas of pattern recognition and feature selection, as well as on surveying some concepts and measurements from traditional graph theory which are potentially useful for complex network research. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the
Community structure in large networks: Natural cluster sizes and the absence of large welldefined clusters
, 2008
"... A large body of work has been devoted to defining and identifying clusters or communities in social and information networks, i.e., in graphs in which the nodes represent underlying social entities and the edges represent some sort of interaction between pairs of nodes. Most such research begins wit ..."
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Cited by 85 (7 self)
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A large body of work has been devoted to defining and identifying clusters or communities in social and information networks, i.e., in graphs in which the nodes represent underlying social entities and the edges represent some sort of interaction between pairs of nodes. Most such research begins with the premise that a community or a cluster should be thought of as a set of nodes that has more and/or better connections between its members than to the remainder of the network. In this paper, we explore from a novel perspective several questions related to identifying meaningful communities in large social and information networks, and we come to several striking conclusions. Rather than defining a procedure to extract sets of nodes from a graph and then attempt to interpret these sets as a “real ” communities, we employ approximation algorithms for the graph partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be interpreted as communities. In particular, we define the network community profile plot, which characterizes the “best ” possible community—according to the conductance measure—over a wide range of size scales. We study over 100 large realworld networks, ranging from traditional and online social networks, to technological and information networks and
An Emulator Network for
 SIMD Machine Interconnection Networks, in: Proc. 6 th annual symposium on Computer architecture
, 1979
"... Fig. 0.1. [Proposed cover figure.] The largest connected component of a network of network scientists. This network was constructed based on the coauthorship of papers listed in two wellknown review articles [13,83] and a small number of additional papers that were added manually [86]. Each node is ..."
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Cited by 39 (4 self)
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Fig. 0.1. [Proposed cover figure.] The largest connected component of a network of network scientists. This network was constructed based on the coauthorship of papers listed in two wellknown review articles [13,83] and a small number of additional papers that were added manually [86]. Each node is colored according to community membership, which was determined using a leadingeigenvector spectral method followed by KernighanLin nodeswapping steps [64, 86, 107]. To determine community placement, we used the FruchtermanReingold graph visualization [45], a forcedirected layout method that is related to maximizing a quality function known as modularity [92]. To apply this method, we treated the communities as if they were themselves the nodes of a (significantly smaller) network with connections rescaled by intercommunity links. We then used the KamadaKawaii springembedding graph visualization algorithm [62] to place the nodes of each individual community (ignoring intercommunity links) and then to rotate and flip the communities for optimal placement (including intercommunity links). We gratefully acknowledge Amanda Traud for preparing this figure. COMMUNITIES IN NETWORKS
Dynamics of Large Networks
, 2008
"... A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models ..."
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Cited by 23 (0 self)
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A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models that explain processes which govern the network evolution, fit such models to real networks, and use them to generate realistic graphs or give formal explanations about their properties. In addition, our work has a wide range of applications: it can help us spot anomalous graphs and outliers, forecast future graph structure and run simulations of network evolution. Another important aspect of our research is the study of “local ” patterns and structures of propagation in networks. We aim to identify building blocks of the networks and find the patterns of influence that these blocks have on information or virus propagation over the network. Our recent work included the study of the spread of influence in a large persontoperson
Community structure in the united states house of representatives
 PHYSICA A: STATISTICAL MECHANICS AND ITS APPLICATIONS 386
, 2007
"... We investigate the networks of committee and subcommittee assignments in the United States House of Representatives from the 101st–108th Congresses, with committees connected according to “interlocks” or common membership. We examine the House’s community structure using several methods, which revea ..."
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Cited by 17 (1 self)
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We investigate the networks of committee and subcommittee assignments in the United States House of Representatives from the 101st–108th Congresses, with committees connected according to “interlocks” or common membership. We examine the House’s community structure using several methods, which reveal strong links between different committees as well as the intrinsic hierarchical structure within the House as a whole. We identify structural changes, including additional hierarchical levels and higher modularity, resulting from the 1994 elections, in which the Republican party earned majority status in the House for the first time in more than forty years. We also combine our network approach with analysis of roll call votes using singular value decomposition to uncover correlations between the political and organizational structure of House committees.
Largescale community detection on youtube for topic discovery and exploration
 in Proc. of the Fifth international AAAI Conference on Weblogs and Social Media
"... Detecting coherent and wellconnected communities inside largescale graphs is an interesting problem that can provide useful insight into the graph structure and individual communities. It can also serve as the basis for content exploration and discovery within the graph. Clustering is a popular te ..."
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Cited by 9 (2 self)
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Detecting coherent and wellconnected communities inside largescale graphs is an interesting problem that can provide useful insight into the graph structure and individual communities. It can also serve as the basis for content exploration and discovery within the graph. Clustering is a popular technique for community detection, however, the two main categories of clustering algorithms, i.e, global and local algorithms, have either scalability or usability issues, e.g, global algorithms do not scale well, and local algorithms may cover only a portion of the graph. Such onestage algorithms typically optimize one objective function and do not work well in settings where we need to optimize various coverage, coherence and connectivity metrics. In this paper, we study largescale community detection over a realworld graph composed of millions of YouTube videos. In particular, we present a multistage scalable clustering algorithm, combining a preprocessing stage, a local clustering stage, and a postprocessing stage to generate clusters of YouTube videos with coherent content. We formalize coverage, coherence, and connectivity metrics and evaluate the quality of the proposed multistage clustering algorithms for YouTube videos. We also use extracted entities to attach meaningful labels to our clusters. Our use of local algorithms for global clustering, and its implementation and practical evaluation on such a large scale is a first of its kind.
Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics
 PLoS One
, 2010
"... Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Fin ..."
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Cited by 6 (1 self)
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Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Findings: Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence functionbased, centralitytype community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoomin analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics. Conclusions/Significance: The concept opens a wide range of possibilities to develop new approaches and applications