Community structure in social and biological networks
11 Jun 2002-Proceedings of the National Academy of Sciences of the United States of America (National Academy of Sciences)-Vol. 99, Iss: 12, pp 7821-7826
TL;DR: This article proposes a method for detecting communities, built around the idea of using centrality indices to find community boundaries, and tests it on computer-generated and real-world graphs whose community structure is already known and finds that the method detects this known structure with high sensitivity and reliability.
Abstract: A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases.
Citations
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08 May 2017
TL;DR: A SEP Protocol based on community structure of node degree (SEP-CSND) is proposed, which balances the energy consumption of the entire network and significantly prolongs network lifetime.
Abstract: Analyzing the Stable election protocol (SEP) in wireless sensor networks and aiming at the problem of inhomogeneous cluster-heads distribution and unreasonable cluster-heads selectivity and single hop transmission in the SEP, a SEP Protocol based on community structure of node degree (SEP-CSND) is proposed. In this algorithm, network node deployed by using grid deployment model, and the connection between nodes established by setting up the communication threshold. The community structure constructed by node degree, then cluster head is elected in the community structure. On the basis of SEP, the node’s residual energy and node degree is added in cluster-heads election. The information is transmitted with mode of multiple hops between network nodes. The simulation experiments showed that compared to the classical LEACH and SEP, this algorithm balances the energy consumption of the entire network and significantly prolongs network lifetime.
2 citations
31 Jul 2017
TL;DR: A novel and parallel community detection algorithm, PCDU algorithm, based on distance dynamics, which is not only as accurate as the traditional way and more efficient, but also has less space complexity.
Abstract: In recent years, community detection has drawn more and more researchers' attention. With the development of Internet, the scale of network data is growing fast. It is necessary to find an effective parallel community detection algorithm for large-scale network. In this paper, we propose a novel and parallel community detection algorithm, PCDU algorithm, based on distance dynamics. We send distances information to nodes and update distances of edges constantly, based on previous values and the unified model, which is introduced to quantify different influences from nodes and edges. It ends until the distances are stable. Then we remove some special edges from the original graph and get all subgraphs, which are the community partitions. It still inherits the advantage of uncovering small communities and outliers. Experiments based on synthetic networks and real world networks, show that our algorithm execute more efficient than stand-alone version. Since it is based on the Spark platform and designed in parallelization, the algorithm is very suitable for large datasets. We also provide a novel method taking use of double summation to calculate the NMI value of community partition result and the embedded community structure. Compared with the traditional way, it is not only as accurate as the traditional way and more efficient, but also has less space complexity. Experiments show that it is suitable for evaluating community division results in large-scale network.
2 citations
Cites methods from "Community structure in social and b..."
...There are some efficient traditional static community detection algorithms, such as GN algorithm [4] and CPM algorithm [5]....
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27 Nov 2017
TL;DR: In order to achieve a smooth animation of time-varying graphs, the graph layout at each time step is extracted from a super-layout which is based on the super-graph and super-community.
Abstract: Drawing a large graph into the limited display space often raises visual clutter and overlapping problems. The complex structure hinders the exploration of significant patterns of connections. For time-varying graphs, it is difficult to reveal the evolution of structures. In this paper, we group nodes and links into partitions, where objects within a partition are more closely related. Besides, partitions maintain stable across time steps. The complex structure of a partition is simplified by mapping to a pattern and the evolution is exposed by comparing patterns of two consecutive time steps. We created various visual designs to present different scenarios of changes. In order to achieve a smooth animation of time-varying graphs, we extract the graph layout at each time step from a super-layout which is based on the super-graph and super-community. The effectiveness of our approach is verified with two datasets, one is a synthetic dataset, and the other is the DBLP dataset.
2 citations
TL;DR: The proposed ComDet uses data clustering as a pre-processing step for the community detection process in order to identify similar nodes that are directly or indirectly linked and organize them in cohesive and possibly overlapping communities.
Abstract: Community detection is an important network analysis task that has been studied by academy and industry for the last years. Community detection algorithms try to maximize the number of connections in each community and minimize the number of connections between different communities. Some of them consider not only the topological aspects of the networks but also try to explore existing information about the context of the application available in attributes of nodes and/or connections in order to find cohesive content communities. Those algorithmswere designed to run exclusively over homogeneous networks and cannot deal with heterogeneous structures. Nevertheless, typical real-world networks are heterogeneous. Thus, this article proposes ComDet, a community detection approach that fills this gap by taking into account topological and contextual information to detect communities in heterogeneous networks. The proposed approach uses data clustering as a pre-processing step for the community detection process in order to identify similar nodes that are directly or indirectly linked and organize them in cohesive and possibly overlapping communities. Experiments in three attributed heterogeneous networks show that ComDet leads to interesting partitions with cohesive content communities.
2 citations
TL;DR: In this article, the exact recovery of the maximum likelihood estimation (MLE) with various weighted adjacency matrices was studied, where edges are only allowed between distinct communities, and the number of vertices in different communities are not necessarily equal.
Abstract: We study the vertex classification problem on a graph whose vertices are in $$k\ (k\ge 2)$$
different communities, edges are only allowed between distinct communities, and the number of vertices in different communities are not necessarily equal. The observation is a weighted adjacency matrix, perturbed by a scalar multiple of the Gaussian Orthogonal Ensemble (GOE), or Gaussian Unitary Ensemble (GUE) matrix. For the exact recovery of the maximum likelihood estimation (MLE) with various weighted adjacency matrices, we prove sharp thresholds of the intensity $$\sigma $$
of the Gaussian perturbation. Roughly speaking, when $$\sigma $$
is below (resp. above) the threshold, exact recovery of MLE occurs with probability tending to 1 (resp. 0) as the size of the graph goes to infinity. These weighted adjacency matrices may be considered as natural models for the electric network. Surprisingly, these thresholds of $$\sigma $$
do not depend on whether the sample space for MLE is restricted to such classifications that the number of vertices in each group is equal to the true value. In contrast to the $${{\mathbb {Z}}}_2$$
-synchronization, a new complex version of the semi-definite programming (SDP) is designed to efficiently implement the community detection problem when the number of communities k is greater than 2, and a common region (independent of k) for $$\sigma $$
such that SDP exactly recovers the true classification is obtained.
2 citations
References
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TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
39,297 citations
"Community structure in social and b..." refers background or methods in this paper
...Examples include social networks [2, 3, 4] such as acquaintance networks [5] and collaboration networks [6], technological networks such as the Internet [7], the World-Wide Web [8, 9], and power grids [4, 5], and biological networks such as neural networks [4], food webs [10], and metabolic networks [11, 12]....
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...This effect is quantified by the clustering coefficient C [4, 18], defined by...
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TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
33,771 citations
"Community structure in social and b..." refers background in this paper
...The degree of a vertex in a network is the number of other vertices to which it is connected, and one finds that there are typically many vertices in a network with low degree and a small number with high degree, the precise distribution often following a power-law or exponential form [1, 5, 15]....
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...Another is the right-skewed degree distributions that many networks possess [8, 9, 15, 16, 17]....
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Book•
01 Jan 1993TL;DR: In-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models are presented.
Abstract: A comprehensive introduction to network flows that brings together the classic and the contemporary aspects of the field, and provides an integrative view of theory, algorithms, and applications. presents in-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models. emphasizes powerful algorithmic strategies and analysis tools such as data scaling, geometric improvement arguments, and potential function arguments. provides an easy-to-understand descriptions of several important data structures, including d-heaps, Fibonacci heaps, and dynamic trees. devotes a special chapter to conducting empirical testing of algorithms. features over 150 applications of network flows to a variety of engineering, management, and scientific domains. contains extensive reference notes and illustrations.
8,496 citations
01 Mar 1977
TL;DR: A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced in this paper, which define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication.
Abstract: A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication. They may be used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected.
8,026 citations
TL;DR: This work aims to understand how an enormous network of interacting dynamical systems — be they neurons, power stations or lasers — will behave collectively, given their individual dynamics and coupling architecture.
Abstract: The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems-be they neurons, power stations or lasers-will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.
7,665 citations
"Community structure in social and b..." refers background in this paper
...The degree of a vertex in a network is the number of other vertices to which it is connected, and one finds that there are typically many vertices in a network with low degree and a small number with high degree, the precise distribution often following a power-law or exponential form [1, 5, 15]....
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...Many systems take the form of networks, sets of nodes or vertices joined together in pairs by links or edges [1]....
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