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Journal ArticleDOI

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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Journal ArticleDOI
01 Jan 2003-Siam Review
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

16,520 citations


Cites methods from "Community structure in social and b..."

  • ...Recently a number of authors have had success with methods based on “edge betweenness,” which is the count of how many geodesic paths between vertices run along each edge in the network [171, 185, 197, 422]....

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Journal ArticleDOI
26 Feb 2004-Physical Review E
TL;DR: It is demonstrated that the algorithms proposed are highly effective at discovering community structure in both computer-generated and real-world network data, and can be used to shed light on the sometimes dauntingly complex structure of networked systems.
Abstract: We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

11,600 citations


Cites background from "Community structure in social and b..."

  • ...Since the publication of our first paper on this topic [25], several other authors have made use of the shortest-path version of our algorithm....

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Journal ArticleDOI
Abstract: We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks.

11,078 citations


Journal ArticleDOI
TL;DR: This work proposes a heuristic method that is shown to outperform all other known community detection methods in terms of computation time and the quality of the communities detected is very good, as measured by the so-called modularity.
Abstract: We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2.6 million customers and by analyzing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad-hoc modular networks. .

10,260 citations


Journal ArticleDOI
Mark Newman1Institutions (1)
Abstract: Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as “modularity” over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets.

8,969 citations


References
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Journal ArticleDOI
Duncan J. Watts1, Steven H. Strogatz1Institutions (1)
04 Jun 1998-Nature
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.

35,972 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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Journal ArticleDOI
15 Oct 1999-Science
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.

30,921 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 1993-
TL;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.

8,345 citations


Journal ArticleDOI
Steven H. Strogatz1Institutions (1)
08 Mar 2001-Nature
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.

7,139 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]....

    [...]

  • ...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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Journal ArticleDOI
Linton C. Freeman1Institutions (1)
01 Mar 1977-
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.

6,934 citations


Network Information
Performance
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No. of citations received by the Paper in previous years
YearCitations
202221
2021952
20201,146
20191,126
20181,067
20171,037