Finding community structure in networks using the eigenvectors of matrices
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A modularity matrix plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations, and a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong are proposed.Abstract:
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as ``modularity'' over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.read more
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A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities
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TL;DR: In this paper, the authors compared the performance of the adjacency matrix, the standard Laplacian matrix, normalized LaplACian, the modularity matrix, and the correlation matrix for the detection of community structure.
References
More filters
Journal ArticleDOI
Collective dynamics of small-world networks
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.
Journal ArticleDOI
The Strength of Weak Ties
TL;DR: In this paper, it is argued that the degree of overlap of two individuals' friendship networks varies directly with the strength of their tie to one another, and the impact of this principle on diffusion of influence and information, mobility opportunity, and community organization is explored.
Journal ArticleDOI
Emergence of Scaling in Random Networks
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.
疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A
TL;DR: PfPMP1）与感染红细胞、树突状组胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作�ly.
Journal ArticleDOI
The Structure and Function of Complex Networks
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.