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
Citations
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Finding Communities by Their Centers.
TL;DR: This work develops a simple yet effective approach that simultaneously uncovers communities and their centers, based on the premise that organization of a community generally can be viewed as a high-density node surrounded by neighbors with lower densities, and community centers reside far apart from each other.
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A Hybrid CPU-GPU Accelerated Framework for Fast Mapping of High-Resolution Human Brain Connectome
Yu Wang,Haixiao Du,Mingrui Xia,Ling Ren,Mo Xu,Teng Xie,Gaolang Gong,Ningyi Xu,Huazhong Yang,Yong He +9 more
TL;DR: This paper proposes a hybrid CPU-GPU framework to accelerate the computation of the human brain connectome, and reveals that high-resolution functional brain networks have efficient small-world properties, significant modular structure, a power law degree distribution and highly connected nodes in the medial frontal and parietal cortical regions.
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Methods to find community based on edge centrality
Peng Gang Sun,Yang Yang +1 more
TL;DR: Three edge centralities based on network topology, walks and paths are studied to quantify the relevance of each edge in a network, and a divisive algorithm based on the rationale of GN algorithm for finding communities that removes edges iteratively according to the edge centrality values in a certain order is proposed.
Proceedings ArticleDOI
Decompositions of triangle-dense graphs
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GMAC: A Seed-Insensitive Approach to Local Community Detection
TL;DR: A seed-insensitive method called GMAC is presented, which estimates the similarity between vertices via the investigation on vertices' neighborhoods, and reveals a local community by maximizing its internal similarity and minimizing its external similarity simultaneously.
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