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Finding community structure in networks using the eigenvectors of matrices

Mark Newman
- 11 Sep 2006 - 
- Vol. 74, Iss: 3, pp 036104-036104
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TLDR
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.

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Citations
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Topological structural classes of complex networks

TL;DR: It is shown that neither of three network growth mechanisms--random with uniform distribution, preferential attachment, and random with the same degree sequence as real network--is able to reproduce the four structural classes of complex networks.
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Improved centrality indicators to characterize the nodal spreading capability in complex networks

TL;DR: This paper systematically compares the ranking similarity and monotonicity under various centrality algorithms over 6 real-world networks and Barabasi-Albert model networks and indicates that the mixed measure of gravitational centrality combining the k − shell value and degree will display the best performance.
Journal ArticleDOI

Measuring mixing patterns in complex networks by Spearman rank correlation coefficient

TL;DR: In this paper, the Spearman rank correlation coefficient is used to measure mixing patterns in complex networks, which is more effective to assess linking patterns of diverse networks, especially for large-size networks.
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Integrating cross-frequency and within band functional networks in resting-state MEG: A multi-layer network approach

TL;DR: Results suggest that the healthy human brain operates at the transition point between these regimes, allowing for integration and segregation between layers, and show that a complete picture of global brain network connectivity requires integration of connectivity patterns across the full frequency spectrum.
Proceedings Article

Large-Scale Community Detection on YouTube for Topic Discovery and Exploration

TL;DR: This work presents a multi-stage algorithm based on local-clustering that is highly scalable, combining a pre- processing stage, a lo- cal clustering stage, and a post-processing stage and applies it to the YouTube video graph to generate named clusters of videos with coherent content.
References
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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

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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

Mark Newman
- 01 Jan 2003 - 
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.
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