Finding community structure in networks using the eigenvectors of matrices
Reads0
Chats0
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.read more
Citations
More filters
Journal ArticleDOI
How to Identify the Most Powerful Node in Complex Networks? A Novel Entropy Centrality Approach
Tong Qiao,Wei Shan,Chang Zhou +2 more
TL;DR: A novel mechanism is proposed to quantitatively measure centrality using the re-defined entropy centrality model, which is based on decompositions of a graph into subgraphs and analysis on the entropy of neighbor nodes.
Journal ArticleDOI
Properties of latent variable network models
TL;DR: The Gaussian latent position model with random effects is introduced, and it is shown that it can represent the heavy-tailed degree distributions, positive asymptotic clustering coefficients, and small-world behaviors that often occur in observed social networks.
Journal ArticleDOI
Complex networks, community structure, and catchment classification in a large-scale river basin
TL;DR: In this article, the authors introduced the concepts of complex networks, especially community structure, to classify catchments in large-scale river basins, and employed six community structure methods: edge betweenness, greedy algorithm, multilevel modularity optimization, leading eigenvector, label propagation, and walktrap.
Proceedings ArticleDOI
DDGK: Learning Graph Representations for Deep Divergence Graph Kernels
TL;DR: The experimental results show that Deep Divergence Graph Kernels can learn an unsupervised alignment between graphs, and that the learned representations achieve competitive results when used as features on a number of challenging graph classification tasks.
Proceedings ArticleDOI
Active learning for node classification in assortative and disassortative networks
TL;DR: This paper proposes a batch mode active learning method which uses information-theoretic techniques and random walk to select which nodes to label and significantly outperforms existing batch active learning methods.
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.