title: Identifying and characterizing nodes important to community structure using the spectrum of the graph.
abstract: BACKGROUND
  Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and accurate is a very challenging and open problem.
  
  
  RESULTS
  In this manuscript, we introduce a new approach to characterize the node importance to communities. First, a centrality metric is proposed to measure the importance of network nodes to community structure using the spectrum of the adjacency matrix. We define the node importance to communities as the relative change in the eigenvalues of the network adjacency matrix upon their removal. Second, we also propose an index to distinguish two kinds of important nodes in communities, i.e., "community core" and "bridge".
  
  
  CONCLUSIONS
  Our indices are only relied on the spectrum of the graph matrix. They are applied in many artificial networks as well as many real-world networks. This new methodology gives us a basic approach to solve this challenging problem and provides a realistic result.
authors: Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, Beijing, People's Republic of China.
authors: Yang
authors: Y
authors: Wang
authors: Zengru
authors: Z
authors: Di
authors: Ying
authors: Y
authors: Fan
mesh_terms: D000818:Animals; D017173:Caenorhabditis elegans / Q000166:cytology; D003196:Computer Graphics; D003299:Cooperative Behavior; D008962:Models, Theoretical; D009415:Nerve Net; D016571:Neural Networks, Computer