Abstract
BackgroundMany 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.Methodology/Principal FindingsIn 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/SignificanceOur 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.
Highlights
Networks, despite their simplicity, represent the interaction structure among components in a wide range of real complex systems, from social relationships among individuals, to interactions of proteins in biological systems, to the interdependence of function calls in large software projects
Exploring network communities is important for the reasons listed below [7]: 1) communities reveal the network at a coarse level, 2) communities provide a new aspect for understanding dynamic processes occurring in the network and 3) communities uncover relationships among the nodes that, they can typically be attributed to the function of the system, are not apparent when inspecting the graph as a whole
We characterize the node importance to community structure using the spectrum of the graph
Summary
Despite their simplicity, represent the interaction structure among components in a wide range of real complex systems, from social relationships among individuals, to interactions of proteins in biological systems, to the interdependence of function calls in large software projects. One would like to find the important nodes to understand the dynamic processes, which could yield an efficient method to immunize modular networks [20]. Such strategies would greatly benefit from a quantitative characterization of the node importance to community structure. In 2006, Newman proposed a community-based metric called ‘‘Community Centrality’’ to measure node importance to communities [8]. His basic idea relies on the modularity function Q. The development of a method to detect nodes important to communities that is both fast and accurate is a very challenging and open problem
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