Today I read a paper titled “Detecting Important Nodes to Community Structure Using the Spectrum of the Graph”
The abstract is:
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
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”
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