Community Finding of Scale-Free Network: Algorithm and Evaluation Criterion

Abstract

Recently, topology structures of many social, biological and technological networks have been discovered to display a scale-free property. For a network, a community is a natural division of network nodes into groups in which there are more links between nodes within the groups than to nodes outside of it. Many methods of community finding have been proposed to seek a fast, feasible and reasonable partition algorithm for the whole network nodes. In this chapter, we introduce the topology of the network to evaluate the feasibility and correctness of a community finding algorithm. A relationship between the rough number of communities and the magnitude of the number of hub nodes in the network is given in detail firstly. Then, an algorithm based on Laplace matrix spectral decomposition is proposed and its key technology, threshold selection of Euclidean distance between nodes, is discussed. Based on the scale-free topology of complex network, the evaluation criterion of community finding algorithm including three conditions is obtained. Numerical results show that the algorithm of community finding is an effective one and the evaluation criterion is feasible, fast and easy to operate.

Evaluating links through spectral decomposition

“…Those works do not use spectral measurements. Spectral techniques are often used to express centrality measures of nodes [17] and for community detection [9,18,19], but were also used for the network vulnerability problem [20,21,22]. None of these works used spectral decomposition.…”

“…Those works do not use spectral measurements. Spectral techniques are often used to express centrality measures of nodes [17] and for community detection [9,18,19], but were also used for addressing the network vulnerability problem [20]- [22]. Also in the study of expander graphs [23], spectral techniques are used with respect to resilience against attacks or faults.…”