Divisive Algorithm Based on Node Clustering Coefficient for Community Detection

Abstract

This paper studies the relationship between the clustering coefficient of nodes and the community structure of the network. Communities in a network are regarded as node-induced subgraphs of the network in this study. We define the border of a subgraph and the node network density of a node and present a formal definition of community from the view of examining the subgraph borders. Afterward, we analyze the relationship between the change in node clustering coefficients and in node network density and set the rule for identifying inter community edges. Finally, we propose a novel divisive algorithm for community detection by iteratively removing inter community edges. The time complexity of our algorithm is O(Nd <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) , which increases linearly with the network size. Experiments on both synthetic and real-world networks show that introducing node clustering coefficients into the divisive algorithm can greatly improve the time efficiency of the algorithm while guaranteeing the accuracy of community detection.