The comparison of significance of fuzzy community partition across optimization methods

Abstract

The analysis of fuzzy(overlapping) community structure in complex networks is an important problem in data mining of network data sets. However, due to the exist of random factors and error edges in real networks, how to measure the significance of community structure efficiently is a crucial question. In this paper, we present a novel statistical framework comparing the significance of fuzzy community structure across various optimization models. Different from the universal approaches, we calculate the similarity between a given node and its leader and employ the distribution of link tightness to derive the significance score, instead of a direct comparison to a randomized model. Based on the distribution of community tightness, a new p- value form significance measure is proposed for community structure analysis. Specially, the well-known approaches and their corresponding quality functions are unified to a novel general formulation, which facilitate providing a detail comparison across them. To determine the position of leaders and their corresponding followers, an efficient algorithm is proposed based on the spectral theory. Finally, we apply the significance analysis to some famous benchmark networks and the good performance verified the effectiveness and efficiency of our framework.