Compactness Preserving Community Computation Via a Network Generative Process

Abstract

The research on network community structure recently has some emerging aspects, such as community hiding for privacy protection in social networks, information transmission between different functional structures in brain networks and community structure’s stability in ecological networks. However, all these attractive topics require us to drill down to the understanding of community structure, among which the key is how to define a reliable community and carry out an effective community computation. The goal of community computation is to find a community structure efficiently, in which nodes in a common community are densely connected, while nodes distributed in different communities are sparsely connected. Here we first define a new metric called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">compactness</i> to measure the significance of a network’s community structure. For a target community, compactness is able to differentiate the impact of other nearby communities to the target community on network’s community significance, meanwhile the size of these communities is also taken into consideration. Then, we extend compactness and develop a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fuzzy compactness</i> via a network generation process to measure a fuzzy community structure’s significance where the impact of other nearby communities to the target community can be differentiated in a differentiable manner. Further, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FCOCD</i> —an effective approach with fuzzy compactness optimization for overlapping community detection in networks. Comprehensive experiments were conducted on several real-world and synthetic networks (including a case study on a bottlenose dolphin ecological network), and the results show that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FCOCD</i> can yield good performance in terms of detection accuracy as well as scalability.