Finding Communities by Their Centers

Detecting communities or clusters in a real-world, networked system is of considerable interest in various fields such as sociology, biology, physics, engineering science, and interdisciplinary subjects, with significant efforts devoted in recent years. Many existing algorithms are only designed to identify the composition of communities, but not the structures. Whereas we believe that the local structures of communities can also shed important light on their detection. In this work, we develop a simple yet effective approach that simultaneously uncovers communities and their centers. The idea is based on the premise that organization of a community generally can be viewed as a high-density node surrounded by neighbors with lower densities, and community centers reside far apart from each other. We propose so-called "community centrality" to quantify likelihood of a node being the community centers in such a landscape, and then propagate multiple, significant center likelihood throughout the network via a diffusion process. Our approach is an efficient linear algorithm, and has demonstrated superior performance on a wide spectrum of synthetic and real world networks especially those with sparse connections amongst the community centers.