Finding Statistically Significant Communities in Networks with Weighted Label Propagation

Various networks exist in the world today including biological, social, information, and communication networks with the Internet as the largest network of all. One salient structural feature of these networks is the formation of groups or communities of vertices that tend to be more connected to each other within the same group than to those outside. Therefore, the detection of these communities is a topic of great interest and importance in many applications and different algorithms including label propagation have been developed for such purpose. Speaker-listener label propagation algorithm (SLPA) enjoys almost linear time complexity, so desirable in dealing with large networks. As an extension of SLPA, this study presented a novel weighted label propagation algorithm (WLPA), which was tested on four real world social networks with known community structures including the famous Zachary's karate club network. Wilcoxon tests on the communities found in the karate club network by WLPA demonstrated an improved statistical significance over SLPA. With the help of Wilcoxon tests again, we were able to determine the best possible formation of two communities in this network relative to the ground truth partition, which could be used as a new benchmark for assessing community detection algorithms. Finally WLPA predicted better communities than SLPA in two of the three additional real social networks, when compared to the ground truth.