Non-Parametric Detection of Network Communities; The Natural Way; A Cascaded Stackelberg Game

Real-World networks have an inherently dynamic structure and are often composed of communities that are constantly changing in membership. Identifying these communities is of great importance when analyzing structural properties of networks. Hence, recent years have witnessed intense research in of solving the challenging problem of detecting such evolving communities. The mainstream approach towards community detection involves optimization of a global partition quality metric (e.g. modularity) over the network [1]. Optimization of this global quality metric is often akin to community assignment by a centralized decision-making model. Another technique, Spectral Clustering [2], involves mapping of original data points in a lower dimensional space, where the clustering properties of a graph are much more evident, and then applying standard clustering techniques such as K-Means or Fuzzy C-means for identifying communities. However, the traditional spectral clustering techniques cannot naturally learn the number of communities in networks [1]. These techniques are based on external community connectivity properties such as graph cuts, and often fail to identify smaller community structures in dense networks. In this article, we propose an algorithm, namely, the Cascaded Stackelberg Community Detection Algorithm (CASCODE) inspired by the Stackelberg Duopoly Game [3]. This algorithm uses the notion of a leader-follower relationship between the nodes to influence the actions of either. The intuition of the algorithm is based on the natural expected internal structure in evolving communities in networks. Thus, the algorithm is able to naturally learn the number of communities in a network in contrast with other techniques such as Spectral Clustering, which require the expected number of communities as an input. Because this Stackelberg Model-based Community Detection algorithm detects communities through their internal structure, we are able to obtain a finer community structure resolution in dense networks. Keywords— Non-Parametric Community Detection; Game Theory; Stackelberg Duopoly Game; Clique; Modularity Optimization; Normalized Mutual Information