Computing Ranking and Dynamics in Social Networks

Understanding network structure is key to understanding the behavior of participants in networks. We present a community structure algorithm based on a probabilistic model to detect communities within a network. The algorithm involves the search for the optimal path between nodes that minimizes the expected cost subject to the constraint of a constant relative entropy distributed throughout the network. Within the framework of density-based clustering, a normalized Gauss influence function applied to each node, is used to take into account the impact of the node within its neighborhood. This results in a ranked tree-like network, the community tree, wherein each node is assigned a score that reflects its relative importance within the community. We then use a time-dependent formulation of degree evolution to gain insights into the dynamics and structure changes within the community. The results of simulation are presented and analyzed.