Extracting Analyzing and Visualizing Triangle K-Core Motifs within Networks

Cliques are topological structures that usually provide important information for understanding the structure of a graph or network. However, detecting and extracting cliques efficiently is known to be very hard. In this paper, we define and introduce the notion of a Triangle K-Core, a simpler topological structure and one that is more tractable and can moreover be used as a proxy for extracting clique-like structure from large graphs. Based on this definition we first develop a localized algorithm for extracting Triangle K-Cores from large graphs. Subsequently we extend the simple algorithm to accommodate dynamic graphs (where edges can be dynamically added and deleted). Finally, we extend the basic definition to support various template pattern cliques with applications to network visualization and event detection on graphs and networks. Our empirical results reveal the efficiency and efficacy of the proposed methods on many real world datasets.