Complex Networks Exploration With Triangles.

Triangles are an essential structure in complex network analysis representing metrics such as clustering coefficient and transitivity. In this work, we employ the recently introduced “Triangle Centrality” in exploring cohesive sub-networks of interest within the maximum $k -$core of complex networks. Motivated by the recent interest in higher-order connectivity patterns to understand fundamental structures that control behaviour of complex systems, we employ triangles as “higher-order” structural units in complex systems. Each triangle in the network is attributed with a numeric score, the so called $k -$count, to indicate its “influence” calculated based on the number of other triangles it is associated with. We demonstrate our proposed method to perform visual exploration of cohesive sub-networks of interest on a well-studied benchmark social network “Lusseau’s Dolphin Social Network”.