Shaping Communities out of Triangles

Abstract: Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its importance in many fields such as biology, social networks or network traffic analysis. The metrics proposed to shape communities are generic and follow two approaches: maximizing the internal density of such communities or reducing the connectivity of the internal vertices with those outside the community. However, these metrics take the edges as a set and do not consider the internal layout of the edges in the community. We define a set of properties oriented to social networks that ensure that communities are cohesive, structured and well defined. Then, we propose the Weighted Community Clustering (WCC), which is a community metric based on triangles. We proof that analyzing communities by triangles gives communities that fulfill the listed set of properties, in contrast to previous metrics. Finally, we experimentally show that WCC correctly captures the concept of community in social networks using real and syntethic datasets, and compare statistically some of the most relevant community detection algorithms in the state of the art.