Criterions for locally dense subgraphs

Abstract: Community detection is one of the most investigated problems in the field of complex networks. Although several methods were proposed, there is still no precise definition of communities. As a step towards a definition, I highlight two necessary properties of communities, separation and internal cohesion, the latter being a new concept. I propose a local method of community detection based on two-dimensional local optimization, which I tested on common benchmarks and on the word association database.