Thermodynamic approach for community discovering within the complex networks: LiveJournal study

The thermodynamic approach of concentration mapping is used to discover communities in the directional friendship network of LiveJournal users. We show that this Internet-based social network has a power-law region in degree distribution with exponent \gamma = 3.45. It is also a small-world network with high clustering of nodes. To study the community structure we simulate diffusion of a virtual substance immersed in such a network as in a multi-dimensional porous system. By analyzing concentration profiles at intermediate stage of the diffusion process the well-interconnected cliques of users can be identified as nodes with equal values of concentration.