An Efficient homophilic model and Algorithms for Community Detection using Nash Dynamics

The problem of community detection is important as it helps in understanding the spread of information in a social network. All real complex networks have an inbuilt structure which captures and characterizes the network dynamics between its nodes. Linkages are more likely to form between similar nodes, leading to the formation of some community structure which characterizes the network dynamic. The more friends they have in common, the more the influence that each person can exercise on the other. We propose a disjoint community detection algorithm, $\mathit{\text{NashDisjoint}}$ that detects disjoint communities in any given network. We evaluate the algorithm $\mathit{\text{NashDisjoint}}$ on the standard LFR benchmarks, and we find that our algorithm works at least as good as that of the state of the art algorithms for the mixing factors less than 0.55 in all the cases. We propose an overlapping community detection algorithm $\mathit{\text{NashOverlap}}$ to detect the overlapping communities in any given network. We evaluate the algorithm $\mathit{\text{NashOverlap}}$ on the standard LFR benchmarks and we find that our algorithm works far better than the state of the art algorithms in around 152 different scenarios, generated by varying the number of nodes, mixing factor and overlapping membership. We run our algorithm $\mathit{\text{NashOverlap}}$ on DBLP dataset to detect the large collaboration groups and found very interesting results. Also, these results of our algorithm on DBLP collaboration network are compared with the results of the $\mathit{\text{COPRA}}$ algorithm and $\mathit{\text{OSLOM}}$.