Spanning tree based method for a social network analysis

The social network is a useful theoretical construction to study the relation between individuals, groups... The social network analysis is based on graph theory, in order to provide more opportunities to the participants to enlarge or make their social network more efficient. In this paper, we propose a promising approach based on the contraction of nodes that facilitate the enumeration of spanning trees in a social network containing a large number of individuals and interactions such as a social network represented by a closed chain of the same graphs (particular case) and a social network represented by a closed chain of the different types of graphs (general case). As application, we establish recursive functions to evaluate the complexity of a social network representing by a closed chain of the same cycle graphs, the complexity of a social network by multiplying the number of interactions between two individuals and the complexity of a social network by multiplying the number of neighbors between two individuals. Finally, we give some numerical results to show the efficiency of our combinatorial approach.