Abstract
Social networks are generally sets of individuals or organizations that are connected with one or more links. Usually, social networks are presented by undirected graphs, where the set of vertices V and the set of edges E state the individuals and relation between them respectively. One of the most applicable problems in these networks is the centrality values allocation problem to the vertices and edges. Recently, a new evaluation criterion for the edge centrality so called centrality index of k paths has been proposed which is based on intranet issuing the messages along with random paths composed of k edges. From the other side, it has been vivid the importance of computing the edges centrality through these years. In this study, by referring to message propagation along random paths, a new diffusion model was reached by applying heat diffusion algorithm. This model was based such that the vertex on the way of heat diffusion of most of vertices could be considered as an important node and it could obtain centrality edges by scoring the edges on the heat diffusion path. The proposed technique was compared with centrality drawing method by means of random paths of length $k$ and the results of analyzing the algorithm performance on online large social networks' data set show a remarkable efficacy of the proposed method to the mentioned method. Utilizing known large social networks in evaluation proves the efficiency of the proposed method for analyzing the large scale network.