The Identification of Social Networks by the Least-Square Algorithm

In recent years, the identification of social networks systems has attracted more and more research attention. This paper is based on French-DeGroot model. We assume that there exist some information sources which can influence other agents in the social network but cannot be influenced. Since the model is linear, the least-square algorithm is applied to estimate the parameter matrix of the underlying social network. We prove the strong consistency of the algorithm, i.e. the estimate for the parameter matrix converging almost surely to the true matrix. The algorithm in this paper only need to trace and record the evolution of agents' opinions for certain topics, which enriched the existing identification algorithms for social network matrices.