Local Weak Convergence Based Analysis of a New Graph Model

Different random graph models have been proposed as an attempt to model individuals’ behavior. Each of these models proposes a unique way to construct a random graph that covers some properties of the real-world networks. In a recent work [4], the proposed model tries to capture the self-optimizing behavior of the individuals in which the links are made based on the cost/benefit of the connection. In this paper, we analyze the asymptotics of this graph model. We prove the model locally weakly converges [1] to a rooted tree associated with a branching process which we named Erlang Weighted Tree(EWT) and analyze the main properties of the EWT.