Spectral analysis of dynamically evolving networks with linear preferential attachment

This paper is devoted to study the eigenvalues of the adjacency matrix for the random graph process proposed by Barabasi and Albert in [2]. While many structural characteristics of the Barabasi-Albert (BA) process are well known, analytical results concerning its spectral properties are still an open question. In this paper, we present new results regarding the distribution of eigenvalues of the adjacency matrix associated to this random graph model. In particular, we derive closed-form expressions for the spectral moments of the adjacency matrix and study the evolution of the spectral moments as the network grows. Based on our results, we extract information regarding the evolution of the spectral radius of the adjacency matrix as the network grows.