Structural and spectral properties of the generalized corona networks

Abstract

In this paper, we present a growing complex network model, namely, the generalized corona network (GCN) which is built on a base network and a sequence of networks by using corona product of graphs. This construction generalizes several existing complex network models. We study the structural properties of the special classes of generalized corona networks and show that these networks have small diameter, the cumulative betweenness distribution follows a power-law distribution, the degree distribution decay exponentially, small average path length with the network order, high clustering coefficient and small-world behavior. Further, we obtain the spectra of the adjacency matrix and the signless Laplacian matrix of GCN when the constituting networks are regular. Also, we obtain the Laplacian spectra for all generalized corona networks. In addition, explicitly give eigenvector corresponding to the adjacency and Laplacian eigenvalues. Finally, we derive the spectral radius and the algebraic connectivity of GCN.