Role of links on the structural properties of different network topologies

Abstract

Complex networks are of major importance in many areas of science. The network property analysis of such networks can help researchers to understand many real-world systems. Different collective phenomena emerge in complex networks, synchronization is one of the most interesting states. The number of links plays a major role in synchronizability. In this paper, the specific properties of the different well-known network topologies are studied, and their synchronizability is compared. Networks with different structures, such as the regular, star, random, small-world, and scale-free networks, are investigated. For each topology, the clustering coefficient, average and variance of the path length, and the eigenvalues of the Laplacian matrix of connections are obtained by varying the number of links. The results show some relations between the network's properties and synchronizability. One of the obtained results is that the type-one networks in a small number of links show better synchronization in the lowest average and variance of path length. However, for a greater number of links, the best synchronizability belongs to the topologies with lower clustering coefficient.