A deterministic pseudo-fractal networks with time-delay

Abstract

In this paper, inspired by the pseudo-fractal networks (PFN) and the delayed pseudo-fractal networks (DPFN), we present a novel delayed pseudo-fractal networks model, denoted by NDPFN. Different from the generation algorithm of those two networks, every edge of the novel model has a time-delay to generate new nodes after producing one node. We derive exactly the main structural properties of the novel networks: degree distribution, clustering coefficient, diameter and average path length. Analytical results show that the novel networks have small-world effect and scale-free topology. Comparing topological parameters of these three networks, we find that the degree exponent of the novel networks is the largest while the clustering coefficient and the average path length are the smallest. It means that this kind of delay could weaken the heterogeneity and the small-world features of the network. Particularly, the delay effect in the NDPFN is contrary to that in the DPFN, which illustrates the variety of delay method could produce different effects on the network structure. These present findings may be helpful for a deeper understanding of the time-delay influence on the network topology.