Deterministically delayed pseudofractal networks

On the basis of pseudofractal networks (PFNs), we propose a family of delayed pseudofractal networks (DPFNs) with a special feature that newly added edges delay producing new nodes, differing from the evolution algorithms of PFNs where all existing edges simultaneously generate new nodes. We obtain analytical formulae for degree distribution, clustering coefficient (C) and average path length (APL). We compare DPFNs and PFNs, and show that the exponent of the degree distribution of DPFNs is smaller than that of PFNs, meaning that the heterogeneity of this kind of delayed network is higher. Compared to PFNs, small-world features of DPFNs are more prominent (larger C and smaller APL). We also find that the delay strengthens the scale-free and small-world characteristics of DPFNs. In addition, we calculate and compare the mean first passage time (MFPT) numerically, revealing that the MFPT of DPFNs is shorter. Our study may help with a deeper understanding of various deterministically growing delayed networks. © 2011 IOP Publishing Ltd and SISSA.