Average path length and degree distribution of networks generated by random sequence

Considering that many real networks do not have strict self-similarity property, compared with deterministic evolutionary fractal networks, networks with random sequence structure may be more in accordance with the properties of real networks. In this paper, we generate a hierarchical network by a random sequence based on BRV model. Using the encoding method, we present a way to judge whether two nodes are neighbors and calculate the total path length of the network. We get the degree distribution and limit formula of the average path length of a class of networks, which are obtained by analytical method and iterative calculation.