Crossover behavior in a communication network.

Abstract

We address the problem of message transfer in a communication network. The network consists of nodes and links, with the nodes lying on a two-dimensional lattice. Each node has connections with its nearest neighbors, whereas some special nodes, which are designated as hubs, have connections to all the sites within a certain area of influence. The degree distribution for this network is bimodal in nature and has finite variance. The distribution of travel times between two sites situated at a fixed distance on this lattice shows fat-fractal behavior as a function of hub density. If extra assortative connections are now introduced between the hubs so that each hub is connected to two or three other hubs, the distribution crosses over to power-law behavior. Crossover behavior is also seen if end-to-end short cuts are introduced between hubs whose areas of influence overlap, but this is much milder in nature. In yet another information transmission process, namely, the spread of infection on the network with assortative connections, we again observed crossover behavior of another type, viz., from one power law to another for the threshold values of disease transmission probability. Our results are relevant for the understanding of the role of network topology in information spread processes.