Cross-over behaviour in a communication network

TL;DR

This paper investigates message transfer and infection spread in a 2D lattice network with hubs, revealing how adding connections alters travel time distributions and transmission thresholds, highlighting the impact of network topology.

Contribution

It demonstrates how introducing assortative hub connections causes a crossover from fat fractal to power-law behaviors in travel times and transmission thresholds.

Findings

Travel time distribution shifts from fat fractal to power-law with hub connections.

Infection transmission thresholds exhibit crossover behavior due to network topology.

Adding hub-to-hub links influences the efficiency of information and disease spread.

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 neighbours, 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 behaviour 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 behaviour. Cross-over behaviour 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 cross-over behaviour 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.