Epidemic Analyses on Small Worlds of Tree Topologies of Wireless Sensor Networks

Tree topologies, which construct spatial graphs with large characteristic path lengths and small clustering coefficients, are ubiquitous in deployments of wireless sensor networks. Due to link additions, small world phenomena exist in tree topologies. Epidemics on small worlds of tree topologies are studied, and we calculate the percolation threshold at which the outbreak of the epidemic takes place. Compared with Cayley tree, the small world has a smaller percolation threshold suffering from the epidemic. In the further study, Epidemiological processes are observed by simulations. The infection extends exponentially with time for the existence of shortcuts.