Accounting for topology in spreading contagion in non-complete networks

We are interested in investigating the spread of contagion in a network, G, which describes the interactions between the agents in the system. The topology of this network is often neglected due to the assumption that each agent is connected with every other agents; this means that the network topology is a complete graph. While this allows for certain simplifications in the analysis, we fail to gain insight on the diffusion process for non-complete network topology. In this paper, we offer a continuous-time Markov chain infection model that explicitly accounts for the network topology, be it complete or non-complete. Although we characterize our process using parameters from epidemiology, our approach can be applied to many application domains. We will show how to generate the infinitesimal matrix that describes the evolution of this process for any topology. We also develop a general methodology to solve for the equilibrium distribution by considering symmetries in G. Our results show that network topologies have dramatic effect on the spread of infections.