Keywords: clustering coefficient, network, isomorphic graphs, diffusion modeling
Through this study, we would like to better understand how clustering in a network affects diffusion. This will help policy-makers to determine intervention strategies in given communities, after being able to draw conclusions about network vulnerability. First, we examine isomorphic networks for six, eight and ten node regular networks, all with degree three. We believe that this will be able to give insight on larger network structures. By closely examining these smaller networks, we then are able to test our diffusion functions on larger networks. For our six, eight and ten node networks, we simulate 10,000 simulations using multiple diffusion models (SI and SIR). We took the average number of time periods until the network is either saturated or no one else is infected. For these graphs, we use the complete set of isomorphic graphs. We compare the effect of the clustering coefficient and other network characteristics on the diffusion time and impact. For the second part of the project, we explore the impact of this analysis on larger scale networks through diffusion simulations. We will also briefly explore bounds on network clustering estimators.