Is network clustering detectable in transmission trees?

Networks are often used to model the contact processes that allow pathogens to spread between hosts but it remains unclear which models best describe these networks. One question is whether clustering in networks, roughly defined as the propensity for triangles to form, affects the dynamics of disease spread. We perform a simulation study to see if there is a signal in epidemic transmission trees of clustering. We simulate susceptible-exposed-infectious-removed (SEIR) epidemics (with no re-infection) over networks with fixed degree sequences but different levels of clustering and compare trees from networks with the same degree sequence and different clustering levels. We find that the variation of such trees simulated on networks with different levels of clustering is barely greater than those simulated on networks with the same level of clustering, suggesting that clustering can not be detected in transmission data when re-infection does not occur.