Contagion in Graphons

Abstract

We consider a threshold contagion process over networks sampled from a graphon, which we interpret as a stochastic network formation model. We investigate whether the contagion outcome in the sampled networks can be predicted by only exploiting information about the graphon. To do so, we formally define a threshold contagion process on a graphon. Our main result shows that contagion in large but finite sampled networks is well approximated by contagion in a graphon. We illustrate our results by providing analytical characterizations for the extent of contagion and for optimal seeding policies in graphons with finite and with infinite agent types.

Keywords: Graphons, Networks, Contagion, Network Games, Optimal Seeding, Interventions