Using Degree Correlation to Amplify Contagion in Networks

Networks facilitate the spread of contagious phenomena, wherein the behavior of an individual node is affected by the interactions with its neighbors. We investigate how the structure of a network affects the outcome of a contagious process. By accounting for the joint degree-degree distribution of the network within a message passing model, we can characterize how degree assortativity affects both the onset of global outbreaks in a network and the size of outbreaks triggered by individual nodes. We find that the critical point defining the onset of global outbreaks has a non-monotonic relationship with degree-degree correlation. In addition, the choice of nodes to seed largest outbreak is also largely affected by the degree-degree correlation. Specifically, when this correlation is negative, the largest degree nodes, hubs, trigger biggest outbreaks. However, when assortativity is positive, then contrary to traditional wisdom, low degree nodes are more likely to generate largest outbreaks. Our work suggests that it may be possible to tailor the spread of contagions by manipulating higher order structure of networks.