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We consider SIS contagion processes over networks where, a classicalassumption is that individuals' decisions to adopt a contagion are based ontheir immediate neighbors. However, recent literature shows that someattributes are more correlated between two-hop neighbors, a concept referred toas monophily. This motivates us to explore monophilic contagion, the case wherea contagion (e.g. a product, disease) is adopted by considering two-hopneighbors instead of immediate neighbors (e.g. you ask your friend about thenew iPhone and she recommends you the opinion of one of her friends). We showthat the phenomenon called friendship paradox makes it easier for themonophilic contagion to spread widely. We also consider the case where theunderlying network stochastically evolves in response to the state of thecontagion (e.g. depending on the severity of a flu virus, people restrict theirinteractions with others to avoid getting infected) and show that the dynamicsof such a process can be approximated by a differential equation whosetrajectory satisfies an algebraic constraint restricting it to a manifold. Ourresults shed light on how graph theoretic consequences affect contagions and,provide simple deterministic models to approximate the collective dynamics ofcontagions over stochastic graph processes.

Contagions in Social Networks: Effects of Monophilic Contagion, Friendship Paradox and Reactive Networks