Title: Contagions in Social Networks: Effects of Monophilic Contagion, Friendship Paradox and Reactive Networks,
Abstract: We consider SIS contagion processes over networks where, a classical
assumption is that individuals' decisions to adopt a contagion are based on
their immediate neighbors. However, recent literature shows that some
attributes are more correlated between two-hop neighbors, a concept referred to
as monophily. This motivates us to explore monophilic contagion, the case where
a contagion (e.g. a product, disease) is adopted by considering two-hop
neighbors instead of immediate neighbors (e.g. you ask your friend about the
new iPhone and she recommends you the opinion of one of her friends). We show
that the phenomenon called friendship paradox makes it easier for the
monophilic contagion to spread widely. We also consider the case where the
underlying network stochastically evolves in response to the state of the
contagion (e.g. depending on the severity of a flu virus, people restrict their
interactions with others to avoid getting infected) and show that the dynamics
of such a process can be approximated by a differential equation whose
trajectory satisfies an algebraic constraint restricting it to a manifold. Our
results shed light on how graph theoretic consequences affect contagions and,
provide simple deterministic models to approximate the collective dynamics of
contagions over stochastic graph processes.