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

TL;DR

This paper explores how monophilic contagion, influenced by the friendship paradox and reactive networks, affects the spread of contagions in social networks, providing new models for understanding complex contagion dynamics.

Contribution

It introduces the concept of monophilic contagion considering two-hop neighbors and analyzes the impact of the friendship paradox and reactive network evolution on contagion spread.

Findings

Monophilic contagion facilitates wider spread due to the friendship paradox.

Reactive networks' evolution can be approximated by differential equations on a constrained manifold.

The models provide insights into contagion dynamics over stochastic graph processes.

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.