A novel self-adaptive SIS model based on the mutual interaction between a graph and its line graph

What is it about?

It is well known that in communication between individuals, especially on online platforms, a single message is unlikely to lead to the formation of an established opinion or to the adoption of a given behavior. In processes of this kind, it is often necessary for an individual to receive multiple messages before he or she can adopt a specific behavior. The presence of this reinforcing action in the transmission of information significantly affects its dissemination in social networks, radically altering the effect that network topology has on the extent and speed of message spread itself. Standard contagion and information diffusion models fail to explain such a complex interaction between the dynamic process and the underlying network structure. In the current paper, we propose a new paradigm to design a network-based self-adaptive epidemic model that relies on the interplay between the network and its line graph. We implement this proposal on a susceptible-infected-susceptible (SIS) model in which both nodes and edges are considered susceptible and their respective probabilities of being infected result in a real-time re-modulation of the weights of both the graph and its line graph. The new model can be considered as an appropriate perturbation of the standard SIS model on networks, and the coupling between the graph and its line graph is interpreted as an endogenous reinforcement factor that fosters diffusion through a continuous adjustment of the parameters involved. We study the existence and stability conditions of the endemic and disease-free states for general network topologies, and we introduce, through the asymptotic values in the endemic steady states, a new type of eigenvector centrality where the score of a node depends on both the neighboring nodes and the edges connected to it. We also investigate the properties of this new model on some specific synthetic graphs, such as cycle, regular, and star graphs. Finally, after a series of numerical simulations, we prove its effectiveness in capturing the empirical evidence on behavioral adoption mechanisms acting in online social networks.

Featured Image

Photo by Brooke Cagle on Unsplash

Photo by Brooke Cagle on Unsplash

Why is it important?

Communication on online platforms and social networks requires to be described with appropriate tools to better understand its mechanisms and differences with ordinary face-to-face communication between individuals.

Perspectives