A Novel Self-Adaptive SIS Model Based on the Mutual Interaction between a Graph and its Line Graph

TL;DR

This paper introduces a self-adaptive epidemic model based on the interaction between a network and its line graph, allowing real-time parameter adjustments and revealing new centrality measures, with applications to various graph types.

Contribution

It presents a novel self-adaptive SIS model leveraging network-line graph interplay, including stability analysis and a new eigenvector centrality measure.

Findings

Model captures real-time epidemic dynamics effectively.

Introduces a new centrality measure based on network and edge interactions.

Demonstrates applicability on synthetic graphs like cycles, regular, and star graphs.

Abstract

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 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 Susceptible-Infected-Susceptible model, and the coupling between the graph and its line graph is interpreted as a 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. Moreover, 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, we perform a series of numerical simulations and prove their effectiveness in capturing some empirical evidence on behavioral adoption mechanisms.