# Optimal interlayer structure for promoting spreading of SIS model in two-layer networks

## TL;DR

This paper introduces a strategy to enhance SIS epidemic spreading in multilayer networks by adding a single interlayer edge, using a derived index based on a modified Katz centrality, which outperforms traditional methods.

## Contribution

The study develops a novel index for optimal interlayer edge placement to promote spreading in multilayer networks, validated through both small and large network experiments.

## Key findings

- The proposed index effectively predicts the impact of interlayer edges on spreading.
- Adding a single optimal interlayer edge significantly increases spreading prevalence.
- The method outperforms traditional static strategies like degree and eigenvector centrality.

## Abstract

Real-world systems, ranging from social and biological to infrastructural, can be modeled by multilayer networks. Promoting spreading dynamics in multilayer networks may significantly facilitate electronic advertising and predicting popular scientific publications. In this study, we propose a strategy for promoting the spreading dynamics of the susceptible-infected-susceptible model by adding one interconnecting edge between two isolated networks. By applying a perturbation method to the discrete Markovian chain approach, we derive an index that estimates the spreading prevalence in the interconnected network. The index can be interpreted as a variant of Katz centrality, where the adjacency matrix is replaced by a weighted matrix with weights depending on the dynamical information of the spreading process. Edges that are less infected at one end and its neighborhood but highly infected at the other will have larger weights. We verify the effectiveness of the proposed strategy on small networks by exhaustively examining all latent edges and demonstrate that performance is optimal or near-optimal. For large synthetic and real-world networks, the proposed method always outperforms other static strategies such as connecting nodes with the highest degree or eigenvector centrality.