Containing rumors spreading on correlated multiplex networks

TL;DR

This paper develops a theoretical framework for containing rumor spread on multiplex networks by blocking users based on their degree product, showing that targeted strategies can significantly reduce outbreaks especially in heterogeneous and correlated networks.

Contribution

It introduces a novel degree product-based containment strategy and a heterogeneous edge-based compartmental theory for rumor dynamics on multiplex networks.

Findings

Blocking high-degree users reduces rumor size and increases thresholds.

Targeted strategies perform best on networks with high degree heterogeneity and specific inter-layer correlations.

Theoretical predictions align well with simulation results across various network configurations.

Abstract

Rumors flooding on rapidly-growing online social networks has geared much attention from many fronts. Individuals can transmit rumors via numerous channels since they can be active on multiple platforms. However, no systematic theoretical research of rumors containing dynamics on multiplex networks has been conducted yet. In this study, we propose a family of containing strategies based on the degree product $\mathcal{K}$ of each user on the multiplex networks. Then, we develop a heterogeneous edge-based compartmental theory to comprehend the containing dynamics. The simulation results demonstrate that strategies with preference to block users with large $\mathcal{K}$ can significantly reduce the rumor outbreak size and enlarge the threshold. Besides, better performance can be expected on heterogeneous multiplex networks with the increasing of preference intensity and degree heterogeneity. Moreover, take the inter-layer degree correlations $r_s$ into consideration, the strategy performs best on multiplex networks with $r_s=-1$, $r_s=1$ the second, and $r_s=0$ the last. On the contrary, if we prefer to block users with small $\mathcal{K}$ rather than large $\mathcal{K}$, the containing performance will be worse than that of blocking users randomly on most multiplex networks except for uncorrelated multiplex networks with uniform degree distribution. We found that the blocking preferences have no influence on the containing results on uncorrelated multiplex networks with uniform degree distribution. Our theoretical analysis can well predict the rumors containing results and performance differences in all the cases studied. The systematic theoretical research of rumors containing dynamics on multiplex networks in this study will offer inspirations for further investigations on this issue.