Influence Spread in the Heterogeneous Multiplex Linear Threshold Model

TL;DR

This paper extends the linear threshold model to heterogeneous multiplex networks, analyzing how different sensing modalities and agent heterogeneity influence the spread dynamics and steady-state activation levels.

Contribution

It introduces the heterogeneous multiplex LTM, develops algorithms for steady-state analysis, and explores the impact of heterogeneity and sensing modalities on influence spread.

Findings

Heterogeneity affects the balance between sensitivity and robustness in spreading.

Algorithms accurately compute steady-state spread for various initial conditions.

Different sensing modalities significantly influence the spread dynamics.

Abstract

The linear threshold model (LTM) has been used to study spread on single-layer networks defined by one inter-agent sensing modality and agents homogeneous in protocol. We define and analyze the heterogeneous multiplex LTM to study spread on multi-layer networks with each layer representing a different sensing modality and agents heterogeneous in protocol. Protocols are designed to distinguish signals from different layers: an agent becomes active if a sufficient number of its neighbors in each of any $a$ of the $m$ layers is active. We focus on Protocol OR, when $a=1$, and Protocol AND, when $a=m$, which model agents that are most and least readily activated, respectively. We develop theory and algorithms to compute the size of the spread at steady state for any set of initially active agents and to analyze the role of distinguished sensing modalities, network structure, and heterogeneity. We show how heterogeneity manages the tension in spreading dynamics between sensitivity to inputs and robustness to disturbances.