On irreversible spread of influence in edge-weighted graphs

TL;DR

This paper analyzes how influence spreads irreversibly in weighted graphs, providing bounds and algorithms for activation processes, with applications to real-world social and virtual networks.

Contribution

It introduces a graph theoretical framework for weighted influence spread, extending existing models to weighted networks and deriving extremal bounds and algorithms.

Findings

Derived extremal bounds for influence spread in weighted graphs

Developed algorithms for activation processes in directed and undirected weighted graphs

Presented a real-world example illustrating weighted influence activation

Abstract

Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the networks. In most cases the nature of influence is weighted and the spread of influence depends on the weight of edges. The ordinary formulation and results for dynamic monopolies do not work for such models. In this paper we present a graph theoretical analysis for spread of weighted influence and mention a real world example realizing the activation model with weighted influence. Then we obtain some extremal bounds and algorithmic results for activation process and dynamic monopolies in directed and undirected graphs with weighted edges.