Unifying information propagation models on networks and influence maximization

TL;DR

This paper introduces a unified model for information propagation on networks that generalizes classical models, formulates influence maximization as a complex optimization problem, and proposes specialized solution methods with demonstrated effectiveness.

Contribution

It unifies existing propagation models, extends them with continuous variables and feedback, and develops new optimization and solution techniques for influence maximization.

Findings

Exact solutions for linear dynamics relate to Katz centrality.

Customized direct search method shows close-to-optimal performance.

Model generalizes classical independent cascade and linear threshold models.

Abstract

Information propagation on networks is a central theme in social, behavioral, and economic sciences, with important theoretical and practical implications, such as the influence maximization problem for viral marketing. Here, we consider a model that unifies the classical independent cascade models and the linear threshold models, and generalise them by considering continuous variables and allowing feedback in the dynamics. We then formulate its influence maximization as a mixed integer nonlinear programming problem and adopt derivative-free methods. Furthermore, we show that the problem can be exactly solved in the special case of linear dynamics, where the selection criterion is closely related to the Katz centrality, and propose a customized direct search method with local convergence. We then demonstrate the close-to-optimal performance of the customized direct search numerically on both synthetic and real networks.