Work

Targeting Influence in a Harmonic Opinion Model

Year: 2025

Type: article

Abstract: . Influence propagation in social networks is a central problem in modern social network analysis, with important societal applications in politics and advertising. A large body of work has focused on cascading models, viral marketing, and finite-horizon diffusion. There is, however, a need for more developed, mathematically principled adversarial models, in which multiple, opposed actors strategically select nodes whose influence will maximally sway the crowd to their point of view. In the present work, we develop and analyze such a model based on harmonic functions and linear diffusion. Our general problem is known to be NP-hard and that the objective function is monotone and submodular; consequently, we can greedily approximate the solution within a constant factor. Introducing and analyzing a convex relaxation, we show that the problem can be approximately solved using smooth optimization methods. We illustrate the effectiveness of our approach on a variety of example networks.

Source: SIAM Journal on Applied Mathematics

DOI: 10.1137/24m1697013

Authors: Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola, Peter J. Mucha, Braxton Osting

Institutions: Brigham Young University, University of North Carolina at Chapel Hill, Dartmouth College, University of Utah

Language: English

Topic: Complex Network Analysis Techniques

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Banff International Research Station for Mathematical Innovation and Discovery, Multidisciplinary University Research Initiative, Army Research Office