HEMI: Hyperedge Majority Influence Maximization

TL;DR

This paper extends influence maximization to hypergraphs, proving submodularity for the traditional problem and non-submodularity for a new hyperedge-focused variant, with implications for influence strategies.

Contribution

It introduces a hypergraph influence model, proves submodularity for the classic problem, and reveals non-submodularity in a hyperedge-majority variant.

Findings

Traditional influence maximization remains submodular on hypergraphs.

The hyperedge majority influence problem (HEMI) is non-submodular.

Implications for influence maximization strategies in hypergraph settings.

Abstract

In this work, we consider the problem of influence maximization on a hypergraph. We first extend the Independent Cascade (IC) model to hypergraphs, and prove that the traditional influence maximization problem remains submodular. We then present a variant of the influence maximization problem (HEMI) where one seeks to maximize the number of hyperedges, a majority of whose nodes are influenced. We prove that HEMI is non-submodular under the diffusion model proposed.