Influence Maximization in Hypergraphs using Multi-Objective Evolutionary Algorithms

TL;DR

This work tackles Influence Maximization on hypergraphs, a problem arising from higher-order interactions that are not well-captured by traditional graphs. It introduces hn-moea, a multi-objective evolutionary algorithm based on NSGA-II, with smart initialization and hypergraph-aware mutation to optimize a seed set $S$ by jointly maximizing the spread $\sigma(S)$ and minimizing the seed size $|S|$. The approach is evaluated on nine real-world hypergraphs across three propagation models (WC, SICP, LT) and compared against five baselines, achieving state-of-the-art hypervolume and greater solution diversity in most settings, particularly for higher-order models. These results demonstrate the method’s robustness and flexibility across propagation dynamics and network domains, marking a significant step toward effective optimization for IM in hypergraphs, with open-source implementation and avenues for future many-objective extensions.

Abstract

The Influence Maximization (IM) problem is a well-known NP-hard combinatorial problem over graphs whose goal is to find the set of nodes in a network that spreads influence at most. Among the various methods for solving the IM problem, evolutionary algorithms (EAs) have been shown to be particularly effective. While the literature on the topic is particularly ample, only a few attempts have been made at solving the IM problem over higher-order networks, namely extensions of standard graphs that can capture interactions that involve more than two nodes. Hypergraphs are a valuable tool for modeling complex interaction networks in various domains; however, they require rethinking of several graph-based problems, including IM. In this work, we propose a multi-objective EA for the IM problem over hypergraphs that leverages smart initialization and hypergraph-aware mutation. While the existing methods rely on greedy or heuristic methods, to our best knowledge this is the first attempt at applying EAs to this problem. Our results over nine real-world datasets and three propagation models, compared with five baseline algorithms, reveal that our method achieves in most cases state-of-the-art results in terms of hypervolume and solution diversity.

Figures (3)

• Figure 1: Graphical representation of the WC, SICP, and LT models. Each colored polygon indicates a hyperedge. The first row represents the hypergraph at time $t_0$, where only the nodes of the seed set (Red) are activated. The second row shows the nodes that are activated at timestep $t_1$ (Orange), while the bottom row depicts the nodes that are activated at timestep $t_2$ (Purple). The second column displays the hyperedges that SICP randomly selects to spread the influence (Green). The third column highlights the activation of hyperedges based on the LT propagation model, assuming a threshold value of $0.5$ (Yellow).
• Figure 2: Results obtained by the compared IM algorithms on the Email-w3c and Bars datasets, using WC, SICP, and LT as influence propagation models.
• Figure 3: Violin plot w.r.t the Pareto Front of hn-moea and baselines. The dotted red lines correspond to the avg. degree of the hypergraph. Red lines inside the violin plots correspond to the avg. degree of the solutions in the Pareto Front.