Graph Neural Networks for Influence Maximization in Social Networks: An Unsupervised Minimum Dominating Set Approach

Influence maximization (IM) is a fundamental problem in complex network analysis, with a wide range of real-world applications. To date, existing approaches to influential node identification in IM have predominantly relied on standard graphs, failing to capture higher-order intrinsic interactions embedded in many real-world systems. Hypergraphs can be employed to better capture higher-order interactions. However, using hypergraphs may lead to an excessively large search space and increased complexity in modeling cascading dynamics, making it challenging to accurately identify influential nodes. Therefore, in this study, we propose a new hypergraph-modeled IM method, based on the Discrete Particle Swarm Optimization algorithm and the threshold model. In the proposed method, a particle (i.e., a candidate solution) represents the selection information of seed nodes, and the fitness function is designed to accurately and efficiently evaluate the influence of seed nodes via a two-layer local influence approximation. We also propose a degree-based initialization strategy to improve the quality of initial solutions and develop rules for updating particles' velocity and position, incorporated with a local search to drive particles toward better solutions. Experimental results demonstrate that the proposed method outperforms baseline methods on both synthetic and real-world hypergraphs. In addition, ablation studies validate the effectiveness of both the local search and the initialization strategies.

Existing learning-based influence maximization frameworks rely heavily on complex neural architectures and continuous optimization over seed representations. We challenge this paradigm with SIMBA, a diffusion-model-agnostic framework pairing a lightweight neural surrogate with direct discrete search. SIMBA introduces three key components: 1) uniformly anchored node embeddings that eliminate initialization noise and encourage learning driven by graph topology and diffusion pattern, 2) a shallow two-layer graph neural network surrogate predicting final infection states, and 3) batched multi-swap simulated annealing that explores combinatorial seed space without gradients or continuous relaxation. By shifting compute from complex representation learning to effective discrete search, SIMBA drastically cuts time-to-solution while achieving superior influence spread and data efficiency. Our code is available at https://github.com/yl489/rethink-IM.

We study a graph bandit setting where the objective of the learner is to detect the most influential node of a graph by requesting as little information from the graph as possible. One of the relevant applications for this setting is marketing in social networks, where the marketer aims at finding and taking advantage of the most influential customers. The existing approaches for bandit problems on graphs require either partial or complete knowledge of the graph. In this paper, we do not assume any knowledge of the graph, but we consider a setting where it can be gradually discovered in a sequential and active way. At each round, the learner chooses a node of the graph and the only information it receives is a stochastic set of the nodes that the chosen node is currently influencing. To address this setting, we propose BARE, a bandit strategy for which we prove a regret guarantee that scales with the detectable dimension, a problem dependent quantity that is often much smaller than the number of nodes.