IMVoteRank: Identifying multiple influential nodes in complex networks based on an improved voting model

Efficiently identifying multiple influential nodes is crucial for maximizing information diffusion and minimizing rumor spread in complex networks. Selecting multiple influential seed nodes requires to take into consider both their individual influence potential and their spatial dispersion within the network topology to avoid overlapping propagation ranges (“rich-club effect”). Traditional VoteRank method has two key limitations: 1) the voting contributions from a node is assumed to be consistent to all its neighbors, and the influence of topological similarity (structural homophily) on the voting preferences observed in real-world scenarios is neglected, and 2) a homogeneous voting attenuation strategy is used, which is insufficient to suppress propagation range overlap between selected seed nodes. To address these shortcomings, IMVoteRank, an improved VoteRank algorithm featuring dual innovations, is proposed in this work. First, a structural similarity-driven voting contribution mechanism is introduced. By recognizing that voters (nodes) are more likely to support candidates (neighbors) with stronger topological relationships with them, the voting contribution of neighbors is decomposed into two parts: direct connection contribution and a structural similarity contribution (quantified using common neighbors). A dynamic weight parameter <i>θ</i>, adjusted based on the candidate node’s degree, balances these components, significantly refining vote allocation accuracy. Second, we devise a dynamic group isolation trategy. In each iteration, after selecting the highest-scoring seed node <i>v</i><sub>max</sub>, a tightly-knit group (OG) centered around it is identified and isolated. This involves: 1) forming an initial group based on neighbor density shared with <i>v</i><sub>max</sub>, 2) expanding it by merging nodes with more connections inside the group than outside, and 3) isolating this group by setting the voting capacity (<i>V</i><sub><i>a</i></sub>) of all its members to zero and virtually removing their connections from the adjacency matrix. Neighbors of <i>v</i><sub>max</sub> not in OG have their <i>V</i><sub><i>a</i></sub> values reduced by half. This strategy actively forces spatial dispersion among seeds. Extensive simulations using the susceptible-infected-recovered (SIR) propagation model on nine different real-world networks (ECON-WM3, Facebook-SZ, USAir, Celegans, ASOIAF, Dnc-corecipient, ERIS1176, DNC-emails, Facebook-combined) demonstrate the superior performance of IMVoteRank. Compared with seven benchmark methods (Degree, <i>k</i>-shell, VoteRank, NCVoteRank, VoteRank++, AIGCrank, EWV), IMVoteRank consistently achieves significantly larger final propagation coverage (infected scale) for a given number of seed nodes and transmission probability (<i>β</i> = 0.1). Furthermore, seeds selected by IMVoteRank exhibit a consistently larger average shortest path length (<i>L</i><sub>s</sub>) in most networks, which proves their effective topological dispersion. This combination of high personal influence potential (optimized voting) and low redundancy (group isolation) directly translates to more effective global information dissemination, as evidenced by the SIR results. Tests on LFR benchmark networks further validate these advantages, particularly at transmission rates above the epidemic threshold. IMVoteRank effectively overcomes the limitations of traditional voting models by integrating structural similarity into the voting process and employing dynamic group isolation to ensure seed dispersion. It provides a highly effective and physically reliable method for identifying multiple influential nodes in complex networks and optimizing the trade-off between influence strength and spatial coverage. Future work will focus on improving the computational efficiency of large-scale networks and exploring the influence of meso-scale community structures.