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在复杂网络中高效识别一组关键传播节点对信息扩散与谣言控制至关重要。对于多传播源节点选取问题，一种有效的方法不仅要考虑种子节点自身的影响力，还要考虑其分散性。传统投票模型算法VoteRank假设一个节点对其每个邻居的投票都是一样的，忽视了拓扑相似性对投票倾向的影响；其次，采用邻域均质化投票衰减策略，难以有效抑制种子节点的传播范围重叠。本文提出一种改进的基于VoteRank的复杂网络多影响力节点识别算法IMVoteRank，通过双重创新提高算法效果：首先，设计基于结构相似性的投票贡献机制，模拟真实世界中选民更倾向于投票给自己关系相近的人，算法认为节点之间拓扑结构越相似邻居节点越有可能将票投给对方，因此将邻居节点的投票贡献拆分为直接连接贡献与拓扑相似性贡献，通过动态权重平衡二者的贡献从而优化投票精准度；其次，引入动态群组隔离策略，在迭代过程中以种子节点为核心检测紧密连接群组，通过抑制群组内节点投票能力并断开其连接，保证种子节点的空间分散性从而有效克服了传播范围重叠问题。在多个真实数据集上基于易感-感染-恢复（ Susceptible-Infected-Recovered） SIR模型的传播实验证明，所提方法能更有效识别网络中多影响力节点。Efficiently identifying multiple influential nodes is crucial for maximizing information diffusion and minimizing rumor spread in complex networks. Selecting multiple influential seed nodes requires consideration of both their individual influence potential and their spatial dispersion within the network topology to avoid overlapping propagation ranges ("rich-club effect"). Traditional VoteRank method suffer from two key limitations: (1) they assume uniform voting contributions from a node to all its neighbors, neglecting the impact of topological similarity (structural homophily) on voting preferences observed in real-world scenarios, and (2) they employ a homogeneous voting attenuation strategy which inadequately suppresses the propagation range overlap among selected seed nodes. To address these shortcomings, this paper proposes IMVoteRank, an improved VoteRank algorithm featuring dual innovations. First, we introduce a Structural Similarity-Driven Voting Contribution Mechanism. Recognizing that voters (nodes) are more likely to support candidates (neighbors) with whom they share stronger topological ties, we decompose a neighbor's voting contribution into two components: a Direct Connection Contribution and a Structural Similarity Contribution (quantified using common neighbors). A dynamic weight parameter θ, adjusted based on the candidate node's degree, balances these components, significantly refining vote allocation accuracy. Second, we devise a Dynamic Group Isolation Strategy. During each iteration, after selecting the highest-scoring seed node vmax, we identify and isolate a tightly-knit group (OG) centered around it. This involves: (i) forming an initial group based on shared neighbor density with vmax, (ii) expanding it by incorporating nodes with more connections inside the group than outside, and (iii) isolating this group by setting the voting capacity (Va) of all its members to zero and virtually removing their connections from the adjacency matrix. Neighbors of vmax not in OG have their Va halved. This strategy proactively enforces spatial dispersion among seeds. Extensive simulations using the Susceptible-Infected-Recovered (SIR) propagation model on nine diverse real-world networks (ECON-WM3, Facebook-SZ, USAir, Celegans, ASOIAF, Dnc-corecipient, ERIS1176, DNC-emails, Facebook-combined) demonstrate the superior performance of IMVoteRank. Compared to seven benchmark methods (Degree, K-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 (β=0.1). Furthermore, seeds selected by IMVoteRank exhibit a consistently larger average shortest path length (Ls) among themselves across most networks, confirming their effective topological dispersion. This combination of high individual influence potential (optimized voting) and low redundancy (group isolation) directly translates to more efficient global information spread, 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 well-grounded approach for identifying multiple influential nodes in complex networks, optimizing the trade-off between influence strength and spatial coverage. Future work will focus on enhancing computational efficiency for large-scale networks and exploring the impact of meso-scale community structures.
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Keywords:
- complex network /
- multiple influential nodes /
- voting model /
- isolation strategy
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