Weighted cycle-based identification of influential node groups in complex networks

TL;DR

The paper tackles the limitation of node-centric influence measures by introducing Weighted Cycle (WCycle), a centrality that fuses basic cycle structures with edge weights to evaluate node importance. WCycle_i is computed as $\mathrm{WCycle}_i = \frac{1}{|B|} \sum_{c_i \in B} \sum_{e \in c_i} w(e)$, leveraging a cycle basis derived from a spanning tree and weighting interactions to capture both topology and behavior. Empirical evaluation on six real-world weighted networks shows WCycle consistently achieves higher spreading performance, better structural differentiation, and superior cost-effectiveness than five benchmarks, while producing dispersed and unique seed groups. The work demonstrates WCycle as a scalable tool for influence maximization with practical implications for information diffusion and epidemic control, and discusses limitations including zero scores for nodes outside cycles and directions for modeling dynamic feedback with network dynamics.

Abstract

Identifying influential node groups in complex networks is crucial for optimizing information dissemination, epidemic control, and viral marketing. However, traditional centrality-based methods often focus on individual nodes, resulting in overlapping influence zones and diminished collective effectiveness. To overcome these limitations, we propose Weighted Cycle (WCycle), a novel indicator that incorporates basic cycle structures and node behavior traits (edge weights) to comprehensively assess node importance. WCycle effectively identifies spatially dispersed and structurally diverse key node group, thereby reducing influence redundancy and enhancing network-wide propagation. Extensive experiments on six real-world networks demonstrate WCycle's superior performance compared to five benchmark methods across multiple evaluation dimensions, including influence propagation efficiency, structural differentiation, and cost-effectiveness. The findings highlight WCycle's robustness and scalability, establishing it as a promising tool for complex network analysis and practical applications requiring effective influence maximization.

Figures (10)

• Figure 1: Illustration of the WCycle centrality calculation process. (a) An example network $G$. (b) The weighted cycle basis $B$ of $G$. (c) Computation of cumulative edge weights for basic cycles. (d) Calculation of the WCycle centrality for each node.
• Figure 2: The average correlation matrix for the six indices of node importance over six real-world networks.
• Figure 3: Frequency distribution of the same ranking for the six indicators over the real-world networks.
• Figure 4: Top-50 nodes identified by six indicators in Bible networks. (a) WD; (b) WH; (c) WC; (d) WBC; (e)2RW; (f) WCycle
• Figure 5: The variation of the average shortest path length $d_c$ with different values of $c$ for the six indicators across six networks.