CycRank: a universal optimization framework for vital nodes identification in complex networks

Abstract Identifying influential nodes to maximize the spread of information within networks is a vital combinatorial optimization problem with extensive practical applications. Unlike proposing a specific node ranking method to identify vital nodes, this study introduces CycRank, a universal framework to optimize the strategies for selecting vital nodes in existing methods by leveraging cycle structures. The experimental results demonstrate that, compared to directly selecting top-k nodes from centrality rankings and state-of-the-art optimization frameworks, the influencers identified by CycRank increase the average dissemination range by up to 17%. Additionally, regardless of the centrality measures or network types, these influencers exhibit lower degree and greater average distances, effectively striking a delicate trade-off between their influence, dispersion, and hub properties. Our study not only paves the way for novel strategies in vital nodes identification but also underscores the unique potential of underappreciated cycle structures.