Crucial Triangle Structures for Network Control May Not Be Equally Important for Spreading and Structural Robustness

Identifying important nodes in complex networks is a crucial research area. While numerous metrics exist for evaluating individual node importance, methods for characterizing important sets of nodes are less well-developed and explored. This paper investigates the role of typical node sets-nodes that forming triangle structures, examining their influence on synchronization, information spreading, and network structural robustness. Extensive simulations on synthetic and real-world networks reveal that triangles essential for network synchronization often exhibit weaker spreading capabilities and do not consistently enhance robustness. Furthermore, correlations among different measures for triangle importance show that the synchronization capacity indicator (based on the Fiedler value of Laplacian matrix) has low correlation with traditional centralities, highlighting their inadequacy in capturing the synchronization capacity of triangle structures. These findings underscore the domain-specific nature of measures for triangle importance and the need for a more nuanced understanding of triangle influence.