Disruptive coefficient and 2-step disruptive coefficient: Novel measures for identifying vital nodes in complex networks

The identification and ranking of vital nodes in complex networks have been a critical issue for a long time. In this paper, we present an extension of existing disruptive metrics and introduce new ones, namely the disruptive coefficient (D) and 2-step disruptive coefficient (2-step D), as innovative tools for identifying critical nodes in complex networks. Our approach emphasizes the importance of disruptiveness in characterizing nodes within the network and detecting their criticality. Our new measures take into account both prior and posterior information of the focal nodes, by evaluating their ability to disrupt the previous network paradigm, setting them apart from traditional measures. We conduct an empirical analysis of four real-world networks to compare the rankings or identification of nodes using D and 2stepD with those obtained from four renowned benchmark measures, namely, degree, h-index, PageRank, and the CD index. Our analysis reveals significant differences between the nodes identified by D and 2stepD and those identified by the benchmark measures. We also examine the correlation coefficient and efficiency of the metrics and find that D and 2stepD have significant correlations with the CD index, but have weak correlations with the benchmark measures. Furthermore, we show that D and 2stepD outperform CD index and random ways in intentional attacks. We find power law distributions for D, 2stepD, and CD, indicating a small number of highly disruptive nodes and a large number of less disruptive nodes in the networks. Our results suggest that D and 2stepD are capable of providing valuable and distinct insights for identifying critical nodes in complex networks.