“…Hence, the identification of influential nodes in complex networks play an important role [11] in both structural and functional aspects [12,13], and is an important area of research [14]. The identification of influential nodes can be applied across various fields [15] such as disease [16], network system [17], biology [18], social system [19,20,4], time series [21], information propagation [22] and Parrondo's paradox [23,24,25,26,27]. Besides, identifying the vital nodes [28] can allow us to discover and address real-world problems [29,30] such as transportation hubs identifying, influence maximizing, rumor controlling [31], disease controlling [32], advertising and community finding [33,34].…”