A modified efficiency centrality to identify influential nodes in weighted networks

It is still a crucial issue to identify influential nodes effectively in the study of complex networks. As for the existing efficiency centrality (EffC), it cannot be applied to a weighted network. In this paper, a modified efficiency centrality (EffCm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\mathrm{m}$$\end{document}) is proposed by extending EffC into weighted networks. The proposed measure trades off the node degree and global structure in a weighted network. The influence of both the sum of the average degree of nodes in the whole network and the average distance of the network is taken into account. Numerical examples are used to illustrate the efficiency of the proposed method.