Coreness and $h$ -Index for Weighted Networks.

This paper presents a unified framework to generalize the traditional $k$ -core decomposition method for both weighted and unweighted networks. It not only subsumes previous $k$ -core decomposition methods but provides some new ones. With the help of the definition of $n$ -th order h-index, we prove that all $k$ -core indexes can be regarded as some steady state of h-index series with $n$ going to infinity. Furthermore, all $h$ -indexes we obtain in intermediate calculation steps can be used as ranking scores to assess node importance in networks. Finally, we apply the provided new methods as well as two existing ones to four real networks and compare their performances on spreading influences ranking. [ABSTRACT FROM AUTHOR]