Simplifying Weighted Heterogeneous Networks by Extracting h-Structure via s-Degree

In this study, we developed a method to extract the core structure of weighted heterogeneous networks by transforming the heterogeneous networks into homogeneous networks. Using the standardized z-score, we define the s-degree by summing all the z-scores of adjacent edges into base-nodes for a weighted heterogeneous network. Then, we rank all the s-degrees in decreasing order to obtain the core structure via the h-index of a base-homogeneous-network. After reducing all adjacent edges between the attribute nodes and base-nodes to the core structure, we obtain the heterogeneous core structure of the weighted network, which is called the h-structure. We find that the h-structure in a heterogeneous network contains less than 1% nodes and edges, which results in the construction of a highly effective simplification of a weighted heterogeneous network. Two practical cases, the citation network and the co-purchase network, were examined in this study.