H-core decomposition for directed networks and its application

In this paper, we introduce a directed weighted h-index and a bi-directional h-core decomposition for directed networks, aimed at better identifying important nodes and dense subgraphs. This directed weighted h-index combines the edges’ direction and weight in a directed network, and it can effectively measure the centrality of nodes. To obtain the h-core, we design an iterative algorithm, and we develop a bi-directional h-core decomposition method for partitioning the nodes in a network. As an application, we apply the directed weighted h-index and algorithm to the CEL neural network, USAir network and Social network to identify dense subgraphs and important nodes. Comparative analysis with existing h-type indices demonstrates that our proposed directed weighted h-index is a superior measure of centrality in terms of its ability to identify important nodes and dense subgraphs more accurately.