A centrality measure in dense networks based on two-way random walk betweenness

Many scholars have tried to address the identification of critical nodes in complex networks from different perspectives. For instance, by means of the betweenness methods based on shortest paths and random walk, it is possible to measure the global importance of a node as an intermediate node. All these metrics have the common characteristic of not taking into account the density of the clusters. In this paper, we apply an analysis of network centrality, from a perspective oriented to ranking nodes, reinforcing dense communities using evaluating graphs using a two-trip transition probability matrix. We define a new centrality measure based on random walk betweenness. We study and analyse the new metric as a betweenness centrality measure with common characteristics with Pagerank, presenting through its practical implementation in some examples based on synthetic, and testing with well-known real-world networks. This method helps to increase the ranking of nodes belonging to dense clusters with a higher average degree than the remaining clusters, and it can detect the weakness of a network comparing it with the classical betweenness centrality measure.