A novel measure to identify influential nodes: Return Random Walk Gravity Centrality

To identify influential nodes in real networks, it is essential to note the importance of considering the local and global information in a network. In addition, it is also key to consider the dynamic information. Accordingly, the main aim of this paper is to present a new centrality measure based on return random walk and the effective distance gravity model (CRRWG). This new metric increases the relevance of nodes with a dual role: i) at the local level, they are important in their community or cluster, and ii) at the global level, they give cohesion to the network. It has advantages over other traditional models of centrality since it considers the global and local information, as well as the information of the dynamic interaction between the nodes, as recent studies on community-aware centrality measures demonstrate. Thus, the combination of dynamic and static information makes it easier to detect influential nodes in complex networks. To validate the effectiveness of the proposed centrality measure, it is compared with classic measures, such as Degree, Closeness, Betweenness, PageRank, and other measures based on the gravity model, effective distance and community-aware approaches. The experimental results show the effectiveness of CRRWG through a set of experiments on different types of networks.