A new network centrality measure: Relative edge importance method

A network is an important tool for modeling data in different domains including physics, chemistry, biology, sociology, engineering, and computer science. Most of the graphs created in these areas are non-symmetric networks where all edges are directional. Furthermore, in such networks, the number of connections between any two nodes (vertices) can be more than one in a given time period. Determination of effective nodes in complex networks is a fundamental and practical issue nowadays. Degree, closeness and betweenness measures are the most important centrality measures commonly used to analyze networks. As a local metric, degree is relatively simple and less effective, although global measures such as the measure of closeness and betweenness can better define effective nodes. However, there are still some disadvantages and limitations of all of these measures. In this study, focusing on the edges is the main feature that distinguishes the proposed Relative Edge Importance Method from the other metrics, while all of the existing centrality measures most commonly used in the literature focus on the nodes in the network. Using this property, each edge is evaluated in terms of the contribution to the centrality of the nodes it connects, and through this contribution, the relative importance of that edge for two nodes is determined. By pairwise comparisons of each edge throughout the entire network, the centrality of nodes are determined A software is developed for comparisons of network centrality measures and a real electronic information exchange system data set known as "Freeman's EIES Data Set" in the literature is also studied and the results obtained demonstrate the effectiveness, applicability and superiority of the proposed method over the other metrics in the literature. Key Words: Network Analysis, Centrality Measures, Central Nodes, Relative Edge Importance