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Abstract Researchers of complex networks have always sought to discover hidden information in networks. Centrality measures are quantitative data used to display information that cannot be seen at first glance in the network and indicate the importance of a node or edge. Due to the limitation of processing power and the complexity of real-world problems, processes are moving towards localization. This paper proposes a new method to represent edge importance based on the number of edges involved in 3 and 4-cycles. Also, an algorithm with O (n* ( (m/n) ²) ) time complexity is presented to find these cycles. The number assigned to each edge indicates how many times it appears in short cycles. The delta coefficient is defined to increase the effect of 3-cycles. This measure can be calculated for nodes by summing the centrality of edges and dividing by two. Using the willingness centrality measure in issues such as community detection and its acceptable result shows the practicality of the proposed method.
Kivi et al. (Tue,) studied this question.