Complex networks analysis: centrality measures

The centrality of an edge in a graph is proposed to be the degree of sensitivity of a graph distance function to the weight of the edge under consideration. Many centrality metrics are available in network analysis and are effectively used in the investigation of social network properties. Node position is one of them. In this paper, we propose a novel importance of nodes showing how to locate the most essential nodes in a network and to construct a centrality measure for each node in the network, sort the nodes by centralities, and focus on the top ranked nodes, which are the most relevant in terms of this centrality measure. Our research aims to explain how to identify the most important nodes in networks. A centrality metric should be established for each node in the network, and then the nodes based on their centralities, focusing on the top-ranked nodes, which in light of this importance, might be regarded as the most pertinent measure.