New centrality measure: ksi-centrality

We introduce new centrality measures, called ksi-centrality and normalized ksi-centrality measure the importance of a node up to the importance of its neighbors. First, we show that normalized ksi-centrality can be rewritten in terms of the Laplacian matrix such that its expression is similar to the local clustering coefficient. After that we introduce average normalized ksi-coefficient and show that for a random Erdos-Renyi graph it is almost the same as average clustering coefficient. It also shows behavior similar to the clustering coefficient for the Windmill and Wheel graphs. Finally, we show that the distributions of ksi centrality and normalized ksi centrality distinguish networks based on real data from artificial networks, including the Watts-Strogatz, Barabasi-Albert and Boccaletti-Hwang-Latora small-world networks. Furthermore, we show the relationship between normalized ksi centrality and the average normalized ksi coefficient and the algebraic connectivity of the graph and the Chegeer number.