Theoretical relations between basic centrality measures in real-world networks

Abstract

We establish new relationships among several fundamental measures of real-world networks, including the average clustering coefficient, the global clustering coefficient, the average shortest-path length and degree centrality, closeness centrality, betweenness centrality and ksi-centrality. We further develop the theory of $j$-neighborhood centrality, which encompasses degree centrality and ksi-centrality as special cases.