Linking the network centrality measures closeness and degree

Measuring the importance of nodes in a network with centrality measure is core task any application. There are many measures available and it speculated that encode similar information. We give an explicit non-linear relationship between two most popular node centrality: degree closeness. Based on shortest-path tree approximation, we analytic derivation shows inverse closeness linearly dependent logarithm degree. show our hypothesis works well for range networks produced from stochastic models derived 130 real-world data sets. connect results previous other distance scales such as average distance. Our imply measuring broadly redundant unless used to remove dependence The success suggests can be approximated by spanning trees which all statistically or more steps away their root nodes.