Dependence of the average to-node distance on the node degree for random graphs and growing networks

Abstract

In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $ξ$ to other nodes). Here we investigate how $ξ$ depends on $k$. Our earlier algorithm of the construction of the distance matrix is applied to the random graphs. Numerical calculations are performed for the random graphs and the growing networks: the scale-free ones and the exponential ones. The results are relevant for search strategies in different networks.