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

Original · EN

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.