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

In a connected graph, nodes can be characterised locally (with their degree k) or globally (e.g. with their average length path <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\xi$</EquationSource> </InlineEquation> to other nodes). Here we investigate how <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\xi$</EquationSource> </InlineEquation> depends on k. The numerical algorithm based on the construction of the distance matrix is applied to random graphs and the growing networks: the scale-free ones and the exponential ones. The results are relevant for search strategies in different networks. Copyright Springer-Verlag Berlin/Heidelberg 2004