Eur. Phys. J. B 41, 333-336 (2004)
https://doi.org/10.1140/epjb/e2004-00326-3

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

Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland

Corresponding author: ^a malarz@agh.edu.pl

Received: 19 February 2004
Revised: 15 June 2004
Published online: 21 October 2004

Abstract

In a connected graph, nodes can be characterised 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. 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.