title: Degree-dependent intervertex separation in complex networks.
abstract: We study the mean length (l)(k) of the shortest paths between a vertex of degree k and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law correction to a logarithmic dependence, (l)(k) = A ln[N/k((gamma-1)/2)]-Ck(gamma-1)/N+ in a wide range of network sizes. Here N is the number of vertices in the network, gamma is the degree distribution exponent, and the coefficients A and C depend on a network. We compare this law with a corresponding (l)(k) dependence obtained for random scale-free networks growing through the preferential attachment mechanism. In stochastic and deterministic growing trees with an exponential degree distribution, we observe a linear dependence on degree, (l)(k)approximately A ln N-Ck. We compare our findings for growing networks with those for uncorrelated graphs.
authors.affiliation: Departamento de Física da Universidade de Aveiro, Portugal. sdorogov@fis.ua.pt
authors.forename: S N
authors.initials: SN
authors.lastname: Dorogovtsev
authors.forename: J F F
authors.initials: JF
authors.lastname: Mendes
authors.forename: J G
authors.initials: JG
authors.lastname: Oliveira