title: Universal scaling of distances in complex networks.
abstract: Universal scaling of distances between vertices of Erdos-Rényi random graphs, scale-free Barabási-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k(i) and k(j) equals to (l(ij)) = A - B log(k(i)k(j)). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree (k)nn calculated for the nearest neighbors and on network clustering coefficients.
authors.affiliation: Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
authors.forename: Janusz A
authors.initials: JA
authors.lastname: Hołyst
authors.forename: Julian
authors.initials: J
authors.lastname: Sienkiewicz
authors.forename: Agata
authors.initials: A
authors.lastname: Fronczak
authors.forename: Piotr
authors.initials: P
authors.lastname: Fronczak
authors.forename: Krzysztof
authors.initials: K
authors.lastname: Suchecki