title: Linear relation on the correlation in complex networks.
abstract: Correlation in complex networks follows a linear relation between the degree of a node and the total degrees of its neighbors for six different classes of real networks. This general linear relation is an extension of the Aboav-Weaire law in two-dimensional cellular structures and provides a simple and different perspective on the correlation in complex networks, which is complementary to an existing description using Pearson correlation coefficients and a power law fit. Analytical expression for this linear relation for three standard models of complex networks: the Erdos-Renyi, Watts-Strogatz, and Barabasi-Albert networks is provided. The slope and intercept of this linear relation are described by a single parameter a together with the first and second moment of the degree distribution of the network. The assortivity of the network can be related to the sign of the intercept.
authors.affiliation: Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China.
authors.forename: C W
authors.initials: CW
authors.lastname: Ma
authors.forename: K Y
authors.initials: KY
authors.lastname: Szeto