Eur. Phys. J. B (2013) 86: 510
https://doi.org/10.1140/epjb/e2013-40920-6

Regular Article

Degree correlation in scale-free graphs

Department of Electrical and Computer Engineering McGill University, H3A 0E9 Montréal, Québec, Canada

^a e-mail: babak.fotouhi@mail.mcgill.ca

Received: 16 October 2013
Received in final form: 12 November 2013
Published online: 18 December 2013

Abstract

We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination preferential attachment growth model, where incoming nodes at each timestep attach to β existing nodes, selected by degree-proportional probabilities. By the conditional degree distribution p(ℓ|k), we mean the degree distribution of nodes that are connected to a node of degree k. By the joint degree distribution p(k,ℓ), we mean the proportion of links that connect nodes of degrees k and ℓ. In addition to this growth model, we consider the shifted-linear preferential growth model and solve for the same quantities, as well as a closed form expression for its steady-state degree distribution.