The European Physical Journal B

, 86:510

Degree correlation in scale-free graphs

Authors

    • Department of Electrical and Computer EngineeringMcGill University
  • Michael G. Rabbat
    • Department of Electrical and Computer EngineeringMcGill University
Regular Article

DOI: 10.1140/epjb/e2013-40920-6

Cite this article as:
Fotouhi, B. & Rabbat, M.G. Eur. Phys. J. B (2013) 86: 510. doi:10.1140/epjb/e2013-40920-6

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(|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 . 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.

Keywords

Statistical and Nonlinear Physics

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013