Annals of Combinatorics

, Volume 6, Issue 2, pp 125–145

Connected Components in Random Graphs with Given Expected Degree Sequences

  • Fan Chung
  • Linyuan Lu

DOI: 10.1007/PL00012580

Cite this article as:
Chung, F. & Lu, L. Annals of Combinatorics (2002) 6: 125. doi:10.1007/PL00012580


We consider a family of random graphs with a given expected degree sequence. Each edge is chosen independently with probability proportional to the product of the expected degrees of its endpoints. We examine the distribution of the sizes/volumes of the connected components which turns out depending primarily on the average degree d and the second-order average degree d~. Here d~ denotes the weighted average of squares of the expected degrees. For example, we prove that the giant component exists if the expected average degree d is at least 1, and there is no giant component if the expected second-order average degree d~ is at most 1. Examples are given to illustrate that both bounds are best possible.

Keywords: random graphs, connected components, expected degree sequence, power law, power law graphs 

Copyright information

© Birkhäuser Verlag Basel, 2002

Authors and Affiliations

  • Fan Chung
    • 1
  • Linyuan Lu
    • 1
  1. 1.Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA, e-mail:; llu@euclid.ucsd.eduUS

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