Correlations in connected random graphs

Details Correlations in connected random graphs Correlations in connected random graphs

2007-10-17

arxiv.org/abs/0710.3319v3

P. Bialas and A. K. Oles, Phys. Rev. E 77, 036124 (2008).

Physics

Condensed Matter

Statistical Mechanics

Synchronized with the published version; 11 pages and 11 figures.

Scientific paper

10.1103/PhysRevE.77.036124

We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated and derive analytic formulas for the joint nearest-neighbor degree probability distribution. Using those results we describe the correlations in maximal entropy connected random graphs. We show that connected graphs are disassortative and that correlations are strongly related to the presence of one-degree nodes (leaves). We propose an efficient algorithm for generating connected random graphs. We illustrate our results with several examples.

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