Reciprocity of Networks with Degree Correlations and Arbitrary Degree Sequences

Details Reciprocity of Networks with Degree Correlations and Arbitrary Degree Sequences Reciprocity of Networks with Degree Correlations and Arbitrary Degree Sequences

2007-06-22

arxiv.org/abs/0706.3372v2

Physics

Condensed Matter

Statistical Mechanics

8 pages, 3 figures, added a new table and a new figure, accepted for publication in Phys.Rev.E

Scientific paper

10.1103/PhysRevE.77.016106

Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity $r$ has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with an arbitrary degree sequence and a broad class of degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to $r$ is revealed. Numerical experiments using novel network randomization methods show very good agreement to our analytical estimations.

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