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arXiv · 0706.3372

Reciprocity of Networks with Degree Correlations and Arbitrary Degree Sequences

Gorka Zamora--López·Vinko Zlatić·Changsong Zhou·Hrvoje Štefančić·Jürgen Kurths
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Abstract

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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Gorka Zamora--López, Vinko Zlatić, Changsong Zhou, Hrvoje Štefančić, Jürgen Kurths. 2007-11-14. Reciprocity of Networks with Degree Correlations and Arbitrary Degree Sequences. https://doi.org/10.1103/physreve.77.016106

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