Reciprocity of networks with degree correlations and arbitrary degree sequences
Gorka Zamora-López1, Vinko Zlatić, Changsong Zhou
1Institute of Physics, University of Potsdam, PF 601553, 14415 Potsdam, Germany.
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 arbitrary input and output degree sequences and given 2-node 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 network randomization methods show very good agreement to our analytical estimations.
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