Reciprocity of networks with degree correlations and arbitrary degree sequences.
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.
Zamora-López
Gorka
G
Institute of Physics, University of Potsdam, PF 601553, 14415 Potsdam, Germany.
Zlatić
Vinko
V
Zhou
Changsong
C
Stefancić
Hrvoje
H
Kurths
Jürgen
J