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.
|Number of pages||8|
|Journal||Physical Review. E, Statistical, Nonlinear and Soft Matter Physics|
|Publication status||Published - 16 Jan 2008|