 The useful information from reciprocity is not the value itself, but whether mutual links occur more or less often than expected by chance.Besides, in those networks containing self-linking loops (links starting and ending at the same vertex), the self-linking loops should be excluded when calculating L.

In order to overcome the defects of the above definition, Garlaschelli and Loffredo defined reciprocity as the correlation coefficient between the entries of the adjacency matrix of a directed graph (formula_5 if a link from i to j is there, and formula_6 if not)