Reciprocity in network

In network science, reciprocity is a measure of the likelihood of vertices in a directed network to be mutually linked. Like the clustering coefficient, scale-free degree distribution, or community structure, reciprocity is a quantitative measure used to study complex networks.

A traditional way to define the reciprocity r is using the ratio of the number of links pointing in both directions ${\displaystyle L^{<->}}$ to the total number of links L ${\displaystyle r={\frac {L^{<->}}{L}}}$

With this definition, ${\displaystyle r=1}$ is for a purely bidirectional network while ${\displaystyle r=0}$ for a purely unidirectional one. Real networks have an intermediate value between 0 and 1.

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