The measure of reciprocity defines the proporsion of mutual
connections, in a directed graph. It is most commonly defined as
the probability that the opposite counterpart of a directed edge is
also included in the graph. Or in adjacency matrix notation:
$\sum_{ij} (A\cdot A')_{ij}$,
where $A\cdot A'$ is the element-wise product of matrix
$A$ and its transpose. This measure is calculated if the mode
argument is default
.Prior to igraph version 0.6, another measure was implemented,
defined as the probability of mutual connection between a vertex
pair, if we know that there is a (possibly non-mutual) connection
between them. In other words, (unordered) vertex pairs are
classified into three groups: (1) not-connected, (2)
non-reciprocaly connected, (3) reciprocally connected.
The result is the size of group (3), divided by the sum of group
sizes (2)+(3). This measure is calculated if mode
is
ratio
.