Calculates the reciprocity of a directed graph.
The graph object.
Logical constant, whether to ignore loop edges.
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(i, j,
(A.*A')ij) / sum(i, j, Aij), where A.*A' is the
element-wise product of matrix A and its transpose. This measure is
calculated if the
mode argument is
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
A numeric scalar between zero and one.