Calculates the reciprocity of a directed graph.
reciprocity(graph, ignore.loops = TRUE, mode = c("default", "ratio"))
A numeric scalar between zero and one.
The graph object.
Logical constant, whether to ignore loop edges.
See below.
Tamas Nepusz ntamas@gmail.com and Gabor Csardi csardi.gabor@gmail.com
The measure of reciprocity defines the proportion 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-reciprocally 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
.
g <- sample_gnp(20, 5/20, directed=TRUE)
reciprocity(g)
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