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