Reciprocity of graphs
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 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(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-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.
A numeric scalar between zero and one.
Tamas Nepusz ntamas@gmail.com and Gabor Csardi csardi.gabor@gmail.com
g <- sample_gnp(20, 5/20, directed=TRUE) reciprocity(g)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.