Calculates the reciprocity of a directed graph.
Usage
reciprocity(graph, ignore.loops = TRUE, mode = c("default", "ratio"))Arguments
- graph
The graph object.
- ignore.loops
Logical constant, whether to ignore loop edges.
- mode
See below.
Details
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:
\(1 - \left(\sum_{i,j} |A_{ij} - A_{ji}|\right) / \left(2\sum_{i,j} A_{ij}\right)\).
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.
See also
Other structural.properties:
bfs(),
component_distribution(),
connect(),
constraint(),
coreness(),
degree(),
dfs(),
distance_table(),
edge_density(),
feedback_arc_set(),
girth(),
is_acyclic(),
is_dag(),
is_matching(),
k_shortest_paths(),
knn(),
subcomponent(),
subgraph(),
topo_sort(),
transitivity(),
unfold_tree(),
which_multiple(),
which_mutual()
Author
Tamas Nepusz ntamas@gmail.com and Gabor Csardi csardi.gabor@gmail.com
Examples
g <- sample_gnp(20, 5 / 20, directed = TRUE)
reciprocity(g)
#> [1] 0.2247191