Calculates the reciprocity of a directed graph.

## Usage

`reciprocity(graph, ignore.loops = TRUE, mode = c("default", "ratio"))`

## 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] 0.1980198
```