# reciprocity

##### Reciprocity of graphs

Calculates the reciprocity of a directed graph.

- Keywords
- graphs

##### 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: \(\sum_{ij} (A\cdot A')_{ij}\), 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-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`

.

##### Value

A numeric scalar between zero and one.

##### Examples

```
# NOT RUN {
g <- sample_gnp(20, 5/20, directed=TRUE)
reciprocity(g)
# }
```

*Documentation reproduced from package igraph, version 1.2.4.2, License: GPL (>= 2)*