# 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 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:
$\sum_{ij} (A\cdot A')_{ij}$,
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.

##### concept

Reciprocity

##### Examples

```
g <- random.graph.game(20, 5/20, directed=TRUE)
reciprocity(g)
```

*Documentation reproduced from package igraph, version 0.6.5-2, License: GPL (>= 2)*