Use this if you are using igraph from R

reciprocity {igraph} | R Documentation |

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_{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-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)
```

[Package *igraph* version 1.3.4 Index]