R: Reciprocity of graphs

reciprocity {igraph} | R Documentation

## Reciprocity of graphs

### Description

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: sum(i, j, (A.*A')ij) / sum(i, j, Aij), where A.*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`.

### Value

A numeric scalar between zero and one.

### Author(s)

Tamas Nepusz ntamas@gmail.com and Gabor Csardi csardi.gabor@gmail.com

### Examples

    g <- sample_gnp(20, 5/20, directed=TRUE)
    reciprocity(g)

[Package igraph version 1.3.2 Index]