reciprocity: 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.

Value

A numeric scalar between zero and one.

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: $\sum_{i j} (A \cdot A^{'})_{i j}$ , 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.

Examples

Run this code

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

# }