# reciprocity

0th

Percentile

##### 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.

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

# }

Documentation reproduced from package igraph, version 1.2.2, License: GPL (>= 2)

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