These functions offer methods for summarising the closure in configurations in one-, two-, and three-mode networks.

```
network_reciprocity(object, method = "default")
node_reciprocity(object)
network_transitivity(object)
node_transitivity(object)
network_equivalency(object)
network_congruency(object, object2)
```

- object
A one-mode or two-mode matrix, igraph, or tidygraph

- method
For reciprocity, either

`default`

or`ratio`

. See`?igraph::reciprocity`

- object2
Optionally, a second (two-mode) matrix, igraph, or tidygraph

For one-mode networks, shallow wrappers of igraph versions exist via
`network_reciprocity`

and `network_transitivity`

.

For two-mode networks, `network_equivalency`

calculates the proportion of three-paths in the network
that are closed by fourth tie to establish a "shared four-cycle" structure.

For three-mode networks, `network_congruency`

calculates the proportion of three-paths
spanning two two-mode networks that are closed by a fourth tie to establish a
"congruent four-cycle" structure.

`network_reciprocity()`

: Calculate reciprocity in a (usually directed) network`node_reciprocity()`

: Calculate nodes' reciprocity`network_transitivity()`

: Calculate transitivity in a network`node_transitivity()`

: Calculate nodes' transitivity`network_equivalency()`

: Calculate equivalence or reinforcement in a (usually two-mode) network`network_congruency()`

: Calculate congruency across two two-mode networks

Robins, Garry L, and Malcolm Alexander. 2004.
Small worlds among interlocking directors: Network structure and distance in bipartite graphs.
*Computational & Mathematical Organization Theory* 10(1): 69–94.
doi:10.1023/B:CMOT.0000032580.12184.c0
.

Knoke, David, Mario Diani, James Hollway, and Dimitris C Christopoulos. 2021.
*Multimodal Political Networks*.
Cambridge University Press. Cambridge University Press.
doi:10.1017/9781108985000

Other measures:
`centralisation`

,
`centrality`

,
`cohesion()`

,
`diversity`

,
`features`

,
`holes`

,
`tie_centrality`

```
network_reciprocity(ison_southern_women)
#> [1] 1
node_reciprocity(to_unweighted(ison_networkers))
#> `LIN FREEMAN` DOUG W…¹ EV RO…² RICHA…³ PHIPP…⁴ CAROL…⁵ GARY …⁶ RUSS …⁷ JOHN …⁸
#> 1 0.935 0.75 1 0.944 0.286 0.8 1 0.8 0.818
#> # ... with 23 more from this nodeset in the vector.
network_transitivity(ison_adolescents)
#> [1] 0.45
node_transitivity(ison_adolescents)
#> V1 V2 V3 V4 V5 V6 V7 V8
#> 1 NaN 0.333 0.5 1 0.667 0.333 0 NaN
network_equivalency(ison_southern_women)
#> [1] 0.487
```