closure {migraph}

Measures of network closure

Description

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

• network_reciprocity() measures reciprocity in a (usually directed) network.

• node_reciprocity() measures nodes' reciprocity.

• network_transitivity() measures transitivity in a network.

• node_transitivity() measures nodes' transitivity.

• network_equivalency() measures equivalence or reinforcement in a (usually two-mode) network.

• network_congruency() measures congruency across two two-mode networks.

Usage

network_reciprocity(.data, method = "default")

node_reciprocity(.data)

network_transitivity(.data)

node_transitivity(.data)

network_equivalency(.data)

network_congruency(.data, object2)

Arguments

.data

An object of a {manynet}-consistent class:

• matrix (adjacency or incidence) from {base} R

• edgelist, a data frame from {base} R or tibble from {tibble}

• igraph, from the {igraph} package

• network, from the {network} package

• tbl_graph, from the {tidygraph} package

method

For reciprocity, either default or ratio. See ?igraph::reciprocity

object2

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

Details

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.

Equivalency

The network_equivalency() function calculates the Robins and Alexander (2004) clustering coefficient for two-mode networks. Note that for weighted two-mode networks, the result is divided by the average tie weight.

References

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

See Also

Other measures: between_centrality, close_centrality, cohesion(), degree_centrality, eigenv_centrality, features, heterogeneity, hierarchy, holes, net_diffusion, node_diffusion, periods

Examples

network_reciprocity(ison_southern_women)
node_reciprocity(to_unweighted(ison_networkers))
network_transitivity(ison_adolescents)
node_transitivity(ison_adolescents)
network_equivalency(ison_southern_women)