measure_closure function

Measures of network closure

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

• net_reciprocity() measures reciprocity in a (usually directed) network.
• node_reciprocity() measures nodes' reciprocity.
• net_transitivity() measures transitivity in a network.
• node_transitivity() measures nodes' transitivity.
• net_equivalency() measures equivalence or reinforcement in a (usually two-mode) network.
• net_congruency() measures congruency across two two-mode networks.

net_reciprocity(.data, method = "default")

node_reciprocity(.data)

net_transitivity(.data)

node_transitivity(.data)

net_equivalency(.data)

node_equivalency(.data)

net_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 net_reciprocity and net_transitivity.

For two-mode networks, net_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, net_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 net_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.

Examples

net_reciprocity(ison_southern_women)
node_reciprocity(to_unweighted(ison_networkers))
net_transitivity(ison_adolescents)
node_transitivity(ison_adolescents)
net_equivalency(ison_southern_women)
node_equivalency(ison_southern_women)

References

On equivalency or four-cycles

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. tools:::Rd_expr_doi("10.1023/B:CMOT.0000032580.12184.c0") .

On congruency

Knoke, David, Mario Diani, James Hollway, and Dimitris C Christopoulos. 2021. Multimodal Political Networks. Cambridge University Press. Cambridge University Press. tools:::Rd_expr_doi("10.1017/9781108985000")

See Also

Other measures: measure_attributes, measure_central_between, measure_central_close, measure_central_degree, measure_central_eigen, measure_cohesion, measure_diffusion_infection, measure_diffusion_net, measure_diffusion_node, measure_features, measure_heterogeneity, measure_hierarchy, measure_holes, measure_periods, measure_properties, member_diffusion