These functions offer methods for summarising the closure in configurations in one-, two-, and three-mode networks:
net_by_reciprocity() measures reciprocity in a (usually directed) network.
net_by_transitivity() measures transitivity in a network.
net_by_cyclicality() measures cyclicality in a (necessarily directed) network.
net_by_equivalency() measures equivalence or reinforcement
in a (usually two-mode) network.
net_by_congruency() measures congruency across two two-mode networks.
net_by_reciprocity(.data, variant = c("default", "ratio"), method = NULL)
net_by_transitivity(.data)
net_by_cyclicality(.data)
net_by_equivalency(.data)
net_by_congruency(.data, object2)A network object of class stocnet, igraph, tbl_graph, network, or similar.
Internally any of these will be coerced to an efficient implementation.
For more information on possible coercions, see e.g. manynet::as_stocnet().
Character string naming which variant of the measure to compute, where more than one definition of the same quantity is in use. The variant chosen is reported when the result is printed.
Deprecated. The former spelling of variant.
Still accepted, but warns; please use variant instead.
Optionally, a second (two-mode) matrix, igraph, or tidygraph
A network_measure numeric score.
The object also carries the measure it computed, the range its values
can fall within, and whether and how those values were normalized.
These are shown as a one-line header when the object is printed.
Where a measure offers a choice between several ways of counting the
same thing, it also carries the variant it used.
All can be retrieved with attr().
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.
net_by_reciprocity() takes a variant: either "default", the share of
ties that are reciprocated, or "ratio", the share of dyads that are mutual
rather than asymmetric. See ?igraph::reciprocity.
Where transitivity asks how often a two-path \(i \to j \to k\) is closed by a tie \(i \to k\), cyclicality asks how often it is closed in the other direction, by \(k \to i\): $$C = \frac{|\{i \to j \to k \to i\}|}{|\{i \to j \to k\}|}$$ The two capture different social logics. Transitivity is the signature of hierarchy and of "a friend of a friend is a friend", while cyclicality is the signature of generalised exchange, where resources circulate around a loop rather than flowing consistently in one direction.
A two-mode network contains no cycle of odd length, so it scores 0 here,
just as it does for transitivity. Use net_by_equivalency() for closure
in a two-mode network, which counts four-cycles instead.
In an undirected network every two-path closed in one direction is also closed in the other, so cyclicality and transitivity coincide.
The net_by_equivalency() function calculates the Robins and Alexander (2004)
clustering coefficient for two-mode networks.
The coefficient is a proportion of three-paths, and so is defined on
binary data; weighted networks are dichotomised before it is calculated.
Bearman, Peter. 1997. "Generalized Exchange". American Journal of Sociology 102(5): 1383-1415. doi:10.1086/231087
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:
measure_assort_net,
measure_assort_node,
measure_breadth,
measure_broker_node,
measure_broker_tie,
measure_brokerage,
measure_central_between,
measure_central_close,
measure_central_degree,
measure_central_eigen,
measure_central_tie_between,
measure_central_tie_close,
measure_central_tie_degree,
measure_central_tie_eigen,
measure_closure_node,
measure_cohesion,
measure_core,
measure_diffusion_infection,
measure_diffusion_net,
measure_diffusion_node,
measure_diverse_net,
measure_diverse_node,
measure_features,
measure_fit,
measure_fragmentation,
measure_hierarchy,
measure_periods
net_by_reciprocity(ison_southern_women)
#> # Reciprocity, normalized [0, 1]
#> [1] 1
net_by_transitivity(ison_adolescents)
#> # Transitivity, normalized [0, 1]
#> [1] 0.45
net_by_cyclicality(ison_networkers)
#> # Cyclicality, normalized [0, 1]
#> [1] 0.591
net_by_equivalency(ison_southern_women)
#> # Equivalency, normalized [0, 1]
#> [1] 0.468