These function provide different measures of the degree to which nodes fill structural holes, as outlined in Burt (1992). Burt's theory holds that while those nodes embedded in dense clusters of close connections are likely exposed to the same or similar ideas and information, those who fill structural holes between two otherwise disconnected groups can gain some comparative advantage from that position.
node_bridges(object)
node_redundancy(object)
node_effsize(object)
node_efficiency(object)
node_constraint(object)
node_hierarchy(object)An object of a migraph-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
A number of different ways of measuring these structural holes are available.
Note that we use Borgatti's reformulation for unweighted networks in
node_redundancy() and node_effsize().
Redundancy is thus \(\frac{2t}{n}\),
where \(t\) is the sum of ties and \(n\) the sum of nodes in each node's neighbourhood,
and effective size is calculated as \(n - \frac{2t}{n}\).
Node efficiency is the node's effective size divided by its degree.
node_bridges(): Returns the sum of bridges to which each node
is adjacent.
node_redundancy(): Returns a measure of the redundancy of each nodes'
contacts.
node_effsize(): Returns nodes' effective size
node_efficiency(): Returns nodes' efficiency
node_constraint(): Returns nodes' constraint scores for one-mode networks
according to Burt (1992) and for two-mode networks according to Hollway et al (2020).
node_hierarchy(): Returns nodes' exposure to hierarchy,
where only one or two contacts are the source of closure
Burt, Ronald S. 1992. Structural Holes: The Social Structure of Competition. Cambridge, MA: Harvard University Press.
Borgatti, Steven. 1997. “Structural Holes: Unpacking Burt’s Redundancy Measures” Connections 20(1):35-38.
Hollway, James, Jean-Frédéric Morin, and Joost Pauwelyn. 2020. "Structural conditions for novelty: the introduction of new environmental clauses to the trade regime complex." International Environmental Agreements: Politics, Law and Economics 20 (1): 61–83. doi:10.1007/s10784-019-09464-5 .
Other measures:
centralisation,
centrality,
closure,
cohesion(),
diversity,
features,
tie_centrality
node_bridges(ison_adolescents)
#> Betty Sue Alice Jane Dale Pam Carol Tina
#> 1 1 1 0 0 0 1 2 1
node_bridges(ison_southern_women)
#> EVELYN LAURA THERESA BRENDA CHARLOTTE FRANCES ELEANOR PEARL RUTH VERNE MYRA
#> 1 0 0 0 0 0 0 0 0 0 0 0
#> # ... with 7 more from this nodeset in the vector.
#> E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13
#> 1 0 0 0 0 0 0 0 0 0 0 0 0 0
#> # ... with 1 more from this nodeset in the vector.
node_redundancy(ison_adolescents)
#> Betty Sue Alice Jane Dale Pam Carol Tina
#> 1 6 2.5 2.5 4 3.33 4 2 2
node_redundancy(ison_southern_women)
#> EVELYN LAURA THERESA BRENDA CHARLOTTE FRANCES ELEANOR PEARL RUTH VERNE MYRA
#> 1 12.5 12.9 14.2 13.1 12 16 18 20.7 20 19.5 17.5
#> # ... with 7 more from this nodeset in the vector.
#> E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13
#> 1 12.7 13.3 10.7 11.5 9.5 10.2 10 9 8 10 7.5 9.43 12
#> # ... with 1 more from this nodeset in the vector.
node_effsize(ison_adolescents)
#> Betty Sue Alice Jane Dale Pam Carol Tina
#> 1 -5 1.5 1.5 -2 -0.333 -1 0 -1
node_effsize(ison_southern_women)
#> EVELYN LAURA THERESA BRENDA CHARLOTTE FRANCES ELEANOR PEARL RUTH VERNE MYRA
#> 1 -4.5 -5.86 -6.25 -6.14 -8 -12 -14 -17.7 -16 -15.5 -13.5
#> # ... with 7 more from this nodeset in the vector.
#> E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13
#> 1 -9.67 -10.3 -4.67 -7.5 -1.5 -2.25 0 5 4 -4 -3.5 -2.43 -8
#> # ... with 1 more from this nodeset in the vector.
node_efficiency(ison_adolescents)
#> V1 V2 V3 V4 V5 V6 V7 V8
#> 1 -5 0.375 0.375 -1 -0.111 -0.333 0 -1
node_efficiency(ison_southern_women)
#> V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
#> 1 -0.562 -0.837 -0.781 -0.878 -2 -3 -3.5 -5.89 -4 -3.88 -3.38 -1.28
#> # ... with 6 more from this nodeset in the vector.
#> V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
#> 1 -3.22 -3.44 -0.778 -1.88 -0.188 -0.281 0 0.357 0.333 -0.667 -0.875 -0.347
#> # ... with 2 more from this nodeset in the vector.
node_constraint(ison_southern_women)
#> EVELYN LAURA THERESA BRENDA CHARLOTTE FRANCES ELEANOR PEARL RUTH VERNE MYRA
#> 1 0.276 0.306 0.294 0.317 0.384 0.412 0.415 0.461 0.398 0.407 0.434
#> # ... with 7 more from this nodeset in the vector.
#> E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13
#> 1 0.476 0.476 0.338 0.394 0.275 0.241 0.192 0.170 0.161 0.327 0.308 0.292 0.432
#> # ... with 1 more from this nodeset in the vector.
node_hierarchy(ison_adolescents)
#> Betty Sue Alice Jane Dale Pam Carol Tina
#> 1 0 0.0306 0.0274 0.00587 0.0333 0.00612 0.102 0
node_hierarchy(ison_southern_women)
#> EVELYN LAURA THERESA BRENDA CHARLOTTE FRANCES ELEANOR PEARL RUTH VERNE
#> 1 0.0341 0.0359 0.0334 0.0301 0.0234 0.0207 0.0124 0.0154 0.0172 0.0221
#> # ... with 8 more from this nodeset in the vector.
#> E1 E2 E3 E4 E5 E6 E7 E8 E9 E10
#> 1 0.00150 0.000819 0.00602 0.00576 0.00572 0.0101 0.00573 0.00565 0.0150 0.0111
#> # ... with 4 more from this nodeset in the vector.