holes: Measures of structural holes

In migraph: Multimodal Network Analysis and More

Measures of structural holes

Description

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.

Usage

node_bridges(.data)

node_redundancy(.data)

node_effsize(.data)

node_efficiency(.data)

node_constraint(.data)

node_hierarchy(.data)

node_eccentricity(.data)

node_neighbours_degree(.data)

tie_cohesion(.data)

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

Details

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.

Functions

• 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

• node_eccentricity(): Returns nodes' eccentricity or Koenig number, a measure of farness based on number of links needed to reach most distant node in the network

• node_neighbours_degree(): Returns nodes' average nearest neighbors degree, or knn, a measure of the type of local environment a node finds itself in

• tie_cohesion(): Returns the ratio between common neighbors to ties' adjacent nodes and the total number of adjacent nodes, where high values indicate ties' embeddedness in dense local environments

References

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10784-019-09464-5")}.

Barrat, Alain, Marc Barthelemy, Romualdo Pastor-Satorras, and Alessandro Vespignani. 2004. "The architecture of complex weighted networks", Proc. Natl. Acad. Sci. 101: 3747.

See Also

Other measures: between_centrality, close_centrality, closure, cohesion(), degree_centrality, eigenv_centrality, features, heterogeneity, hierarchy

Examples

node_bridges(ison_adolescents)
node_bridges(ison_southern_women)
node_redundancy(ison_adolescents)
node_redundancy(ison_southern_women)
node_effsize(ison_adolescents)
node_effsize(ison_southern_women)
node_efficiency(ison_adolescents)
node_efficiency(ison_southern_women)
node_constraint(ison_southern_women)
node_hierarchy(ison_adolescents)
node_hierarchy(ison_southern_women)

migraph documentation built on Nov. 2, 2023, 5:47 p.m.