measure_broker_node: Measuring nodes brokerage

In netrics: Many Ways to Measure and Classify Membership for Networks, Nodes, and Ties

Measuring nodes brokerage

Description

These function provide different measures of the degree to which nodes fill structural holes, as outlined in Burt (1992):

• node_by_bridges() measures the sum of bridges to which each node is adjacent.

• node_by_redundancy() measures the redundancy of each nodes' contacts.

• node_by_effsize() measures nodes' effective size.

• node_by_efficiency() measures nodes' efficiency.

• node_by_constraint() measures nodes' constraint scores for one-mode networks according to Burt (1992) and for two-mode networks according to Hollway et al (2020).

• node_by_hierarchy() measures nodes' exposure to hierarchy, where only one or two contacts are the source of closure.

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

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_by_bridges(.data)

node_by_redundancy(.data)

node_by_effsize(.data)

node_by_efficiency(.data)

node_by_constraint(.data)

node_by_hierarchy(.data)

node_by_neighbours_degree(.data)

Arguments

.data

A network object of class mnet, igraph, tbl_graph, network, or similar. For more information on the standard coercion possible, see manynet::as_tidygraph().

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.

Value

A node_measure numeric vector the length of the nodes in the network, providing the scores for each node. If the network is labelled, then the scores will be labelled with the nodes' names.

References

On structural holes

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.

Burchard, Jake, and Benjamin Cornwell. 2018. “Structural Holes and Bridging in Two-Mode Networks.” Social Networks 55:11–20. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.socnet.2018.04.001")}

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")}

On neighbours average degree

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 brokerage: measure_broker_tie, measure_brokerage, member_brokerage, motif_brokerage_net, motif_brokerage_node

Other measures: measure_assort_net, measure_assort_node, measure_breadth, measure_broker_tie, measure_brokerage, measure_central_between, measure_central_close, measure_central_degree, measure_central_eigen, measure_centralities_between, measure_centralities_close, measure_centralities_degree, measure_centralities_eigen, measure_closure, 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_fragmentation, measure_hierarchy, measure_periods

Other nodal: mark_core, mark_degree, mark_diff, mark_nodes, mark_select_node, measure_assort_node, measure_brokerage, measure_central_between, measure_central_close, measure_central_degree, measure_central_eigen, measure_closure_node, measure_core, measure_diffusion_node, measure_diverse_node, member_brokerage, member_cliques, member_community, member_community_hier, member_community_non, member_components, member_core, member_diffusion, member_equivalence, motif_brokerage_node, motif_exposure, motif_node, motif_path

Examples

node_by_bridges(ison_adolescents)
node_by_bridges(ison_southern_women)
node_by_redundancy(ison_adolescents)
node_by_redundancy(ison_southern_women)
node_by_effsize(ison_adolescents)
node_by_effsize(ison_southern_women)
node_by_efficiency(ison_adolescents)
node_by_efficiency(ison_southern_women)
node_by_constraint(ison_southern_women)
node_by_hierarchy(ison_adolescents)
node_by_hierarchy(ison_southern_women)

netrics documentation built on July 24, 2026, 5:07 p.m.