measure_central_degree: Measures of degree-like centrality and centralisation

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Measures of degree-like centrality and centralisation

Description

These functions calculate common degree-related centrality measures for one- and two-mode networks:

• node_degree() measures the degree centrality of nodes in an unweighted network, or weighted degree/strength of nodes in a weighted network; there are several related shortcut functions:

  • node_deg() returns the unnormalised results.

  • node_indegree() returns the direction = 'in' results.

  • node_outdegree() returns the direction = 'out' results.

• node_multidegree() measures the ratio between types of ties in a multiplex network.

• node_posneg() measures the PN (positive-negative) centrality of a signed network.

• node_leverage() measures the leverage centrality of nodes in a network.

• tie_degree() measures the degree centrality of ties in a network

• net_degree() measures a network's degree centralization; there are several related shortcut functions:

  • net_indegree() returns the direction = 'out' results.

  • net_outdegree() returns the direction = 'out' results.

All measures attempt to use as much information as they are offered, including whether the networks are directed, weighted, or multimodal. If this would produce unintended results, first transform the salient properties using e.g. to_undirected() functions. All centrality and centralization measures return normalized measures by default, including for two-mode networks.

Usage

node_degree(
  .data,
  normalized = TRUE,
  alpha = 1,
  direction = c("all", "out", "in")
)

node_deg(.data, alpha = 0, direction = c("all", "out", "in"))

node_outdegree(.data, normalized = TRUE, alpha = 0)

node_indegree(.data, normalized = TRUE, alpha = 0)

node_multidegree(.data, tie1, tie2)

node_posneg(.data)

node_leverage(.data)

tie_degree(.data, normalized = TRUE)

net_degree(.data, normalized = TRUE, direction = c("all", "out", "in"))

net_outdegree(.data, normalized = TRUE)

net_indegree(.data, normalized = TRUE)

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
normalized	Logical scalar, whether the centrality scores are normalized. Different denominators are used depending on whether the object is one-mode or two-mode, the type of centrality, and other arguments.
alpha	Numeric scalar, the positive tuning parameter introduced in Opsahl et al (2010) for trading off between degree and strength centrality measures. By default, alpha = 0, which ignores tie weights and the measure is solely based upon degree (the number of ties). alpha = 1 ignores the number of ties and provides the sum of the tie weights as strength centrality. Values between 0 and 1 reflect different trade-offs in the relative contributions of degree and strength to the final outcome, with 0.5 as the middle ground. Values above 1 penalise for the number of ties. Of two nodes with the same sum of tie weights, the node with fewer ties will obtain the higher score. This argument is ignored except in the case of a weighted network.
direction	Character string, “out” bases the measure on outgoing ties, “in” on incoming ties, and "all" on either/the sum of the two. For two-mode networks, "all" uses as numerator the sum of differences between the maximum centrality score for the mode against all other centrality scores in the network, whereas "in" uses as numerator the sum of differences between the maximum centrality score for the mode against only the centrality scores of the other nodes in that mode.
tie1	Character string indicating the first uniplex network.
tie2	Character string indicating the second uniplex network.

Value

A single centralization score if the object was one-mode, and two centralization scores if the object was two-mode.

Depending on how and what kind of an object is passed to the function, the function will return a tidygraph object where the nodes have been updated

Degree centrality

A node's degree is the number of connections it has. It is also sometimes called the valency of a node, d(v). The maximum degree in a network is often denoted \Delta (G) and the minimum degree in a network \delta (G). The total degree of a network is the sum of all degrees, \sum_v d(v). The degree sequence is the set of all nodes' degrees, ordered from largest to smallest. Directed networks discriminate between outdegree (degree of outgoing ties) and indegree (degree of incoming ties).

Leverage centrality

Leverage centrality concerns the degree of a node compared with that of its neighbours, J:

C_L(i) = \frac{1}{d(i)} \sum_{j \in J(i)} \frac{d(i) - d(j)}{d(i) + d(j)}

References

On multimodal centrality

Faust, Katherine. 1997. "Centrality in affiliation networks." Social Networks 19(2): 157-191. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0378-8733(96)00300-0")}

Borgatti, Stephen P., and Martin G. Everett. 1997. "Network analysis of 2-mode data." Social Networks 19(3): 243-270. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0378-8733(96)00301-2")}

Borgatti, Stephen P., and Daniel S. Halgin. 2011. "Analyzing affiliation networks." In The SAGE Handbook of Social Network Analysis, edited by John Scott and Peter J. Carrington, 417–33. London, UK: Sage. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.4135/9781446294413.n28")}

On strength centrality

Opsahl, Tore, Filip Agneessens, and John Skvoretz. 2010. "Node centrality in weighted networks: Generalizing degree and shortest paths." Social Networks 32, 245-251. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.socnet.2010.03.006")}

On signed centrality

Everett, Martin G., and Stephen P. Borgatti. 2014. “Networks Containing Negative Ties.” Social Networks 38:111–20. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.socnet.2014.03.005")}

On leverage centrality

Joyce, Karen E., Paul J. Laurienti, Jonathan H. Burdette, and Satoru Hayasaka. 2010. "A New Measure of Centrality for Brain Networks". PLoS ONE 5(8): e12200. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1371/journal.pone.0012200")}

See Also

to_undirected() for removing edge directions and to_unweighted() for removing weights from a graph.

Other centrality: measure_central_between, measure_central_close, measure_central_eigen

Other measures: measure_attributes, measure_central_between, measure_central_close, measure_central_eigen, measure_closure, 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

Examples

node_degree(ison_southern_women)
tie_degree(ison_adolescents)
net_degree(ison_southern_women, direction = "in")

manynet documentation built on June 23, 2025, 9:07 a.m.