measure_central_between {manynet} | R Documentation |
Measures of betweenness-like centrality and centralisation
Description
These functions calculate common betweenness-related centrality measures for one- and two-mode networks:
-
node_betweenness()
measures the betweenness centralities of nodes in a network. -
node_induced()
measures the induced betweenness centralities of nodes in a network. -
node_flow()
measures the flow betweenness centralities of nodes in a network, which uses an electrical current model for information spreading in contrast to the shortest paths model used by normal betweenness centrality. -
node_stress()
measures the stress centrality of nodes in a network. -
tie_betweenness()
measures the number of shortest paths going through a tie. -
net_betweenness()
measures the betweenness centralization for a network.
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_betweenness(.data, normalized = TRUE, cutoff = NULL)
node_induced(.data, normalized = TRUE, cutoff = NULL)
node_flow(.data, normalized = TRUE)
node_stress(.data, normalized = TRUE)
tie_betweenness(.data, normalized = TRUE)
net_betweenness(.data, normalized = TRUE, direction = c("all", "out", "in"))
Arguments
.data |
An object of a manynet-consistent class:
|
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. |
cutoff |
The maximum path length to consider when calculating betweenness. If negative or NULL (the default), there's no limit to the path lengths considered. |
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. |
Value
A numeric vector giving the betweenness centrality measure of each node.
Betweenness centrality
Betweenness centrality is based on the number of shortest paths between other nodes that a node lies upon:
C_B(i) = \sum_{j,k:j \neq k, j \neq i, k \neq i} \frac{g_{jik}}{g_{jk}}
Induced centrality
Induced centrality or vitality centrality concerns the change in total betweenness centrality between networks with and without a given node:
C_I(i) = C_B(G) - C_B(G\ i)
Flow betweenness centrality
Flow betweenness centrality concerns the total maximum flow, f
,
between other nodes j,k
in a network G
that a given node mediates:
C_F(i) = \sum_{j,k:j\neq k, j\neq i, k\neq i} f(j,k,G) - f(j,k,G\ i)
When normalized (by default) this sum of differences is divided by the
sum of flows f(i,j,G)
.
Stress centrality
Stress centrality is the number of all shortest paths or geodesics, g
,
between other nodes that a given node mediates:
C_S(i) = \sum_{j,k:j \neq k, j \neq i, k \neq i} g_{jik}
High stress nodes lie on a large number of shortest paths between other nodes, and thus associated with bridging or spanning boundaries.
References
On betweenness centrality
Freeman, Linton. 1977. "A set of measures of centrality based on betweenness". Sociometry, 40(1): 35–41. doi:10.2307/3033543
On induced centrality
Everett, Martin and Steve Borgatti. 2010. "Induced, endogenous and exogenous centrality" Social Networks, 32: 339-344. doi:10.1016/j.socnet.2010.06.004
On flow centrality
Freeman, Lin, Stephen Borgatti, and Douglas White. 1991. "Centrality in Valued Graphs: A Measure of Betweenness Based on Network Flow". Social Networks, 13(2), 141-154.
Koschutzki, D., K.A. Lehmann, L. Peeters, S. Richter, D. Tenfelde-Podehl, and O. Zlotowski. 2005. "Centrality Indices". In U. Brandes and T. Erlebach (eds.), Network Analysis: Methodological Foundations. Berlin: Springer.
On stress centrality
Shimbel, A. 1953. "Structural Parameters of Communication Networks". Bulletin of Mathematical Biophysics, 15:501-507. doi:10.1007/BF02476438
See Also
Other centrality:
measure_central_close
,
measure_central_degree
,
measure_central_eigen
Other measures:
measure_attributes
,
measure_central_close
,
measure_central_degree
,
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_betweenness(ison_southern_women)
node_induced(ison_adolescents)
(tb <- tie_betweenness(ison_adolescents))
plot(tb)
ison_adolescents %>% mutate_ties(weight = tb) %>%
graphr()
net_betweenness(ison_southern_women, direction = "in")