Measures of network eigenvector-like centralisation

• net_by_eigenvector() measures the eigenvector centralization for a network as a single score.

• mode_by_eigenvector() measures eigenvector centralization separately for each mode of a two-mode network (via projection to each mode), returning one score per mode (following Borgatti and Everett, 1997). A multilevel network cannot be projected, so there each mode's scores are read from the whole 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.

For two-mode networks the two modes have different theoretical maxima, so net_by_eigenvector() reports a single network-level score by applying Freeman's general centralization index over the normalized node eigenvector scores, whereas mode_by_eigenvector() reports the per-mode scores directly.

net_by_eigenvector(.data, normalized = TRUE)

mode_by_eigenvector(.data, normalized = TRUE)

Arguments

.data

A network object of class stocnet, igraph, tbl_graph, network, or similar. Internally any of these will be coerced to an efficient implementation. For more information on possible coercions, see e.g. manynet::as_stocnet().

normalized

Logical scalar, whether scores are normalized. Different denominators may be used depending on the measure, whether the object is one-mode or two-mode, and other arguments. By default TRUE.

Value

net_by_eigenvector() returns a network_measure scalar; mode_by_eigenvector() returns a mode_measure numeric vector of length two, giving one centralization score per mode.

Cognitive social structures

A cognitive social structure records each node's report of the ties in the whole network, in a by column that names who reported each tie. Counting every report as a tie of its own would count each tie once for every perceiver who reports it. So the functions here first combine the reports into the locally aggregated structure of Krackhardt (1987), with the intersection rule: a tie exists if both of its ends report it, and a message says so. A tie that names no reporter is kept as it is.

A tie-level function still returns one value for each report, so that the result can be added back to the network it was given. Each report takes the value of the tie that it reports. A report of a tie that is not in the aggregated structure takes NA, or FALSE for a mark. tie_is_random() is the exception, and draws among the reports.

To combine the reports in a different way, do this before the function, e.g. with manynet::to_aggregated(over = "by").

Krackhardt, David. 1987. "Cognitive social structures". Social Networks 9(2): 109-134. doi:10.1016/0378-8733(87)90009-8

References

Borgatti, Stephen P., and Martin G. Everett. 1997. "Network analysis of 2-mode data." Social Networks 19(3): 243-269. doi:10.1016/S0378-8733(96)00301-2

See also

Other eigenvector: measure_central_eigen, measure_central_tie_eigen

Other centrality: measure_central_between, measure_central_close, measure_central_degree, measure_central_eigen, measure_central_tie_between, measure_central_tie_close, measure_central_tie_degree, measure_central_tie_eigen, measure_centralisation_between, measure_centralisation_close, measure_centralisation_degree

Examples

net_by_eigenvector(ison_southern_women)
#> # Eigenvector centralisation, normalized [0, 1]
#> [1] 0.419
mode_by_eigenvector(ison_southern_women)
#> # Eigenvector centralisation, normalized [0, 1]
#> Mode 1 Mode 2 
#> 0.0849 0.2630