Measures of node diversity

These functions offer ways to measure the heterogeneity of an attribute across a network, within groups of a network, or the distribution of ties across this attribute:

• node_by_richness() measures the number of unique categories of an attribute to which each node is connected.

• node_by_diversity() measures the heterogeneity of each node's alters, not including the node itself. Nodes without alters return NA.

node_by_richness(.data, attribute)

node_by_diversity(
  .data,
  attribute,
  diversity = c("blau", "teachman", "variation", "gini")
)

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().

attribute

Name of a nodal attribute, mark, measure, or membership vector.

diversity

Which method to use for *_diversity(). Either "blau" (Blau's index) or "teachman" (Teachman's index) for categorical attributes, or "variation" (coefficient of variation) or "gini" (Gini coefficient) for numeric attributes. Default is "blau". If an incompatible method is chosen for the attribute type, a suitable alternative will be used instead with a message.

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.

The object also carries the measure it computed, the range its values can fall within, and whether and how those values were normalized. These are shown as a one-line header when the object is printed. Where a measure offers a choice between several ways of counting the same thing, it also carries the variant it used. All can be retrieved with attr().

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

See also

Other diversity: measure_assort_net, measure_assort_node, measure_diverse_net, motif_composition, motif_homophily

Other measures: measure_assort_net, measure_assort_node, measure_breadth, measure_broker_node, measure_broker_tie, measure_brokerage, 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_closure, measure_closure_node, measure_cohesion, measure_core, measure_diffusion_infection, measure_diffusion_net, measure_diffusion_node, measure_diverse_net, measure_features, measure_fit, measure_fragmentation, measure_hierarchy, measure_periods

Other nodal: mark_core, mark_degree, mark_diff, mark_nodes, mark_select_node, measure_assort_node, measure_broker_node, measure_brokerage, measure_central_between, measure_central_close, measure_central_degree, measure_central_eigen, measure_closure_node, measure_core, measure_diffusion_node, member_brokerage, member_cliques, member_community, member_community_hier, member_community_modular, member_community_partition, member_community_spread, member_components, member_core, member_diffusion, member_equivalence, motif_brokerage_node, motif_clique, motif_composition, motif_exposure, motif_node, motif_path

Examples

node_by_richness(ison_networkers, "Discipline")
#> # Richness [0, Inf)
#> ▂▃▁▅ 
#>   `Lin Freeman` `Doug White` `Ev Rogers` `Richard Alba` `Phipps Arabie`
#> 1             4            4           2              4               4
#> # ... and 27 more values from this nodeset. Use `print_all(...)` to print all values.
marvel_friends <- to_unsigned(to_uniplex(fict_marvel, "relationship"), "positive")
node_by_diversity(marvel_friends, "Gender")
#> # Blau's index, normalized [0, 1]
#> ▂▁▁▄▂ 
#>   Abomination `Ant-Man` Apocalypse Beast `Black Panther` `Black Widow` Blade
#> 1          NA     0.375          0 0.375           0.351          0.26     0
#> # ... and 46 more values from this nodeset. Use `print_all(...)` to print all values.
node_by_diversity(marvel_friends, "Attractive")
#> # Coefficient of variation (-Inf, Inf)
#> ▂▅▁▁▁▁▁▁ 
#>   Abomination `Ant-Man` Apocalypse Beast `Black Panther` `Black Widow` Blade
#> 1          NA     0.667         NA 0.342           0.324           0.3     0
#> # ... and 46 more values from this nodeset. Use `print_all(...)` to print all values.