Ego-Network Metrics

Extracts the ego network of each requested node (the node, its neighbours up to a given order, and the ties among them) and reports a tidy table of personal-network metrics: size, internal tie counts and densities, and Burt's structural-hole measures. One row per ego.

Usage

ego_networks(
  x,
  nodes = NULL,
  order = 1,
  mode = c("all", "out", "in"),
  directed = NULL,
  ...
)

Arguments

x: Network input: matrix, igraph, network, cograph_network, or tna object.
nodes: Character vector of node names or integer vector of node indices selecting which egos to report. NULL (default) uses every node.
order: Integer neighbourhood order defining the ego network. 1 (default) is the standard ego network (ego + direct neighbours). Burt's effective_size and constraint are only defined for order = 1 and are returned as NA otherwise.
mode: For directed networks, which ties define the neighbourhood: "all" (default), "out", or "in".
directed: Logical or NULL. If NULL (default), auto-detect from matrix symmetry.
...: Additional arguments passed to to_igraph.

Value

A tidy data.frame of class "cograph_ego_networks" with one row per ego and columns:

node: Ego node name.
size: Number of alters (ego-network size, excluding ego).
ego_ties: Number of edges in the ego network (ego + alters).
ego_density: Edge density of the ego network including ego.
alter_ties: Number of edges among the alters only (excluding ego).
alter_density: Edge density among the alters. Low values indicate many structural holes / brokerage opportunities.
effective_size: Burt's effective size of the ego network (order = 1 only).
constraint: Burt's constraint (order = 1 only).

Details

effective_size and constraint are computed on the full network (Burt's measures are defined directly from each node's order-1 ego network), reusing the same implementations as centrality so results match centrality(x, measures = c("effective_size", "constraint")).

References

Burt, R.S. (1992). Structural Holes: The Social Structure of Competition. Harvard University Press.

Examples

adj <- matrix(c(
  0, 1, 1, 0, 0,
  1, 0, 1, 0, 0,
  1, 1, 0, 1, 1,
  0, 0, 1, 0, 1,
  0, 0, 1, 1, 0
), 5, 5, byrow = TRUE)
rownames(adj) <- colnames(adj) <- LETTERS[1:5]
cograph::ego_networks(adj)
#> Ego Networks (order = 1, mode = all)
#> ================================================== 
#>  node size ego_ties ego_density alter_ties alter_density effective_size
#>     A    2        3         1.0          1     1.0000000              1
#>     B    2        3         1.0          1     1.0000000              1
#>     C    4        6         0.6          2     0.3333333              3
#>     D    2        3         1.0          1     1.0000000              1
#>     E    2        3         1.0          1     1.0000000              1
#>  constraint
#>    0.953125
#>    0.953125
#>    0.562500
#>    0.953125
#>    0.953125