Ego-Network Metrics

Extracts the ego network of each requested node and computes a table of personal-network metrics with one row per ego. An ego network consists of the node, its neighbors up to a given order and the ties among them. The metrics are the network size, tie counts and densities, and Burt's structural-hole measures.

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. An unknown name or an index out of range raises an error.
order: Integer neighborhood order defining the ego network. 1 (default) is the standard ego network (ego and direct neighbors). 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 neighborhood: "all" (default), "out", or "in". The Burt measures do not depend on mode.
directed: Logical or NULL. If NULL (default), auto-detect from matrix symmetry.
...: Passed to to_igraph, which takes no further arguments, so any argument supplied here raises an error.

Value

A 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 and alters).
ego_density: Edge density of the ego network including ego. NA for an ego without alters.
alter_ties: Number of edges among the alters only (excluding ego).
alter_density: Edge density among the alters. NA for an ego with fewer than two alters. Low values indicate many structural holes and brokerage opportunities.
effective_size: Burt's effective size of the ego network (order = 1 only).
constraint: Burt's constraint (order = 1 only).

The arguments order and mode and the directedness of the network are stored as attributes. Printing the result shows order and mode above the table.

Details

Self-loops are dropped before ties are counted. In a directed network the tie counts are counts of directed edges, and the densities divide by \(m(m-1)\) for \(m\) members.

effective_size and constraint are computed on the full network from all ties of each node, with the same implementations as centrality, so the values equal centrality(x, measures = c("effective_size", "constraint")). Effective size uses the unweighted ties. Constraint uses the edge weights.

References

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

Examples

cograph::ego_networks(regulation_net, nodes = "Plan")
#> Ego Networks (order = 1, mode = all)
#> ================================================== 
#>  node size ego_ties ego_density alter_ties alter_density effective_size
#>  Plan    6       15   0.3571429          8     0.2666667       4.714286
#>  constraint
#>   0.3609471