Affiliation network clustering coefficients

This function computes a given flavor of transitivity (triadic closure) on a given affiliation network. The calculations are performed locally. Each flavor is defined as a proportion of "wedges" that are "closed", for suitable definitions of both terms. The function transitivity_an is a shell that proceeds across actors and computes wedges using the provided wedgeFun. These functions count the "wedges", and among them the "closed" ones, centered at a given actor node in a given affiliation network. The triads method transitivity_an_triads first classifies every triad centered at each node. The appropriate formula then counts the wedges and closed wedges at each. The method is slower for a single flavor but can be used to produce multiple flavors with negligible additional computational cost. The wedges method transitivity_an_wedges relies on a separate "wedge function" for each statistic. The algorithm calls the appropriate wedge function to run over the necessary wedge centers and return a wedge count matrix, which is returned back into transitivity_an for outputting.

Usage

transitivity_an(
  graph,
  type = "global",
  wedgeFun,
  flavor,
  vids = which(!V(graph)$type),
  add.names = FALSE
)

transitivity_an_triads(graph, vids = which(!V(graph)$type), flavor)

transitivity_an_wedges(graph, vids = which(!V(graph)$type), wedgeFun)

transitivity.an(
  graph,
  type = "global",
  wedgeFun,
  flavor,
  vids = which(!V(graph)$type),
  add.names = FALSE
)

transitivity.an.triads(graph, vids = which(!V(graph)$type), flavor)

transitivity.an.wedges(graph, vids = which(!V(graph)$type), wedgeFun)

indequ_transitivity(graph, type = "global", vids = which(!V(graph)$type))

indequ.transitivity(graph, type = "global", vids = which(!V(graph)$type))

indstr_transitivity(graph, type = "global", vids = which(!V(graph)$type))

indstr.transitivity(graph, type = "global", vids = which(!V(graph)$type))

injact_transitivity(graph, type = "global", vids = which(!V(graph)$type))

injact.transitivity(graph, type = "global", vids = which(!V(graph)$type))

injequ_transitivity(graph, type = "global", vids = which(!V(graph)$type))

injequ.transitivity(graph, type = "global", vids = which(!V(graph)$type))

injstr_transitivity(graph, type = "global", vids = which(!V(graph)$type))

injstr.transitivity(graph, type = "global", vids = which(!V(graph)$type))

opsahl_transitivity(graph, type = "global", vids = which(!V(graph)$type))

opsahl.transitivity(graph, type = "global", vids = which(!V(graph)$type))

excl_transitivity(graph, type = "global", vids = which(!V(graph)$type))

excl.transitivity(graph, type = "global", vids = which(!V(graph)$type))

Arguments

graph: An affiliation network; see is_an.
type: Character; the type of clustering coefficient (defaults to "global").
wedgeFun: The wedge function; overrides flavor.
flavor: The flavor of transitivity to be used; overridden by wedgeFun.
vids: A subset of actor node ids at which to evaluate the local clustering coefficient.
add.names: Logical; whether to label the matrix rows and columns.
triads: A matrix of centered triads.

Value

If type is "global", the global clustering coefficient of the network (a single numeric value); if "local", the local clustering coefficients of the actors (a numeric vector); otherwise, a 2-column matrix, each row of which gives the number of wedges and the number of closed wedges centered at each actor.

Usage

Arguments

Value

See also