igraph (version 1.3.1)

closeness: Closeness centrality of vertices

Description

Closeness centrality measures how many steps is required to access every other vertex from a given vertex.

Usage

closeness(
  graph,
  vids = V(graph),
  mode = c("out", "in", "all", "total"),
  weights = NULL,
  normalized = FALSE,
  cutoff = -1
)

Arguments

graph

The graph to analyze.

vids

The vertices for which closeness will be calculated.

mode

Character string, defined the types of the paths used for measuring the distance in directed graphs. “in” measures the paths to a vertex, “out” measures paths from a vertex, all uses undirected paths. This argument is ignored for undirected graphs.

weights

Optional positive weight vector for calculating weighted closeness. If the graph has a weight edge attribute, then this is used by default. Weights are used for calculating weighted shortest paths, so they are interpreted as distances.

normalized

Logical scalar, whether to calculate the normalized closeness. Normalization is performed by multiplying the raw closeness by \(n-1\), where \(n\) is the number of vertices in the graph.

cutoff

The maximum path length to consider when calculating the betweenness. If zero or negative then there is no such limit.

Value

Numeric vector with the closeness values of all the vertices in v.

Details

The closeness centrality of a vertex is defined by the inverse of the average length of the shortest paths to/from all the other vertices in the graph:

$$\frac{1}{\sum_{i\ne v} d_vi}$$

If there is no (directed) path between vertex v and i, then the total number of vertices is used in the formula instead of the path length.

cutoff or smaller. this can be run for larger graphs, as the running time is not quadratic (if cutoff is small). If cutoff is zero or negative (which is the default), then the function calculates the exact closeness scores. Using zero as a cutoff is deprecated and future versions (from 1.4.0) will treat zero cutoff literally (i.e. no paths considered at all). If you want no cutoff, use a negative number.

estimate_closeness is an alias for closeness with a different argument order, for sake of compatibility with older versions of igraph.

Closeness centrality is meaningful only for connected graphs. In disconnected graphs, consider using the harmonic centrality with harmonic_centrality

References

Freeman, L.C. (1979). Centrality in Social Networks I: Conceptual Clarification. Social Networks, 1, 215-239.

See Also

betweenness, degree, harmonic_centrality

Examples

# NOT RUN {
g <- make_ring(10)
g2 <- make_star(10)
closeness(g)
closeness(g2, mode="in")
closeness(g2, mode="out")
closeness(g2, mode="all")

# }