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 und
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.
concept
Closeness centrality
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:
$$\frac{|V|-1}{\sum_{i\ne v} d_vi}$$
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.
closeness.estimate only considers paths of 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 then the function calculates the
exact closeness scores.
References
Freeman, L.C. (1979). Centrality in Social Networks I:
Conceptual Clarification. Social Networks, 1, 215-239.