# closeness

0th

Percentile

##### Closeness centrality of vertices

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

Keywords
graphs
##### Usage
closeness(graph, v=V(graph), mode = c("all", "out", "in"))
closeness.estimate(graph, vids=V(graph), mode = c("out", "in", "all",
"total"), cutoff)
##### Arguments
graph
The graph to analyze.
v,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 und
cutoff
The maximum path length to consider when calculating the betweenness. If zero or negative then there is no such limit.
##### 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.

##### Value

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

##### concept

Closeness centrality

##### References

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

##### See Also

betweenness, degree

##### Aliases
• closeness
• closeness.estimate
##### Examples
g <- graph.ring(10)
g2 <- graph.star(10)
closeness(g)
closeness(g2, mode="in")
closeness(g2, mode="out")
closeness(g2, mode="all")
Documentation reproduced from package igraph, version 0.5.2-2, License: GPL (>= 2)

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