# 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=igraph.vs.all(graph), mode = "all")
##### Arguments
graph
The graph to analyze.
v
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
##### 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.

##### Value

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

##### References

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

betweenness, degree

• closeness
##### 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 0.1.2, License: GPL version 2 or later (June, 1991)

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