eccentricity

0th

Percentile

Eccentricity and radius

The eccentricity of a vertex is its shortest path distance from the farthest other node in the graph. The smallest eccentricity in a graph is called its radius

Keywords
graphs
Usage
eccentricity(graph, vids=V(graph), mode=c("all", "out", "in", "total"))
radius(graph, mode=c("all", "out", "in", "total"))
Arguments
graph
The input graph, it can be directed or undirected.
vids
The vertices for which the eccentricity is calculated.
mode
Character constant, gives whether the shortest paths to or from the given vertices should be calculated for directed graphs. If out then the shortest paths from the vertex, if in then to it will be c
Details

The eccentricity of a vertex is calculated by measuring the shortest distance from (or to) the vertex, to (or from) all vertices in the graph, and taking the maximum.

This implementation ignores vertex pairs that are in different components. Isolate vertices have eccentricity zero.

Value

  • eccentricity returns a numeric vector, containing the eccentricity score of each given vertex.

    radius returns a numeric scalar.

concept

  • Eccentricity
  • Radius

References

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 35, 1994.

See Also

shortest.paths for general shortest path calculations.

Aliases
  • eccentricity
  • radius
Examples
g <- graph.star(10, mode="undirected")
eccentricity(g)
radius(g)
Documentation reproduced from package igraph, version 0.6.5-2, License: GPL (>= 2)

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