eccentricity: Eccentricity of the vertices in a graph

In igraph: Network Analysis and Visualization

Eccentricity of the vertices in a graph

Description

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

Usage

eccentricity(
  graph,
  vids = V(graph),
  ...,
  weights = NULL,
  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.
...	These dots are for future extensions and must be empty.
weights	Possibly a numeric vector giving edge weights. If this is NULL and the graph has a weight edge attribute, then the attribute is used. If this is NA then no weights are used (even if the graph has a weight attribute). In a weighted graph, the length of a path is the sum of the weights of its constituent edges.
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 considered. If all, the default, then the graph is treated as undirected, i.e. edge directions are not taken into account. This argument is ignored for undirected graphs.

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.

Related documentation in the C library

igraph_eccentricity_dijkstra().

References

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

See Also

radius() for a related concept, distances() for general shortest path calculations.

Other paths: all_simple_paths(), diameter(), distance_table(), graph_center(), radius()

Examples

g <- make_star(10, mode = "undirected")
eccentricity(g)

igraph documentation built on Oct. 20, 2024, 1:06 a.m.