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.

## Value

`eccentricity()` returns a numeric vector, containing the eccentricity score of each given vertex.

## 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.

## References

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

`radius()` for a related concept, `distances()` for general shortest path calculations.
Other paths: `all_simple_paths()`, `diameter()`, `distance_table()`, `graph_center()`, `radius()`
``````g <- make_star(10, mode = "undirected")