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
eccentricity(graph, vids=V(graph), mode=c("all", "out", "in", "total")) radius(graph, mode=c("all", "out", "in", "total"))
- The input graph, it can be directed or undirected.
- The vertices for which the eccentricity is calculated.
- Character constant, gives whether the shortest paths to or
from the given vertices should be calculated for directed graphs. If
outthen the shortest paths from the vertex, if
inthen to it will be c
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.
eccentricityreturns a numeric vector, containing the eccentricity score of each given vertex.
radiusreturns a numeric scalar.
Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 35, 1994.
shortest.paths for general shortest path
g <- graph.star(10, mode="undirected") eccentricity(g) radius(g)