/// <summary>
/// The eccentricity of a vertex v is the length of the shortest path
/// from that vertex to the furthest vertex from v.
/// </summary>
/// <param name="v"></param>
/// <returns></returns>
public int Eccentricity(int v)
{
var bfs = new BreadthFirstPaths(_g, v);
var eccentricity = 0;
for (int u = 0; u < _g.V; u++)
{
eccentricity = Math.Max(eccentricity, bfs.DistanceTo(u));
}
return(eccentricity);
}
/// <summary>
/// The girth is the length of the shortest cycle in the graph.
/// </summary>
/// <returns></returns>
public int Girth()
{
int EndOfPath(IEnumerable <int> path)
{
int lastElement = 0;
foreach (var v in path)
{
lastElement = v;
}
return(lastElement);
}
if (!Cyclic())
{
return(int.MaxValue);
}
var girth = int.MaxValue;
for (int s = 0; s < _g.V; s++)
{
var bfs = new BreadthFirstPaths(_g, s);
for (int v = 0; v < _g.V; v++)
{
if (s == v)
{
continue;
}
var path = bfs.PathTo(v);
var end = EndOfPath(path);
foreach (var u in _g.Adjacent(end))
{
if (u == s && v != u)
{
girth = Math.Min(girth, bfs.DistanceTo(v) + 1);
}
}
}
}
return(girth);
}
/// <summary>
/// The Wiener index of a graph is the sum of the lengths of the shortest possible
/// paths between all pair of vertices.
/// </summary>
/// <returns></returns>
public int WienerIndex()
{
int index = 0;
for (int v = 0; v < _g.V; v++)
{
var bfs = new BreadthFirstPaths(_g, v);
for (int u = 0; u < _g.V; u++)
{
if (v == u)
{
continue;
}
index += bfs.DistanceTo(u);
}
}
// All the paths have been counted twice.
return(index / 2);
}