/// <summary>
///
/// </summary>
/// <param name="n"></param>
/// <param name="p"></param>
/// <param name="k"></param>
/// <returns></returns>
public static MultiDirectedGraph <int, int> GenerateTrees(int n, int p, int k)
{
// Create empty graph and label provider
var graph = new MultiDirectedGraph <int, int>();
graph.Name = "Synthetic_Trees_" + k + "_" + p + "_" + n;
// Find the degree necessary for a k-depth tree to achieve at least p number of nodes
int degree = 1;
while ((int)Math.Pow(degree, k + 1) - 1 < p)
{
degree += 1;
}
int branchSize = (int)Math.Pow(degree, k + 1) - 1;
// Keep adding trees while we lack nodes
for (int treeOffset = 0; treeOffset < n; treeOffset += branchSize)
{
int partitionSize = k + 1;
// Add nodes
for (int i = 0; i < branchSize; i++)
{
graph.AddNode(treeOffset + i);
if (partitionSize < p && Math.Log(i + 1, degree) % 1 != 0)
{
graph.SetNodeLabel(treeOffset + i, i);
partitionSize += 1;
}
else
{
graph.SetNodeLabel(treeOffset + i, branchSize);
}
}
// Add edges
for (int i = 0; i < branchSize / degree; i++)
{
for (int j = 1; j <= degree; j++)
{
graph.AddEdge(treeOffset + i, treeOffset + degree * i + j, 0);
}
}
}
return(graph);
}