public LightWeightGraph GetNormalizedRandomGraph(DistanceMatrix d)
{
int numNodes = d.Count;
var nodes = new LightWeightGraph.LightWeightNode[numNodes];
// make an array to hold all possible edges, less the edges in the mst
List <oneNode> myDistances = new List <oneNode>();
LightWeightGraph mst = LightWeightGraph.GetStackedMST(d, 1);
LightWeightGraph.LightWeightNode[] mstNodes = mst.Nodes;
//Create a list to hold edge values
List <int>[] edges = new List <int> [numNodes];
List <double>[] weights = new List <double> [numNodes];
for (int i = 0; i < numNodes; i++)
{
edges[i] = new List <int>();
weights[i] = new List <double>();
}
double largestMSTEdge = 0.0;
// add edges from the mst to the edges list, to facilitate adding additional edges later on
// Also find the largest edge to use as a cutoff
for (int i = 0; i < numNodes; i++)
{
for (int j = 0; j < mstNodes[i].Edge.Length; j++)
{
largestMSTEdge = Math.Max(largestMSTEdge, mst[i].EdgeWeights[j]);
edges[i].Add(mstNodes[i].Edge[j]);
weights[i].Add(mstNodes[i].EdgeWeights[j]);
}
}
largestMSTEdge *= _cutoffProp;
// cycle through each possible edge
// if the edge exists in the mst, continue
// otherwise, add the edge to distances array, and add distance to the edge to the cummulative total
for (int i = 0; i < numNodes - 1; i++)
{
for (int j = i + 1; j < numNodes; j++)
{
double dist = d[i, j];
if (dist >= largestMSTEdge || mstNodes[i].Edge.Contains(j))
{
continue;
}
else
{
//Probability function goes here
double addlProb = _normAlpha * (1.0 / Math.Exp(_xScale * dist / largestMSTEdge));
oneNode nd = new oneNode {
prob = addlProb, fromNode = i, toNode = j, alreadyExists = false
};
myDistances.Add(nd);
}
}
}
// walk through the array until you find the random number
for (int m = 0; m < myDistances.Count; m++)
{
double rand = Utility.Util.Rng.NextDouble();
if (myDistances[m].prob > rand)
{
// we have found the edge to add.
// add the edge if it does not already exist
if (!myDistances[m].alreadyExists)
{
int from = myDistances[m].fromNode;
int to = myDistances[m].toNode;
double dist = d[from, to];
edges[from].Add(to);
weights[from].Add(dist);
edges[to].Add(from);
weights[to].Add(dist);
myDistances[m].alreadyExists = true;
}
}
}
for (int i = 0; i < numNodes; i++)
{
nodes[i] = new LightWeightGraph.LightWeightNode(i, true, edges[i], weights[i]);
}
return(new LightWeightGraph(nodes, true));
}
/// <summary>
/// Creates a random graph, based on an mst.
/// </summary>
/// <param name="d">distance matrix used to construct the graph</param>
/// <param name="alpha">the resulting average degree of the graph</param>
/// /// <param name="expP">The probability of adding an edge depends on its distance: 1/d^expP</param>
/// <returns></returns>
public static LightWeightGraph GetRandomGraph(DistanceMatrix d, int alpha, double expP)
{
int numNodes = d.Count;
var nodes = new LightWeightGraph.LightWeightNode[numNodes];
// make an array to hold all possible edges, less the edges in the mst
oneNode[] myDistances = new oneNode[numNodes * (numNodes - 1) / 2 - (numNodes - 1)];
LightWeightGraph mst = LightWeightGraph.GetStackedMST(d, 1);
LightWeightGraph.LightWeightNode[] mstNodes = mst.Nodes;
int myDistancesIndex = 0;
double myDistancesTotal = 0;
//Create a list to hold edge values
List <int>[] edges = new List <int> [numNodes];
List <double>[] weights = new List <double> [numNodes];
for (int i = 0; i < numNodes; i++)
{
edges[i] = new List <int>();
}
// add edges from the mst to the edges list, to facilitate adding additional edges later on
for (int i = 0; i < numNodes; i++)
{
for (int j = 0; j < mstNodes[i].Edge.Length; j++)
{
edges[i].Add(mstNodes[i].Edge[j]);
}
}
// cycle through each possible edge
// if the edge exists in the mst, continue
// otherwise, add the edge to distances array, and add distance to the edge to the cummulative total
for (int i = 0; i < numNodes - 1; i++)
{
for (int j = i + 1; j < numNodes; j++)
{
if (mstNodes[i].Edge.Contains(j))
{
continue;
}
else
{
double addlProb = 1.0 / Math.Pow(d[i, j], expP);
myDistancesTotal += addlProb;
oneNode nd = new oneNode {
prob = myDistancesTotal, fromNode = i, toNode = j, alreadyExists = false
};
myDistances[myDistancesIndex] = nd;
myDistancesIndex++;
}
}
}
// how many edges do we want to add?
int desiredNewEdges = (alpha * numNodes) - (numNodes - 1);
Random rnd = Utility.Util.Rng;
// add edges randomly until we have added the desired number of edges
while (desiredNewEdges > 0)
{
// generate a random number between 0 and myDistancesTotal
double rand = rnd.NextDouble() * myDistancesTotal;
// walk through the array until you find the random number
for (int m = 0; m < myDistances.Length; m++)
{
if (myDistances[m].prob > rand)
{
// we have found the edge to add.
// add the edge if it does not already exist
if (!myDistances[m].alreadyExists)
{
edges[myDistances[m].fromNode].Add(myDistances[m].toNode);
edges[myDistances[m].toNode].Add(myDistances[m].fromNode);
myDistances[m].alreadyExists = true;
desiredNewEdges--;
break;
}
}
}
}
for (int i = 0; i < numNodes; i++)
{
nodes[i] = new LightWeightGraph.LightWeightNode(i, true, edges[i], weights[i]);
}
return(new LightWeightGraph(nodes, true));
}
