// This is experimental (for now at least), trying to see if we can swap edges and change assortativity while
// maintaining the degree vector, really need to reorganize this part. Would move it to a new class that inherits
// from Graph, but I want to use it in ER and BA..
public bool SwapRandomEdgesToIncreaseAssortativity()
{
Randomizer rand = new Randomizer();
var edges = EdgesAsNodes.ToList();
var e1 = edges[rand.Next(edges.Count)];
var e2 = edges[rand.Next(edges.Count)];
if (e1.Item1 == e2.Item1 || e1.Item1 == e2.Item2 || e1.Item2 == e2.Item1 || e1.Item2 == e2.Item2)
{
return(false);
}
var currVal = ((double)Math.Max(e1.Item1.Degree, e1.Item2.Degree) /
Math.Min(e1.Item1.Degree, e1.Item2.Degree) +
(double)Math.Max(e2.Item1.Degree, e2.Item2.Degree) /
Math.Min(e2.Item1.Degree, e2.Item2.Degree)) / 2.0;
var e1Ae2A = ((double)Math.Max(e1.Item1.Degree, e2.Item1.Degree) /
Math.Min(e1.Item1.Degree, e2.Item1.Degree) +
(double)Math.Max(e1.Item2.Degree, e2.Item2.Degree) /
Math.Min(e1.Item2.Degree, e2.Item2.Degree)) / 2.0;
var e1Ae2B = ((double)Math.Max(e1.Item1.Degree, e2.Item2.Degree) /
Math.Min(e1.Item1.Degree, e2.Item2.Degree) +
(double)Math.Max(e1.Item2.Degree, e2.Item1.Degree) /
Math.Min(e1.Item2.Degree, e2.Item1.Degree)) / 2.0;
String oldDegSeq = String.Join(",", DegreeVector);
if (e1Ae2A < currVal && e1Ae2A < e1Ae2B &&
!e1.Item1.Neighbors.Contains(e2.Item1) && !e1.Item2.Neighbors.Contains(e2.Item2))
{
RemoveEdge(e1.Item1, e1.Item2);
RemoveEdge(e2.Item1, e2.Item2);
AddEdge(e1.Item1, e2.Item1);
AddEdge(e1.Item2, e2.Item2);
if (oldDegSeq != String.Join(",", DegreeVector))
{
throw new Exception("Holy cow");
}
return(true);
}
else if (e1Ae2B < currVal && e1Ae2B < e1Ae2A &&
!e1.Item1.Neighbors.Contains(e2.Item2) && !e1.Item2.Neighbors.Contains(e2.Item1))
{
RemoveEdge(e1.Item1, e1.Item2);
RemoveEdge(e2.Item1, e2.Item2);
AddEdge(e1.Item1, e2.Item2);
AddEdge(e1.Item2, e2.Item1);
if (oldDegSeq != String.Join(",", DegreeVector))
{
throw new Exception("Holy cow");
}
return(true);
}
return(false);
}
public double GraphAssortativity2()
{
cacheIsEmpty = false;
if (!Double.IsNegativeInfinity(_graphAssortativity2))
{
return(_graphAssortativity2);
}
if (ExcessDegreeVariance == 0) // All vertices are the same degree, automatically perfect assortativity
{
return(_graphAssortativity2 = 1.0);
}
double M = Edges.Count();
double numerator = ((1 / M) * (EdgesAsNodes.Sum(e => e.Item1.Degree * e.Item2.Degree)) -
Math.Pow((1 / M) * 0.5 * EdgesAsNodes.Sum(e => e.Item1.Degree + e.Item2.Degree), 2.0));
double denominator = ((1 / M) * 0.5 *
EdgesAsNodes.Sum(e => Math.Pow(e.Item1.Degree, 2) + Math.Pow(e.Item2.Degree, 2)) -
Math.Pow((1 / M) * 0.5 * EdgesAsNodes.Sum(e => e.Item1.Degree + e.Item2.Degree), 2.0));
return(_graphAssortativity2 = numerator / denominator);
}
public void IterativelySwapEdgesToDecreaseAssortativity()
{
var edges = EdgesAsNodes.OrderByDescending(e => LocalAssort(e)).ToList();
while (edges.Count > 1)
{
var e1 = edges[0];
edges.Remove(e1);
var otherEdges =
edges.Where(
e2 =>
e1.Item1 != e2.Item1 &&
e1.Item1 != e2.Item2 &&
e1.Item2 != e2.Item1 &&
e1.Item2 != e2.Item2).ToList();
var currVal = LocalAssort(e1);
var currMaxImprovement = 0.0;
Tuple <Node, Node> currMaxEdge = null;
EdgeSwap bestEdgeSwap = EdgeSwap.e1Ae2A_e1Be2B; // just need to assign something..
foreach (var e2 in otherEdges)
{
double improvement;
if (!e1.Item1.Neighbors.Contains(e2.Item1) && !e1.Item2.Neighbors.Contains(e2.Item2))
{
improvement = currVal - (LocalAssort(new Tuple <Node, Node>(e1.Item1, e2.Item1)) +
LocalAssort(new Tuple <Node, Node>(e1.Item2, e2.Item2))) /
2.0;
if (improvement > currMaxImprovement)
{
currMaxImprovement = improvement;
currMaxEdge = e2;
bestEdgeSwap = EdgeSwap.e1Ae2A_e1Be2B;
}
}
if (!e1.Item1.Neighbors.Contains(e2.Item2) && !e1.Item2.Neighbors.Contains(e2.Item1))
{
improvement = currVal - (LocalAssort(new Tuple <Node, Node>(e1.Item1, e2.Item2)) +
LocalAssort(new Tuple <Node, Node>(e1.Item2, e2.Item1))) /
2.0;
if (improvement > currMaxImprovement)
{
currMaxImprovement = improvement;
currMaxEdge = e2;
bestEdgeSwap = EdgeSwap.e1Ae2B_e1Be2A;
}
}
}
if (currMaxEdge != null)
{
if (bestEdgeSwap == EdgeSwap.e1Ae2A_e1Be2B)
{
AddEdge(e1.Item1, currMaxEdge.Item1);
AddEdge(e1.Item2, currMaxEdge.Item2);
}
else
{
AddEdge(e1.Item1, currMaxEdge.Item2);
AddEdge(e1.Item2, currMaxEdge.Item1);
}
RemoveEdge(e1.Item1, e1.Item2);
RemoveEdge(currMaxEdge.Item1, currMaxEdge.Item2);
edges.Remove(currMaxEdge);
}
}
}
