protected void MergeCommunities
(LinkedList<Community> oCommunities,CommunityPair oCommunityPairToMerge,DeltaQMaxHeap oDeltaQMaxHeap,Int32 iEdgesInGraph,IDGenerator oIDGenerator)
{
Debug.Assert(oCommunityPairToMerge != null);
Debug.Assert(oCommunities != null);
Debug.Assert(oDeltaQMaxHeap != null);
Debug.Assert(iEdgesInGraph > 0);
Debug.Assert(oIDGenerator != null);
// Merge Community1 and Community2 into a NewCommunity.
Community oCommunity1 = oCommunityPairToMerge.Community1;
Community oCommunity2 = oCommunityPairToMerge.Community2;
Community oNewCommunity = new Community();
oNewCommunity.ID = oIDGenerator.GetNextID();
oNewCommunity.Degree = oCommunity1.Degree + oCommunity2.Degree;
ICollection<IVertex> oNewCommunityVertices = oNewCommunity.Vertices;
foreach (IVertex oVertex in oCommunity1.Vertices)
{
oNewCommunityVertices.Add(oVertex);
}
foreach (IVertex oVertex in oCommunity2.Vertices)
{
oNewCommunityVertices.Add(oVertex);
}
// In the following sorted lists, the sort key is the ID of
// CommunityPair.Community2 and the value is the CommunityPair.
SortedList<Int32, CommunityPair> oCommunity1CommunityPairs =
oCommunity1.CommunityPairs;
SortedList<Int32, CommunityPair> oCommunity2CommunityPairs =
oCommunity2.CommunityPairs;
SortedList<Int32, CommunityPair> oNewCommunityCommunityPairs =
oNewCommunity.CommunityPairs;
Int32 iCommunity1CommunityPairs = oCommunity1CommunityPairs.Count;
Int32 iCommunity2CommunityPairs = oCommunity2CommunityPairs.Count;
IList<Int32> oCommunity1Keys = oCommunity1CommunityPairs.Keys;
IList<CommunityPair> oCommunity1Values =
oCommunity1CommunityPairs.Values;
IList<Int32> oCommunity2Keys = oCommunity2CommunityPairs.Keys;
IList<CommunityPair> oCommunity2Values =
oCommunity2CommunityPairs.Values;
// Step through the community pairs in oCommunity1 and oCommunity2.
Int32 iCommunity1Index = 0;
Int32 iCommunity2Index = 0;
Single fMaximumDeltaQ = Single.MinValue;
CommunityPair oCommunityPairWithMaximumDeltaQ = null;
Single fTwoTimesEdgesInGraph = 2F * iEdgesInGraph;
while (iCommunity1Index < iCommunity1CommunityPairs ||
iCommunity2Index < iCommunity2CommunityPairs)
{
Int32 iCommunity1OtherCommunityID =
(iCommunity1Index < iCommunity1CommunityPairs) ?
oCommunity1Keys[iCommunity1Index] : Int32.MaxValue;
Int32 iCommunity2OtherCommunityID =
(iCommunity2Index < iCommunity2CommunityPairs) ?
oCommunity2Keys[iCommunity2Index] : Int32.MaxValue;
CommunityPair oNewCommunityPair = new CommunityPair();
oNewCommunityPair.Community1 = oNewCommunity;
if (iCommunity1OtherCommunityID == oCommunity2.ID)
{
// This is an internal connection eliminated by the merge.
// Skip it.
iCommunity1Index++;
continue;
}
else if (iCommunity2OtherCommunityID == oCommunity1.ID)
{
// This is an internal connection eliminated by the merge.
// Skip it.
iCommunity2Index++;
continue;
}
else if (iCommunity1OtherCommunityID == iCommunity2OtherCommunityID)
{
// The other community is connected to both commmunity 1 and
// community 2.
//
// This is equation 10a from the paper "Finding Community
// Structure in Very Large Networks," by Clauset, Newman, and
// Moore.
oNewCommunityPair.Community2 =
oCommunity1Values[iCommunity1Index].Community2;
oNewCommunityPair.DeltaQ =
oCommunity1Values[iCommunity1Index].DeltaQ +
oCommunity2Values[iCommunity2Index].DeltaQ;
iCommunity1Index++;
iCommunity2Index++;
}
else if (iCommunity1OtherCommunityID < iCommunity2OtherCommunityID)
{
// The other community is connected only to commmunity 1.
//
// This is equation 10b from the same paper.
Community oOtherCommunity =
oCommunity1Values[iCommunity1Index].Community2;
oNewCommunityPair.Community2 = oOtherCommunity;
Single fAj = oCommunity2.Degree / fTwoTimesEdgesInGraph;
Single fAk = oOtherCommunity.Degree / fTwoTimesEdgesInGraph;
oNewCommunityPair.DeltaQ =
oCommunity1Values[iCommunity1Index].DeltaQ -
2F * fAj * fAk;
iCommunity1Index++;
}
else
{
// The other community is connected only to commmunity 2.
//
// This is equation 10c from the same paper.
Community oOtherCommunity =
oCommunity2Values[iCommunity2Index].Community2;
oNewCommunityPair.Community2 = oOtherCommunity;
Single fAi = oCommunity1.Degree / fTwoTimesEdgesInGraph;
Single fAk = oOtherCommunity.Degree / fTwoTimesEdgesInGraph;
oNewCommunityPair.DeltaQ =
oCommunity2Values[iCommunity2Index].DeltaQ -
2F * fAi * fAk;
iCommunity2Index++;
}
oNewCommunityCommunityPairs.Add(oNewCommunityPair.Community2.ID,
oNewCommunityPair);
Single fNewCommunityPairDeltaQ = oNewCommunityPair.DeltaQ;
if (fNewCommunityPairDeltaQ > fMaximumDeltaQ)
{
fMaximumDeltaQ = oNewCommunityPair.DeltaQ;
oCommunityPairWithMaximumDeltaQ = oNewCommunityPair;
}
// The other community is connected to one or both of the merged
// communities. Update it.
oNewCommunityPair.Community2.OnMergedCommunities(
oCommunity1, oCommunity2, oNewCommunity,
fNewCommunityPairDeltaQ, oDeltaQMaxHeap);
}
oNewCommunity.CommunityPairWithMaximumDeltaQ =
oCommunityPairWithMaximumDeltaQ;
// Update the community list.
oCommunities.Remove(oCommunity1);
oCommunities.Remove(oCommunity2);
oCommunities.AddLast(oNewCommunity);
// Update the max heap.
oDeltaQMaxHeap.Remove(oCommunity1);
oDeltaQMaxHeap.Remove(oCommunity2);
oDeltaQMaxHeap.Add(oNewCommunity, oNewCommunity.MaximumDeltaQ);
}
public void OnMergedCommunities
(Community mergedCommunity1,Community mergedCommunity2,Community newMergedCommunity,Single newCommunityPairDeltaQ,DeltaQMaxHeap deltaQMaxHeap)
{
Debug.Assert(mergedCommunity1 != null);
Debug.Assert(mergedCommunity2 != null);
Debug.Assert(newMergedCommunity != null);
Debug.Assert(deltaQMaxHeap != null);
// If only one of the two merged communities was connected to this
// community, fPreviousCommunityPairDeltaQ is the delta Q for this
// community's community pair for the merged community. If both were
// connected, fPreviousCommunityPairDeltaQ is the larger of the two
// delta Q values.
Single fPreviousCommunityPairDeltaQ = Single.MinValue;
Int32 iMergedCommunity1ID = mergedCommunity1.ID;
Int32 iMergedCommunity2ID = mergedCommunity2.ID;
Debug.Assert(iMergedCommunity1ID != iMergedCommunity2ID);
Int32 iSmallerMergedCommunityID =
Math.Min(iMergedCommunity1ID, iMergedCommunity2ID);
Int32 iLargerMergedCommunityID =
Math.Max(iMergedCommunity1ID, iMergedCommunity2ID);
// Delete the community pair or pairs that connect to one of the merged
// communities.
//
// Go backwards through the community pairs so that they can be deleted
// while looping. (Don't use foreach, because you can't delete while
// enumerating.)
for (Int32 i = m_oCommunityPairs.Count - 1; i >= 0; i--)
{
Int32 iOtherCommunityID = m_oCommunityPairs.Keys[i];
if (iOtherCommunityID > iLargerMergedCommunityID)
{
// We haven't yet reached the range of community pairs that
// might connect to either merged community.
continue;
}
if (iOtherCommunityID < iSmallerMergedCommunityID)
{
// We're beyond the range of community pairs that might connect
// to either merged community.
break;
}
CommunityPair oCommunityPair = m_oCommunityPairs.Values[i];
if (iOtherCommunityID == iLargerMergedCommunityID)
{
// This community pair connects to the merged community with
// the larger ID.
fPreviousCommunityPairDeltaQ = oCommunityPair.DeltaQ;
m_oCommunityPairs.RemoveAt(i);
}
else if (iOtherCommunityID == iSmallerMergedCommunityID)
{
// This community pair connects to the merged community with
// the smaller ID.
fPreviousCommunityPairDeltaQ = Math.Max(
fPreviousCommunityPairDeltaQ, oCommunityPair.DeltaQ);
m_oCommunityPairs.RemoveAt(i);
// There is no reason to continue looking at community pairs.
break;
}
else
{
// This community pair does not connect to either merged
// community.
continue;
}
}
Debug.Assert(fPreviousCommunityPairDeltaQ != Single.MinValue);
// Add a new community pair that connects to the new merged community.
CommunityPair oNewCommunityPair = new CommunityPair();
oNewCommunityPair.Community1 = this;
oNewCommunityPair.Community2 = newMergedCommunity;
oNewCommunityPair.DeltaQ = newCommunityPairDeltaQ;
m_oCommunityPairs.Add(newMergedCommunity.ID, oNewCommunityPair);
// Update m_oCommunityPairWithMaximumDeltaQ if necessary. These rules
// come from section 4.1 of "Finding Community Structure in Mega-scale
// Social Networks," by Ken Wakita and Toshiyuki Tsurumi.
Single fOldMaximumDeltaQ = this.MaximumDeltaQ;
if (fPreviousCommunityPairDeltaQ < fOldMaximumDeltaQ)
{
// The deleted community pair (or pairs) was not the one with the
// maximum delta Q.
if (newCommunityPairDeltaQ <= fPreviousCommunityPairDeltaQ)
{
// The delta Q value for the new community pair is less than or
// equal to the delta Q value of the deleted community pair (or
// pairs). Do nothing.
}
else
{
// The delta Q value for the new community pair is greater than
// the delta Q value of the deleted community pair (or pairs).
if (newCommunityPairDeltaQ > fOldMaximumDeltaQ)
{
// The new community pair is the one with the maximum
// delta Q.
m_oCommunityPairWithMaximumDeltaQ = oNewCommunityPair;
}
}
}
else
{
// The deleted community pair (or pairs) was the one with the
// maximum delta Q.
if (newCommunityPairDeltaQ >= fPreviousCommunityPairDeltaQ)
{
// The new community pair is the one with the maximum
// delta Q.
m_oCommunityPairWithMaximumDeltaQ = oNewCommunityPair;
}
else
{
// Worst case: All community pairs must be scanned.
Single fNewMaximumDeltaQ = Single.MinValue;
foreach (CommunityPair oCommunityPair in
m_oCommunityPairs.Values)
{
if (oCommunityPair.DeltaQ > fNewMaximumDeltaQ)
{
m_oCommunityPairWithMaximumDeltaQ = oCommunityPair;
fNewMaximumDeltaQ = oCommunityPair.DeltaQ;
}
}
}
}
if (fOldMaximumDeltaQ != this.MaximumDeltaQ)
{
// Update the max heap.
deltaQMaxHeap.UpdateValue(this, this.MaximumDeltaQ);
}
}
protected LinkedList<Community> CreateCommunities
(IVertexCollection oVertices, IDGenerator oIDGenerator)
{
Debug.Assert(oVertices != null);
Debug.Assert(oIDGenerator != null);
// This is the list of communities. Initially, there will be one
// community for each of the graph's vertices.
LinkedList<Community> oCommunities = new LinkedList<Community>();
// This temporary dictionary is used to map a vertex ID to a community.
// The key is the IVertex.ID and the value is the corresponding
// Community object.
Dictionary<Int32, Community> oVertexIDDictionary =
new Dictionary<Int32, Community>(oVertices.Count);
// First, create a community for each of the graph's vertices. Each
// community contains just the vertex.
foreach (IVertex oVertex in oVertices)
{
Community oCommunity = new Community();
Int32 iID = oIDGenerator.GetNextID();
oCommunity.ID = iID;
oCommunity.Vertices.Add(oVertex);
// TODO: IVertex.AdjacentVertices includes self-loops. Should
// self-loops be eliminated everywhere, including here and within
// the graph's total edge count? Not sure how self-loops are
// affecting the algorithm used by this class...
oCommunity.Degree = oVertex.AdjacentVertices.Count;
oCommunities.AddLast(oCommunity);
oVertexIDDictionary.Add(oVertex.ID, oCommunity);
}
// Now populate each community's list of community pairs.
foreach (Community oCommunity1 in oCommunities)
{
Debug.Assert(oCommunity1.Vertices.Count == 1);
IVertex oVertex = oCommunity1.Vertices.First();
SortedList<Int32, CommunityPair> oCommunityPairs =
oCommunity1.CommunityPairs;
foreach (IVertex oAdjacentVertex in oVertex.AdjacentVertices)
{
if (oAdjacentVertex == oVertex)
{
// Skip self-loops.
continue;
}
Community oCommunity2 =
oVertexIDDictionary[oAdjacentVertex.ID];
CommunityPair oCommunityPair = new CommunityPair();
oCommunityPair.Community1 = oCommunity1;
oCommunityPair.Community2 = oCommunity2;
oCommunityPairs.Add(oCommunity2.ID, oCommunityPair);
}
}
return (oCommunities);
}