//*************************************************************************
// Constructor: CommunityPair()
//
/// <summary>
/// Initializes a new instance of the <see cref="CommunityPair" /> class.
/// </summary>
//*************************************************************************
public CommunityPair()
{
m_oCommunity1 = null;
m_oCommunity2 = null;
m_fDeltaQ = Community.DeltaQNotSet;
AssertValid();
}
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);
AssertValid();
// 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);
}
}
//*************************************************************************
// Method: OnMergedCommunities()
//
/// <summary>
/// Gets called when two communities merge and one or both of them were
/// connected to this community.
/// </summary>
///
/// <param name="mergedCommunity1">
/// The first community that was merged.
/// </param>
///
/// <param name="mergedCommunity2">
/// The second community that was merged.
/// </param>
///
/// <param name="newMergedCommunity">
/// The new community that the communities were merged into.
/// </param>
///
/// <param name="newCommunityPairDeltaQ">
/// The new delta Q value for the community pair that connects this
/// community to the merged community.
/// </param>
///
/// <param name="deltaQMaxHeap">
/// Max heap, used to keep track of the maximum delta Q value in each
/// community. There is an element in the max heap for each community.
/// The key is the Community and the value is the Community's maximum
/// delta Q.
/// </param>
//*************************************************************************
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);
AssertValid();
// 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);
}
}
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);
}
CreateCommunities
(
IVertexCollection oVertices,
IDGenerator oIDGenerator
)
{
Debug.Assert(oVertices != null);
Debug.Assert(oIDGenerator != null);
AssertValid();
// 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);
}
TryCalculateClustersSnap
(
IGraph oGraph,
SnapGraphMetrics eSnapGraphMetric,
BackgroundWorker oBackgroundWorker,
out ICollection <Community> oGraphMetrics
)
{
Debug.Assert(oGraph != null);
AssertValid();
LinkedList <Community> oCommunities = new LinkedList <Community>();
oGraphMetrics = oCommunities;
if (oBackgroundWorker != null)
{
if (oBackgroundWorker.CancellationPending)
{
return(false);
}
ReportProgress(1, 3, oBackgroundWorker);
}
// Make it easy to find the graph's vertices by vertex ID. The key is
// a vertex ID and the value is the corresponding vertex object.
IVertexCollection oVertices = oGraph.Vertices;
Dictionary <Int32, IVertex> oVertexIDDictionary =
new Dictionary <Int32, IVertex>(oVertices.Count);
foreach (IVertex oVertex in oVertices)
{
oVertexIDDictionary.Add(oVertex.ID, oVertex);
}
// Tell the SNAP graph library to calculate the clusters.
String sOutputFilePath = CalculateSnapGraphMetrics(oGraph,
eSnapGraphMetric);
if (oBackgroundWorker != null)
{
ReportProgress(2, 3, oBackgroundWorker);
}
// The output file for cluster metrics has a header line followed by
// one line for each vertex that identifies which cluster the vertex is
// in. The vertices are sorted by cluster.
using (StreamReader oStreamReader = new StreamReader(
sOutputFilePath))
{
String sLine = oStreamReader.ReadLine();
Debug.Assert(sLine == "Cluster ID\tVertex ID");
Int32 iLastClusterID = -1;
Community oCommunity = null;
while (oStreamReader.Peek() >= 0)
{
sLine = oStreamReader.ReadLine();
String [] asFields = sLine.Split('\t');
Debug.Assert(asFields.Length == 2);
Int32 iClusterID = ParseSnapInt32GraphMetricValue(asFields, 0);
Int32 iVertexID = ParseSnapInt32GraphMetricValue(asFields, 1);
if (iClusterID != iLastClusterID)
{
oCommunity = new Community();
oCommunity.ID = iClusterID;
oCommunities.AddLast(oCommunity);
iLastClusterID = iClusterID;
}
Debug.Assert(oCommunity != null);
oCommunity.Vertices.Add(oVertexIDDictionary[iVertexID]);
}
}
File.Delete(sOutputFilePath);
return(true);
}
TryCalculateClustersWakitaTsurumi
(
IGraph oGraph,
BackgroundWorker oBackgroundWorker,
out ICollection <Community> oGraphMetrics
)
{
Debug.Assert(oGraph != null);
AssertValid();
IVertexCollection oVertices = oGraph.Vertices;
Int32 iVertices = oVertices.Count;
Int32 iEdges = oGraph.Edges.Count;
IDGenerator oIDGenerator = new IDGenerator(1);
// Create and populate a community for each of the graph's vertices.
LinkedList <Community> oCommunities =
CreateCommunities(oVertices, oIDGenerator);
oGraphMetrics = oCommunities;
if (iVertices == 0 || iEdges == 0)
{
// There is no point in going any further.
return(true);
}
// This max heap is used to keep track of the maximum delta Q value in
// each community. There is an element in the max heap for each
// community. The key is the Community and the value is the
// Community's maximum delta Q.
DeltaQMaxHeap oDeltaQMaxHeap = new DeltaQMaxHeap(iVertices);
// Initialize all the delta Q values.
InitializeDeltaQs(oCommunities, oDeltaQMaxHeap, iEdges);
// Run the algorithm outlined in the Wakita/Tsurumi paper.
BinaryHeapItem <Community, Single> oBinaryHeapItemWithMaximumDeltaQ;
Int32 iMergeCycles = 0;
// Retrieve the community pair with the largest delta Q.
while (oDeltaQMaxHeap.TryGetTop(out oBinaryHeapItemWithMaximumDeltaQ))
{
// Check for cancellation and report progress every
// MergeCyclesPerProgressReport calculations.
if (oBackgroundWorker != null &&
iMergeCycles % MergeCyclesPerProgressReport == 0)
{
if (oBackgroundWorker.CancellationPending)
{
return(false);
}
ReportProgress(iMergeCycles, iVertices, oBackgroundWorker);
}
Community oCommunityWithMaximumDeltaQ =
oBinaryHeapItemWithMaximumDeltaQ.Key;
Single fMaximumGlobalDeltaQ =
oBinaryHeapItemWithMaximumDeltaQ.Value;
if (fMaximumGlobalDeltaQ < 0)
{
// Merging additional communities would yield worse results, so
// quit.
break;
}
// Merge the communities in the community pair with maximum
// delta Q, update the maximum delta Q values for all communities,
// and update the global max heap.
CommunityPair oCommunityPairWithMaximumDeltaQ =
oCommunityWithMaximumDeltaQ.CommunityPairWithMaximumDeltaQ;
MergeCommunities(oCommunities, oCommunityPairWithMaximumDeltaQ,
oDeltaQMaxHeap, iEdges, oIDGenerator);
iMergeCycles++;
}
return(true);
}