/// <summary>
/// Return true if the graph is (complete) bipartite
/// Time complexity: O(V + E)
/// </summary>
/// <param name="graph">graph</param>
/// <returns>(bool, bool) - the first item stands for bipartite and the second item stands for complete
/// (true, true) - complete bipartite graph
/// (true, false) - bipartite graph
/// (false, - ) - the graph is not (complete) bipartite</returns>
public static Tuple <bool, bool> IsBipartiteGraph(IGraphInterface graph)
{
// Variable
IVertexInterface vertex;
List <IVertexInterface> neighboursVertexList;
bool isFirstPartite, isBipartite = true;
HashSet <IVertexInterface> firstPartite = new HashSet <IVertexInterface>();
HashSet <IVertexInterface> secondPartite = new HashSet <IVertexInterface>();
Queue <IVertexInterface> vertexQueue = new Queue <IVertexInterface>();
vertex = graph.GetFirstVertex();
vertexQueue.Enqueue(vertex);
firstPartite.Add(vertex);
while (vertexQueue.Count != 0)
{
vertex = vertexQueue.Dequeue();
neighboursVertexList = graph.Neighbours(vertex);
if (firstPartite.Contains(vertex))
{
isFirstPartite = true;
}
else
{
isFirstPartite = false;
}
foreach (IVertexInterface neighbourVertex in neighboursVertexList)
{
if (!firstPartite.Contains(neighbourVertex) && !secondPartite.Contains(neighbourVertex))
{
if (isFirstPartite)
{
secondPartite.Add(neighbourVertex);
}
else
{
firstPartite.Add(neighbourVertex);
}
vertexQueue.Enqueue(neighbourVertex);
}
else
{
if ((firstPartite.Contains(neighbourVertex) && isFirstPartite) || (secondPartite.Contains(neighbourVertex) && !isFirstPartite))
{
isBipartite = false;
}
}
}
}
if (!isBipartite)
{
return(new Tuple <bool, bool>(false, false));
}
// Set bipartites
graph.GetGraphProperty().SetPartites(firstPartite.ToList(), secondPartite.ToList());
// Variable
int countFirstPartiteVertex = firstPartite.Count;
int countSecondPartiteVertex = secondPartite.Count;
// Is the graph a complete bipartite graph
foreach (Vertex firstPartiteVertex in firstPartite)
{
if (graph.CountNeighbours(firstPartiteVertex) != countSecondPartiteVertex)
{
return(new Tuple <bool, bool>(true, false));
}
}
foreach (Vertex secondPartiteVertex in secondPartite)
{
if (graph.CountNeighbours(secondPartiteVertex) != countFirstPartiteVertex)
{
return(new Tuple <bool, bool>(true, false));
}
}
return(new Tuple <bool, bool>(true, true));
}
public void VertexDelete(IVertexInterface vertex)
{
// Component
if (componentsList != null)
{
// More components => copies of components
if (countComponents > 1)
{
// Get component which contains the vertex
IVertexInterface myVertexComponent = null;
IGraphInterface myComponentGraph = null;
foreach (IGraphInterface componentGraph in componentsList)
{
if (componentGraph.ExistsUserName(vertex.GetUserName()))
{
myComponentGraph = componentGraph;
myVertexComponent = myComponentGraph.GetVertexByUserName(vertex.GetUserName());
break;
}
}
// The vertex is component
if (myComponentGraph.CountNeighbours(myVertexComponent) == 0)
{
componentsList.Remove(myComponentGraph);
countComponents--;
isConnected = countComponents == 1 ? true : false;
}
// The vertex is in a component with another vertices
else
{
componentsList = null;
countComponents = null;
isConnected = null;
}
}
else
{
if (cutVertices != null && !cutVertices.Contains(vertex))
{
//componentsList = componentsList;
//countComponents = countComponents;
//isConnected = isConnected;
}
else
{
componentsList = null;
countComponents = null;
isConnected = null;
}
}
}
// Properties
if (isCyclic != null && (bool)isCyclic)
{
isCyclic = null;
}
if (isConnected != null && !(bool)isConnected)
{
isEulerian = EulerianGraphEnum.notEulerian;
}
else
{
isEulerian = EulerianGraphEnum.undefined;
}
// IntegralInvariants
circuitRank = null;
girth = null;
cayleysFormula = null;
// SequencesAndPolynomialsOthers
if (isConnected != null && !(bool)isConnected)
{
spanningTreeBFS = spanningTreeBFS = new List <IEdgeInterface>();
}
else
{
spanningTreeBFS = null;
}
matching = null;
cutVertices = null;
bridges = null;
// DegreeSequence
degreeSequence = null;
maximumVertexDegree = null;
minimumVertexDegree = null;
averageVertexDegree = null;
medianVertexDegree = null;
isDegreeSequenceSorted = false;
isRegular = null;
// Chordal
isChordal = null;
perfectEliminationOrderingList = null;
righNeighborhoodDictionary = null;
// GraphClass
graphClass = GraphClass.GraphClass.GraphClassEnum.undefined;
}
private void Invalid(IGraphInterface graph)
{
// Variable
List <IVertexInterface> vertexList = graph.AllVertices();
List <IVertexInterface> vertexNot2DegreeList = new List <IVertexInterface>();
vertexNot2DegreeList = vertexList.Where(v => graph.CountNeighbours(v) != 2).ToList();
IEdgeInterface edge = new Edge(vertexList.First(), graph.Neighbours(vertexList.First()).First());
// Vertex add
stringBuilder.AppendLine("Vertex add");
stringBuilder.AppendLine("Vertex exists");
try { graph.VertexAdd(vertexList.First()); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
// Vertex delete
stringBuilder.AppendLine("Vertex delete");
stringBuilder.AppendLine("Vertex doesn't exist");
try { graph.VertexDelete(new Vertex()); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
// Vertex contract
stringBuilder.AppendLine("Vertex contract");
stringBuilder.AppendLine("Vertex doesn't exist");
try { graph.VertexContraction(new Vertex()); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
// Vertex suppression
stringBuilder.AppendLine("Vertex suppression");
stringBuilder.AppendLine("Vertex doesn't exist");
try { graph.VertexSuppression(new Vertex()); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
stringBuilder.AppendLine("Invalid vertex degree");
try { graph.VertexSuppression(vertexNot2DegreeList.First()); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
// Vertex expansion
stringBuilder.AppendLine("Vertex expansion");
stringBuilder.AppendLine("Vertex doesn't exist");
try { graph.VertexExpansion(new Vertex()); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
// Edge add
stringBuilder.AppendLine("Edge add");
stringBuilder.AppendLine("Edge exists");
try { graph.EdgeAdd(edge); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
// Edge delete
stringBuilder.AppendLine("Edge delete");
stringBuilder.AppendLine("Edge doesn't exist");
try { graph.EdgeDelete(new Edge(new Vertex(), new Vertex())); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
// Edge contract
stringBuilder.AppendLine("Edge contract");
stringBuilder.AppendLine("Edge doesn't exist");
try { graph.EdgeContraction(new Edge(new Vertex(), new Vertex())); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
// Edge subdivision
stringBuilder.AppendLine("Edge subdivision");
stringBuilder.AppendLine("Edge doesn't exist");
try { graph.EdgeSubdivision(new Edge(new Vertex(), new Vertex())); }
catch (MyException.GraphException.GraphException e) { stringBuilder.AppendLine(e.Message); }
}