/// <summary>
/// Return a subgraph
/// If the graph is not initialized throws GraphInitializationException
/// Time complexity: O(V + E)
/// Space complexity: O(V + E)
/// </summary>
/// <param name="graph">graph</param>
/// <param name="vertexList">list of vertices which will be in the subgraph</param>
/// <returns>subgraph</returns>
public static IGraphInterface SubGraph(IGraphInterface graph, List <IVertexInterface> vertexList)
{
// Variable
IGraphEdgeListInterface subGraph;
List <IVertexInterface> neighboursList;
if (!graph.GetIsInitialized())
{
throw new MyException.GraphException.GraphInitializationException();
}
subGraph = new GraphEdgeList(vertexList.Count);
subGraph.SetName("Subgraph - " + graph.GetName());
foreach (IVertexInterface vertex in vertexList)
{
neighboursList = graph.Neighbours(vertex).Intersect(vertexList).ToList();
if (neighboursList.Count == 0)
{
subGraph.AddVertex(vertex.GetUserName());
continue;
}
foreach (IVertexInterface neighbour in neighboursList)
{
subGraph.AddEdge(vertex.GetUserName(), neighbour.GetUserName());
}
}
subGraph.InitializeGraph();
return(subGraph);
}
/// <summary>
/// Return a complement graph
/// If the graph is not initialized throws GraphInitializationException
/// </summary>
/// <param name="graph">graph</param>
/// <returns>complement graph</returns>
public static IGraphInterface ComplementGraph(IGraphInterface graph)
{
// Variable
IGraphEdgeListInterface complementGraph;
List <IVertexInterface> vertexList;
List <IVertexInterface> neighboursList;
List <IVertexInterface> intersectionVertexAndNeighboursList;
if (!graph.GetIsInitialized())
{
throw new MyException.GraphException.GraphInitializationException();
}
complementGraph = new GraphEdgeList(graph.GetRealCountVertices());
complementGraph.SetName("Complement graph - " + graph.GetName());
vertexList = graph.AllVertices();
// Add edges
foreach (IVertexInterface vertex in vertexList)
{
neighboursList = graph.Neighbours(vertex);
neighboursList.Add(vertex);
intersectionVertexAndNeighboursList = vertexList.FindAll(v => !neighboursList.Contains(v)).ToList();
if (intersectionVertexAndNeighboursList.Count == 0)
{
complementGraph.AddVertex(vertex.GetUserName());
continue;
}
foreach (IVertexInterface neighbour in intersectionVertexAndNeighboursList)
{
complementGraph.AddEdge(vertex.GetUserName(), neighbour.GetUserName());
}
}
complementGraph.InitializeGraph();
return(complementGraph);
}
/// <summary>
/// Copy a graph
/// If the graph is not initialized throws GraphInitializationException
/// Time complexity: O(V + E)
/// Space complexity: O(V + E)
/// </summary>
/// <param name="graph">graph</param>
/// <returns>graph copy</returns>
public static IGraphInterface CopyGraph(IGraphInterface graph)
{
if (!graph.GetIsInitialized())
{
throw new MyException.GraphException.GraphInitializationException();
}
// Variable
IGraphEdgeListInterface graphCopy;
List <IVertexInterface> neighboursVertexList;
List <IVertexInterface> allVerticesList = graph.AllVertices();
graphCopy = new GraphEdgeList(graph.GetGraphProperty().GetCountVertices());
graphCopy.SetName(graph.GetName());
foreach (IVertexInterface vertex1 in allVerticesList)
{
neighboursVertexList = graph.Neighbours(vertex1);
if (neighboursVertexList.Count == 0)
{
graphCopy.AddVertex(vertex1.GetUserName());
continue;
}
foreach (IVertexInterface vertex2 in neighboursVertexList)
{
graphCopy.AddEdge(vertex1.GetUserName(), vertex2.GetUserName());
}
}
graphCopy.InitializeGraph();
return(graphCopy);
}
/// <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));
}
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); }
}
/// <summary>
/// Return a line graph
/// If the graph is not initialized throws GraphInitializationException
/// If teh graph has 0 edges throws GraphLineGraphInvalidCountOfEdges
/// </summary>
/// <param name="graph">graph</param>
/// <returns>line graf</returns>
public static IGraphInterface LineGraph(IGraphInterface graph)
{
// Variable
int idVertex1, idVertex2;
string idNewVertex, userNameNewVertex;
string userNameVertex1, userNameVertex2;
IGraphEdgeListInterface lineGraph;
List <IVertexInterface> vertexList;
List <IVertexInterface> neighboursList;
Dictionary <string, IVertexInterface> vertexMap;
List <IVertexInterface> neighboursNewList;
if (!graph.GetIsInitialized())
{
throw new MyException.GraphException.GraphInitializationException();
}
if (graph.GetGraphProperty().GetCountEdges() == 0)
{
throw new MyException.GraphException.GraphLineGraphInvalidCountOfEdges(graph.GetGraphProperty().GetCountEdges().ToString());
}
lineGraph = new GraphEdgeList(graph.GetGraphProperty().GetCountEdges());
lineGraph.SetName("Line graph - " + graph.GetName());
vertexMap = new Dictionary <string, IVertexInterface>();
vertexList = graph.AllVertices();
foreach (IVertexInterface vertex in vertexList)
{
idVertex1 = vertex.GetIdentifier();
userNameVertex1 = vertex.GetUserName();
neighboursList = graph.Neighbours(vertex);
neighboursNewList = new List <IVertexInterface>();
foreach (IVertexInterface neighbour in neighboursList)
{
idVertex2 = neighbour.GetIdentifier();
userNameVertex2 = neighbour.GetUserName();
if (idVertex1 < idVertex2)
{
idNewVertex = idVertex1.ToString() + idVertex2.ToString();
userNameNewVertex = userNameVertex1 + userNameVertex2;
}
else
{
idNewVertex = idVertex2.ToString() + idVertex1.ToString();
userNameNewVertex = userNameVertex2 + userNameVertex1;
}
if (!vertexMap.TryGetValue(idNewVertex, out IVertexInterface newVertex))
{
newVertex = new Vertex(userNameNewVertex);
vertexMap.Add(idNewVertex, newVertex);
}
neighboursNewList.Add(newVertex);
}
if (neighboursList.Count == 1)
{
lineGraph.AddVertex(neighboursNewList.First().GetUserName());
continue;
}
for (int i = 0; i < neighboursNewList.Count - 1; i++)
{
for (int j = i + 1; j < neighboursNewList.Count; j++)
{
lineGraph.AddEdge(neighboursNewList[i].GetUserName(), neighboursNewList[j].GetUserName());
}
}
}
lineGraph.InitializeGraph();
return(lineGraph);
}