/// <summary>
/// Deletes an edge, if exists, between two vertices.
/// </summary>
/// <returns><c>true</c>, if edge was removed, <c>false</c> otherwise.</returns>
/// <param name="firstVertex">First vertex.</param>
/// <param name="secondVertex">Second vertex.</param>
public bool RemoveEdge(T firstVertex, T secondVertex)
{
bool ret = false;
Clique splitting;
Clique removing = new Clique();
removing.Add(firstVertex);
removing.Add(secondVertex);
foreach (var clan in new HashSet <Clique>(_cliques)) //Iterating over a clone of cliques
{
if (clan.IsSupersetOf(removing))
{
// clan should be eliminated from cliques and replaced by maximal refinements
_cliques.Remove(clan);
splitting = new Clique(clan);
splitting.Remove(firstVertex);
_cliques.Add(splitting);
ExpandToMaximal(splitting);
splitting = new Clique(clan);
splitting.Remove(secondVertex);
_cliques.Add(splitting);
ExpandToMaximal(splitting);
ret = true; // return true when finished
}
}
return(ret);
}
/// <summary>
/// Expands a clique to a maximal complete
/// </summary>
/// <param name="clan">Clique to expand</param>
void ExpandToMaximal(Clique clan)
{
Clique maximalityChecker; // Temporal clique for checking maximality
// Expand NewClique to a maximal complete subgraph
foreach (var z in Vertices)
{
if (!clan.Contains(z))
{
maximalityChecker = new Clique(clan);
maximalityChecker.Add(z);
if (IsComplete(maximalityChecker))
{
clan.Add(z);
}
}
}
// Destroy every no maximal elements of the graph
HashSet <Clique> clone = new HashSet <Clique>(_cliques);
clone.Remove(clan);
foreach (var c in clone) // Iterate over a clone of _cliques
{
if (clan.IsSupersetOf(c))
{
_cliques.Remove(c);
}
}
}
/// <summary>
/// Connects two vertices together.
/// </summary>
/// <returns><c>true</c>, if edge was added, <c>false</c> otherwise.</returns>
/// <param name="firstVertex">First vertex.</param>
/// <param name="secondVertex">Second vertex.</param>
public bool AddEdge(T firstVertex, T secondVertex)
{
if (HasEdge(firstVertex, secondVertex))
{
return(false);
}
Clique NewClique = new Clique(); // The new clique that contains the edge (firstVertex, secondVertex)
_cliques.Add(NewClique);
_vertices.Add(firstVertex);
_vertices.Add(secondVertex);
NewClique.Add(firstVertex);
NewClique.Add(secondVertex);
ExpandToMaximal(NewClique);
return(true);
}
/// <summary>
/// Initializes a new instance of the <see cref="DataStructures.Graphs.CliqueGraph`1"/> class.
/// Copies the model from another graph.
/// </summary>
/// <param name="graph">Graph.</param>
public CliqueGraph(IGraph <T> graph)
: this(graph.Vertices)
{
foreach (var startVert in Vertices)
{
foreach (var endVert in graph.Neighbours(startVert))
{
if (!HasEdge(startVert, endVert))
{
// Add vortex
Clique newClan = new Clique();
newClan.Add(startVert);
newClan.Add(endVert);
ExpandToMaximal(graph, newClan);
_cliques.Add(newClan);
}
}
}
}
/// <summary>
/// Expands a clique to a maximal complete in a given graph
/// </summary>
/// <param name="graph">Graph to use to determine maximality.</param>
/// <param name="clan">Clique to expand.</param>
static void ExpandToMaximal(IGraph <T> graph, Clique clan)
{
Clique tempo; // Temporal clique for checking maximality
// Expand NewClique to a maximal complete subgraph
foreach (var z in graph.Vertices)
{
if (!clan.Contains(z))
{
tempo = new Clique(clan);
tempo.Add(z);
if (IsComplete(graph, tempo))
{
clan.Add(z);
}
}
}
}
