/**
* Removes the vertex and its edges from the graph.
*
* The vertex is removed from the Vertices array by moving all the
* vertices that come after it one place to the left.
*
* The algorithm that removes the edge is illustrated below. Assume
* that the adjacency matrix is (this comments assumes that adjacency
* matrix is used, but using adjacency list or any other data structure
* to store the edges doesn't affect the algorithm presented here):
*
* A B C D E
* A aa ab ac ad ae
* B ba bb bc bd be
* C ca cb cc cd ce
* D da db dc dd de
* E ea eb ec ed ee
*
* where A, B, C, D, E are the vertices. If we're to remove the vertex
* C from the graph, the adjacency matrix transforms into:
*
* A B D E
* A aa ab ad ae
* B ba bb bd be
* D da db dd de
* E ea eb ed ee
*
* The algorithm to remove the edges from/to a given vertex can be split
* in two steps:
*
* 1) The first step handles the edges in the rows above the row to which
* the vertex to be removed belongs to. Note that these edges (such as
* 'ad' or 'be') only need to be copied one column to the left. There's
* no need to change their row in the matrix. The psedo algorithm for
* this step is:
*
* for (i = 0; i < indexof(vertex_to_delete); ++i)
* for (j = indexof(vertex_to_delete) + 1; j < Size; ++j)
* AdjacencyMatrix(i, j - 1) = AdjacencyMatrix(i, j)
*
* where Size is the number of vertices in the graph (including the
* vertex to be removed. This step removes all the edges 'to' the vertex
* that is being removed.
*
* 2) The second step handles the edges in the rows below the row to which
* the vertex to be removed belongs to. Note that edges in the columns
* left to the column to which the deleting vertex belongs to (such as 'da'
* or 'eb') only need to be moved one row up. On the other hand, edges in
* the columns right to the column to which the deleting vertex belongs to
* (such as 'dd' or 'ee') must be moved one row up and one column to the
* left. The psedo code for this is:
*
* for (i = indexof(vertex_to_delete) + 1; i < Size; ++i)
* for (j = 0; j < Size; ++j)
* if (j < indexof(vertex_to_delete))
* AdjacencyMatrix(i - 1, j) = AdjacencyMatrix(i, j)
* else if (j > indexof(vertex_to_delete))
* AdjacencyMatrix(i - 1, j - 1) = AdjacencyMatrix(i, j)
*
* This step removes all the edges 'from' the deleting vertex.
*
* @param vertex_index The index of the vertex to remove.
*/
private void RemoveVertexInternal(int vertex_index)
{
// Remove the vertex from the Vertices array
for (int i = vertex_index + 1; i < Size; ++i)
{
Vertices[i - 1] = Vertices[i];
}
// Remove the edges 'to' the vertex by moving all the edges in
// the columns right to the column to which this vertex belongs
// one column to the left.
for (int i = 0; i < vertex_index; ++i)
{
for (int j = vertex_index + 1; j < Size; ++j)
{
Edges.SetEdge(i, j - 1, Edges.GetEdge(i, j));
}
}
// Remove the edges 'from' the vertex by moving all the edges in
// the rows below the row to which this vertex belongs one row
// up and potentially one column to the left.
for (int i = vertex_index + 1; i < Size; ++i)
{
for (int j = 0; j < Size; ++j)
{
if (j <= vertex_index)
{
// The edges in the columns left to the column to which
// the deleting vertex belongs to only need to be moved
// one row up
Edges.SetEdge(i - 1, j, Edges.GetEdge(i, j));
}
else
{
// The edges in the columns right to the column to which
// the deleting vertex belongs to also need to be moved
// one column to the left.
Edges.SetEdge(i - 1, j - 1, Edges.GetEdge(i, j));
}
}
}
// Decrese the graph size
--Size;
}