提取图中奇数度顶点的边

Question

I have a graph as follows, represented by an adjacency matrix MyCustomVector<MyCustomVector<int>> graph :

0       1       2       3       4       5       6       7       8       9       10      11      12      13      14      15

1       0       1       1       INF     INF     INF     INF     INF     INF     INF     INF     INF     INF     INF     INF
2       1       0       1       1       1       INF     INF     INF     INF     INF     INF     INF     INF     INF     INF
3       1       1       0       INF     INF     1       INF     INF     INF     INF     INF     INF     INF     INF     INF
4       INF     1       INF     0       1       INF     INF     INF     1       INF     INF     INF     INF     INF     INF
5       INF     1       INF     1       0       1       INF     INF     INF     1       1       INF     INF     INF     INF
6       INF     INF     1       INF     1       0       1       INF     1       1       INF     1       INF     INF     INF
7       INF     INF     INF     INF     INF     1       0       1       INF     INF     INF     INF     1       1       1
8       INF     INF     INF     INF     INF     INF     1       0       INF     INF     INF     INF     INF     INF     1
9       INF     INF     INF     1       INF     1       INF     INF     0       INF     INF     INF     INF     INF     INF
10      INF     INF     INF     INF     1       1       INF     INF     INF     0       INF     INF     INF     INF     INF
11      INF     INF     INF     INF     1       INF     INF     INF     INF     INF     0       1       INF     INF     INF
12      INF     INF     INF     INF     INF     1       INF     INF     INF     INF     1       0       INF     INF     INF
13      INF     INF     INF     INF     INF     INF     1       INF     INF     INF     INF     INF     0       1       INF
14      INF     INF     INF     INF     INF     INF     1       INF     INF     INF     INF     INF     1       0       1
15      INF     INF     INF     INF     INF     INF     1       1       INF     INF     INF     INF     INF     1       0

The leftmost and topmost column and row just represent the # node. I thought it was easier to see. All edges are undirected and have a weight of one. INF indicates that there node A and node B do not share a singular edge.

I can calculate all of the odd degree vertices, which are { 3 4 5 7 14 15 } and they are contained in a vector that I have MyCustomVector<int> oddVertices . What I want to do is build a subgraph of this graph with only these vertices and their edges, so something like this.

0       3       4       5       7       14       15   
3       0       INF     INF     INF     INF      INF
4       INF     0       1       INF     INF      INF
5       INF     1       0       INF     INF      INF
7       INF     INF     INF     0       1        1  
14      INF     INF     INF     1       0        1                                             
15      INF     INF     INF     1       1        0

So that I can run the Floyd Warshall Algorithm on this graph and get

0       3       4       5       7       14       15   
3       0       2       2       2       3        3
4       2       0       1       3       4        4
5       2       1       0       2       1        1
7       2       3       2       0       1        1  
14      3       4       3       1       0        1                                             
15      3       4       3       1       1        0

I am having trouble managing the adjacency matrix and grabbing the columns that I need. Essentially what I want to do is

1. Iterate through the graph
2. Notice that the node we are currently on is contained in oddVertices
3. Add the other nodes that are contained in oddVertices .

I cannot use any other data structure than MyCustomVector , and it only has basic functionality like [] , size() , pop_back() and push_back() .

Answer 1

Simply extract the rows and columns corresponding to the subset of indices:

using std::vector;

/*
** input:
**   adjacency list                adj
**   subset of node indices        v
** output:
**   adj list of induced subgraph  subadj
*/
vector<vector<int>> get_subgraph(vector<vector<int>> const &adj, vector<int> const &v)
{
    vector<vector<int>> subadj(v.length(), vector<int>(v.length()));
    for (unsigned int i = 0; i < v.size(); ++i)
        for (unsigned int j = 0; j < v.size(); ++j)
        {
            subadj[i][j] = adj[v[i]][v[j]];
        }
    return subadj;
}