How to obtain all the subgraphs from a graph?

Question

How to obtain all the subgraphs of a fixed size from a graph, in pseudocode? (brute force)

Without external libraries if possible. Thanks!

That would be the cartesian product of the set of all subsets of vertices and the set of all subsets of edges, right? — pau.estalella, Jan 01 '10 at 19:45
Crisco: you've just asked a questions about a clique algorithm. I seriously suggest you try to do your homework yourself, we wont be there during your end of term finals — Alon, Jan 01 '10 at 19:46
If it was homework, believe me I wouldn't be here... Thanks Pau! — Cristo, Jan 01 '10 at 19:49
I don't think Pau's answer is totally correct, as it suggests that the number of edges and number of vertices are independent of each other. Removing a vertex means that certain edges will no longer exist, so a simple Cartesian product of subsets won't do. — avpx, Jan 01 '10 at 19:56
Obviously the resulting graphs should have the edges connecting vertices not in the graph removed. — pau.estalella, Jan 01 '10 at 19:58

pau.estalella · Answer 1 · 2010-01-01T23:19:29.117

4

More or less that would be something along these lines:

GenerateSubgraphs(Graph G):
    powerV = powerset(G.V)
    powerE = powerset(G.E)
    subgraphs = {}
    foreach V in powerV:
        foreach E in powerE:
            accept = true
            foreach edge in E:
                if edge.u not in V or edge.v not in V:
                    accept = false
            if accept:
                subgraphs.insert((V, E))
    return subgraphs

EDIT: Fixed indentation of 'edges.insert' line

EDIT: Removed duplicated graphs

edited Jan 01 '10 at 23:19

answered Jan 01 '10 at 20:41

pau.estalella

2,197
1
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This is ok, but really you don't need to build `edges`. If, for a given combination (V, E), E mentions any vertices not in V, you can just skip it. – Jason Orendorff Jan 01 '10 at 22:57
Whoa, that's right. The fixed edges will be generated in another iteration. Fixing it... – pau.estalella Jan 01 '10 at 23:16

score 1 · Answer 2 · answered Jan 01 '10 at 19:49

1

Since a graph is only edges and vertices, find all possible subsets of the vertices and construct all possible subsets of the edges on them.

answered Jan 01 '10 at 19:49

avpx

1,892
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score 0 · Answer 3 · answered May 21 '14 at 13:33

If you are using in terms of boost subgraph i have a follwing solution to iterate all subgraphs and prepare its vector.

// declare the list types
vector<SubGraph*> m_vecSubgraphContainer;
vector<SubGraph*> m_vecBFSOrderedSubgraphs; 

// construct container of subgraph lists in the vector
m_vecSubgraphContainer.push_back(&gInputGraph);

m_vecBFSOrderedSubgraphs.push_back(&gInputGraph);
iterateChildrenGraphs(m_vecBFSOrderedSubgraphs);

// iterating the subgraphs
for(vector<SubGraph*>::iterator itrSubgraph = m_vecSubgraphContainer.begin();
    itrSubgraph != m_vecSubgraphContainer.end();
    ++itrSubgraph)
{
    // for empty graph add dummy node to that graph
    int iNumVertices = num_vertices(**itrSubgraph);
    if(iNumVertices == 0)
    {
        VertexDescriptor vVertex = m_boostGraphWrapper.addVertex(**itrSubgraph, Enum::InvisibleNode);
        // This dummy node will set the size of cluster
        // set height = 80 nd width = 80;
        int iDummyNodeHeight = 80;
        int iDummyNodeWidth = 80;
        m_boostGraphWrapper.setVertexHeight(vVertex,**itrSubgraph, iDummyNodeHeight);
        m_boostGraphWrapper.setVertexWidth(vVertex, **itrSubgraph, iDummyNodeWidth);
    }
}

void CircularLayoutGenerator::iterateChildrenGraphs(vector<SubGraph *> &subgraphQueue)
{
/*
    we have used queue because it will contains reference of subgraphs.
    adding all the subgraphs in queue to iterate one by one in circular way.
*/

// define local queue which will contains the childrens of main graph
vector<SubGraph*> SubgraphSequence;

try
{
    // To iterate input queue which will contain graph reference
    for( vector<SubGraph*>::iterator itrSubgraphQueue = subgraphQueue.begin();
         itrSubgraphQueue != subgraphQueue.end();
         itrSubgraphQueue++)
    {
        // Finding the children upto deep level
        SubGraph::children_iterator itrSubgraph, itrSubgraphEnd;
        for (boost::tie(itrSubgraph, itrSubgraphEnd) = (**itrSubgraphQueue).children();
             itrSubgraph != itrSubgraphEnd;
             ++itrSubgraph)
        {
            // Add children in the global queue container
            m_vecSubgraphContainer.push_back(&(*itrSubgraph));

            // Add children in the local queue conatainer
            SubgraphSequence.push_back(&(*itrSubgraph));
        }
    }
}

// To iterarte the local queue again if ant children is present
if(!SubgraphSequence.empty())
{
    // Recursive call to iterate children
    iterateChildrenGraphs(SubgraphSequence);
}
}

How to obtain all the subgraphs from a graph?

3 Answers3