如何从一个图中获取所有子图？答案

【问题标题】：How to obtain all the subgraphs from a graph?如何从一个图中获取所有子图？
【发布时间】：2010-01-01 19:40:13
【问题描述】：

如何以伪代码从图中获取所有固定大小的子图？（蛮力）

尽可能不使用外部库。谢谢！

【问题讨论】：

家庭作业？如果是这样，请使用作业标签。
那将是所有顶点子集的集合和所有边子集的集合的笛卡尔积，对吧？
Crisco：你刚刚问了一个关于派系算法的问题。我严重建议你尝试自己做功课，期末期末我们不会在那里
如果是家庭作业，相信我，我不会在这里...谢谢 Pau！
我不认为 Pau 的回答是完全正确的，因为它表明边的数量和顶点的数量是相互独立的。删除一个顶点意味着某些边将不再存在，因此子集的简单笛卡尔积将不会这样做。

标签： algorithm graph brute-force subgraph

【解决方案1】：

或多或少是这样的：

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

编辑：修复了“edges.insert”行的缩进

编辑：删除重复的图表

【讨论】：

这没关系，但实际上你不需要构建edges。如果对于给定的组合 (V, E)，E 提到了不在 V 中的任何顶点，则可以跳过它。
哇，没错。固定边将在另一次迭代中生成。正在修复它...

【解决方案2】：

由于图只有边和顶点，找到所有可能的顶点子集，并在它们上构造所有可能的边子集。

【讨论】：

【解决方案3】：

如果您使用的是 boost 子图，我有一个以下解决方案来迭代所有子图并准备其向量。

// 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);
}
}

【讨论】：