顶点度均匀的随机无向连接图

Question

I need to create random conected undirected graph with even vertex degrees. I have to do that to test the times of finding Euler cycles for different vertex number (N). The representation of the graph is adjacency list. I have such code:

void make_graph()
{
    int i,a,b,c;
    int nasycenie;

    nasycenie=(0.5)*((N*(N-1))/2);

    if(nasycenie<N-1) nasycenie=N-1;
   for(i=1;i<=nasycenie;++i)
   {
        if(i<N)
        {
        a=rand()%i;
        b=i;
        }
        else
        {
        a=rand()%N;
        b=rand()%(N-1);
        b+=(b>=a);
        }
    L1[a].push_back(b);
    L1[b].push_back(a);
   }
}

It makes connected undirected graph but vertex degrees aren't even. How to improve that to have even vertex degrees?

Answer 1

This code will create the graph you specified , but in AdjacencyMatrix (only half a matrix actulay, since graph is undirect) presentation , it wouldn't be hard to turn it into an AdjacencyList.

bool[vNum][vNum] make_graph(int vNum)
{
    bool[vNum][vNum] adjacency;
    int edgeNum = rand()%C(vNum , 2);
    for(int i=0 ; i<vNum; i++)
    {
        int j=0;
        for(j ; j<i; j++)
        {
            adjacency[i][j] = rand()%2; 
        }

        if(hasOddTrue(adjacency[i] , j))
        {
            int selectedIndex = rand()%j;
            adjacency[i][selectedIndex ] = !adjacency[i][selectedIndex ];
        }
    } 
    return adjacency;
}

bool hasOddTrue(bool[] list , int length)
{
    bool b = false;
    for(int i=0 ; i<length ; i++) { b = xor(b,  list[i]); }
    return b;
}