Question

我正在尝试实现一种非常简单的优先附加算法来创建无标度网络。它们具有遵循幂律的度分布，即P（k）~k ^ -g，其中g是指数。下面的算法应该产生指数等于3 +/- 0.1的度分布，我的实现并不是指数更接近2.5 +/- 0.1。我显然不会在某处理解某些事情并继续弄错。

我很抱歉，如果这是在错误的地方，我无法决定它是否应该在stackoverflow或maths.stackexchange.com。

The Algorithm:
Input: Number of Nodes N; Minimum degree d >= 1.
Output: scale-free multigraph
G = ({0,....,N-1}, E)
M: array of length 2Nd
for (v=0,...,n-1)
   for (i=0,...,d-1)
      M[2(vd+i)] = v;
      r = random number selected uniformly at random from {0,.....,2(vd+i)};
      M[2(vd+i)+1] = M[r];
   end
end

E = {};
for (i=0,...,nd-1)
   E[i] = {M[2i], M[2i+1]}
end

我在C / C ++中的实现：

void SF_LCD(std::vector< std::vector<int> >& graph, int N, int d) {
    if(d < 1 || d > N - 1) {
        std::cerr << "Error: SF_LCD: k_min is out of bounds: " << d;
    }

    std::vector<int> M;
    M.resize(2 * N * d);

    int r = -1;
    //Use Batagelj's implementation of the LCD model
    for(int v = 0; v < N; v++) {
        for(int i = 0; i < d; i++) {
            M[2 * (v * d + i)] = v;
             r = mtr.randInt(2 * (v * d + i));
            M[2 * (v * d + i) + 1] = M[r];
        }
    }

    //create the adjacency list
    graph.resize(N);
    bool exists = false;
    for(int v = 0; v < M.size(); v += 2) {
        int m = M[v];
        int n = M[v + 1];

        graph[m].push_back(n);
        graph[n].push_back(m);
    }
}

这是我得到的N = 10,000和d = 1的度数分布的例子：

Answer 1

好的，所以我无法弄清楚如何使这个特定算法正常工作，而是我使用了另一个算法。

The Algorithm:
Input: Number of Nodes N; 
       Initial number of nodes m0; 
       Offset Exponent a; 
       Minimum degree 1 <= d <= m0.
Output: scale-free multigraph G = ({0,....,N-1}, E).

1) Add m0 nodes to G.
2) Connect every node in G to every other node in G, i.e. create a complete graph.
3) Create a new node i.
4) Pick a node j uniformly at random from the graph G. Set P = (k(j)/k_tot)^a.
5) Pick a real number R uniformly at random between 0 and 1.
6) If P > R then add j to i's adjacency list.
7) Repeat steps 4 - 6 until i has m nodes in its adjacency list.
8) Add i to the adjacency list of each node in its adjacency list.
9) Add i to to the graph.
10) Repeat steps 3 - 9 until there are N nodes in the graph.

其中k（j）是图G中节点j的度数，k_tot是图G中边数（总度数）的两倍。

通过改变参数，可以控制度分布的指数。 a = 1.22给出指数g（P（k）~k ^ -g）为3 +/- 0.1。

实现Barabasi-Albert方法创建无标度网络

1 个答案: