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POImplementing Barabasi-Albert Method for Creating Scale-Free Networks
 

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  1. POImplementing Barabasi-Albert Method for Creating Scale-Free Networks
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    <p>I'm trying to implement a very simple preferential attachment algorithm for creating scale-free networks. These have degree distributions that follow a power-law, i.e. P(k) ~ k^-g, where g is the exponent. The algorithm below should produce degree distributions with the exponent equal 3 +/- 0.1, my implementation does not the exponents are closer to 2.5 +/- 0.1. I'm clearly not understanding something somewhere and continue to get it wrong.</p> <p>I'm sorry if this is in the wrong place, I couldn't decide whether it should be in stackoverflow or maths.stackexchange.com.</p> <pre><code>The Algorithm: Input: Number of Nodes N; Minimum degree d &gt;= 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 </code></pre> <p>My Implementation in C/C++:</p> <pre><code>void SF_LCD(std::vector&lt; std::vector&lt;int&gt; &gt;&amp; graph, int N, int d) { if(d &lt; 1 || d &gt; N - 1) { std::cerr &lt;&lt; "Error: SF_LCD: k_min is out of bounds: " &lt;&lt; d; } std::vector&lt;int&gt; M; M.resize(2 * N * d); int r = -1; //Use Batagelj's implementation of the LCD model for(int v = 0; v &lt; N; v++) { for(int i = 0; i &lt; 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 &lt; M.size(); v += 2) { int m = M[v]; int n = M[v + 1]; graph[m].push_back(n); graph[n].push_back(m); } } </code></pre> <p>Here's an example of a degree distribution I get for N = 10,000 and d = 1:</p> <pre><code>1 6674 2 1657 3 623 4 350 5 199 6 131 7 79 8 53 9 57 10 27 11 17 12 20 13 15 14 12 15 5 16 8 17 5 18 10 19 7 20 6 21 5 22 6 23 4 25 4 26 2 27 1 28 6 30 2 31 1 33 1 36 2 37 2 43 1 47 1 56 1 60 1 63 1 64 1 67 1 70 1 273 1 </code></pre>
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