Estimate the expected value and variance of a transitivity ratio in a random graph; see http://math.stackexchange.com/questions/280793.

Question280793.java

import java.util.Random;

public class Question280793 {
    final static int n = 100;
    final static int M = 150;

    final static int N = (n * (n - 1)) / 2;

    final static Random random = new Random ();

    public static void main (String [] args) {
        boolean [] [] edges = new boolean [n] [n];
        
        double p = M / (double) N;
        System.out.println (p / (3 - 2 * p) + " +- " + Math.sqrt (18 * (1 - p) * (1 - p) * (3 + p) / (n * n * n * p * (3 - 2*p) * (3 - 2*p) * (3 - 2*p) * (3 - 2*p))));

        double sum = 0;
        double sum2 = 0;

        for (int ntrials = 1;;ntrials++) {
            int total = N;
            int used = M;
            for (int i = 1;i < n;i++)
                for (int j = 0;j < i;j++) {
                    edges [i] [j] = random.nextDouble () < used / (double) total;
                    total--;
                    if (edges [i] [j])
                        used--;
                }

            int count2 = 0;
            int count3 = 0;

            for (int i = 2;i < n;i++)
                for (int j = 1;j < i;j++)
                    for (int k = 0;k < j;k++) {
                        int count = 0;
                        if (edges [i] [j])
                            count++;
                        if (edges [i] [k])
                            count++;
                        if (edges [j] [k])
                            count++;
                        if (count >= 2)
                            count2++;
                        if (count == 3)
                            count3++;
                    }

            double ratio = count3 / (double) count2;
            if (ratio > 0.05)
                System.out.println ("ratio : " + ratio);
            sum += ratio;
            sum2 += ratio * ratio;
            if (((ntrials - 1) & ntrials) == 0) {
                double mean = sum / ntrials;
                double mean2 = sum2 / ntrials;
                System.out.println (ntrials + " : " + mean + " +- " + Math.sqrt (mean2 - mean * mean));
            }
        }
    }
}