// The goal is to find the 'something' by finding the number of triangles

    // for different values of n and tau

    float tauValues[] = {2.1f, 2.2f, 2.3f, 2.4f, 2.5f, 2.6f, 2.7f, 2.8f, 2.9f};

    Graph g;

    Graph g1;

    Graph g2;

    std::ofstream outfile("graphdata_exponent.m");

    outfile << '{';

    bool outputComma = false;

        for (float tau : tauValues) {

            DegreeSequence ds(numVertices);

            powerlaw_distribution degDist(tau, 1, numVertices);

            //std::poisson_distribution<> degDist(12);

            // For a single n,tau take samples over several instances of

            // the degree distribution.

            // 500 samples seems to give reasonable results

                // Generate a graph

                // might require multiple tries

                for (int i = 1; ; ++i) {

                    std::generate(ds.begin(), ds.end(),

                                  [&degDist, &rng] { return degDist(rng); });

                    // First make the sum even

                    unsigned int sum = std::accumulate(ds.begin(), ds.end(), 0);

                    if (sum % 2) {

                        continue;

                        // Can we do this: ??

                        ds.back()++;

                    }

                    }

                }

                SwitchChain chain;

                if (!chain.initialize(g)) {

                    std::cerr << "Could not initialize Markov chain.\n";

                    return 1;

                }

                std::cout << "Running n = " << numVertices << ", tau = " << tau

                          << ". \t" << std::flush;

                constexpr int measurements = 50;

                constexpr int measureSkip =

                    200; // Take a sample every ... steps

                int movesDone = 0;

                long long trianglesTotal = 0;

                for (int i = 0; i < mixingTime; ++i) {

                    if (chain.doMove())

                        ++movesDone;

                }

Contents of each file

graphdata_exponent_mixN.m

    output: {{n,tau},avgTriangles}

    n from 200 to 2000 with step 200

    initial ErdosGallai

    mixingTime = N * (32.0f - 26.0f*(tau - 2.0f)) * n

    measurements = 50

    measureSkip = 200

graphdata_initialtris.m

    output: {{n,tau},avgTriangles,{gcm1TrisSum,gcm1TrisCount},{gcm1TrisSum,gcm1TrisCount}}

    simulation was stopped halfway through. Was halfway n=1000

    degreeSamples = 200

    avgTriangles was obtained from switchchain with EG start and

    mixingTime = (32.0f - 20.0f * (tau - 2.0f)) * numVertices;

    measurements = 20

    measureSkip = 200

graphdata_initialtris2.m

    same as above but simulation was stopped during (n,tau)=(1400,2.6)

graphdata_gcm_partial.m

    ??

    output: {{n,tau},triangleseq,ds, {...??...} }

graphdata_partial.m

    output: {{n,tau},triangleseq,ds,greedyTriangles1,greedyTriangles2,greedySeq1,greedySeq2}

    degreeSamples = 200

    mixingTime = 0

    measurements = 50000

    measureSkip = 1