#include "exports.hpp" #include "graph.hpp" #include "powerlaw.hpp" #include "switchchain.hpp" #include #include #include #include #include #include double getProperty(const DegreeSequence& ds) { std::vector> vals(ds.size()); for (auto& v : vals) { v.resize(ds.size(), 0); } auto D = 0u; for (auto d : ds) D += d; double factor = 1.0 / double(D); for (auto i = 0u; i < ds.size(); ++i) { for (auto j = i + 1; j < ds.size(); ++j) { vals[i][j] = 1.0 - std::exp(-(ds[i] * ds[j] * factor)); } } double result = 0.0; for (auto i = 0u; i < ds.size(); ++i) { for (auto j = i + 1; j < ds.size(); ++j) { for (auto k = j + 1; k < ds.size(); ++k) { result += vals[i][j] * vals[j][k] * vals[i][k]; } } } return result; } int main() { // Generate a random degree sequence std::mt19937 rng(std::random_device{}()); // Goal: // Degrees follow a power-law distribution with some parameter tau // Expect: #tri = const * n^{ something } // The goal is to find the 'something' by finding the number of triangles // for different values of n and tau float tauValues[] = {2.1f, 2.5f, 2.9f}; Graph g; std::ofstream outfile("graphdata_dsp.m"); outfile << '{'; bool outputComma = false; for (int numVertices = 1000; numVertices <= 1000; numVertices += 1000) { 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 for (int degreeSample = 0; degreeSample < 2000; ++degreeSample) { // Generate a graph // might require multiple tries for (int i = 1; ; ++i) { std::generate(ds.begin(), ds.end(), [°Dist, &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()++; } if (g.createFromDegreeSequence(ds)) break; // When 10 tries have not worked, output a warning if (i % 10 == 0) { std::cerr << "Warning: could not create graph from " "degree sequence. Trying again...\n"; } } 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; int mixingTime = 32*(32.0f - 10.0f*(tau - 2.0f)) * numVertices; //40000; 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; } for (int i = 0; i < measurements; ++i) { for (int j = 0; j < measureSkip; ++j) if (chain.doMove()) ++movesDone; trianglesTotal += chain.g.countTriangles(); } std::cout << movesDone << '/' << mixingTime + measurements * measureSkip << " moves succeeded (" << 100.0f * float(movesDone) / float(mixingTime + measurements * measureSkip) << "%)."; std::cout << std::flush; //std::cout << std::endl; if (outputComma) outfile << ',' << '\n'; outputComma = true; float avgTriangles = float(trianglesTotal) / float(measurements); outfile << '{' << '{' << numVertices << ',' << tau << '}'; outfile << ',' << avgTriangles; outfile << ',' << getProperty(ds) << '}' << std::flush; std::cout << std::endl; } } } outfile << '}'; return 0; }