#include "exports.hpp" #include "graph.hpp" #include "powerlaw.hpp" #include #include #include #include #include #include // Its assumed that u,v are distinct. // Check if all four vertices are distinct bool edgeConflicts(const Edge& e1, const Edge& e2) { return (e1.u == e2.u || e1.u == e2.v || e1.v == e2.u || e1.v == e2.v); } class SwitchChain { public: SwitchChain() : mt(std::random_device{}()), permutationDistribution(0.5) // permutationDistribution(0, 2) { // random_device uses hardware entropy if available // std::random_device rd; // mt.seed(rd()); } ~SwitchChain() {} bool initialize(const Graph& gstart) { if (gstart.edgeCount() == 0) return false; g = gstart; edgeDistribution.param( std::uniform_int_distribution<>::param_type(0, g.edgeCount() - 1)); return true; } bool doMove() { Edge e1, e2; int e1index, e2index; int timeout = 0; // Keep regenerating while conflicting edges do { e1index = edgeDistribution(mt); e2index = edgeDistribution(mt); e1 = g.getEdge(e1index); e2 = g.getEdge(e2index); ++timeout; if (timeout % 100 == 0) { std::cerr << "Warning: sampled " << timeout << " random edges but they keep conflicting.\n"; } } while (edgeConflicts(e1, e2)); // Consider one of the three possible permutations // 1) e1.u - e1.v and e2.u - e2.v (original) // 2) e1.u - e2.u and e1.v - e2.v // 3) e1.u - e2.v and e1.v - e2.u bool switchType = permutationDistribution(mt); return g.exchangeEdges(e1index, e2index, switchType); } Graph g; std::mt19937 mt; std::uniform_int_distribution<> edgeDistribution; //std::uniform_int_distribution<> permutationDistribution; std::bernoulli_distribution permutationDistribution; }; 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, 2.2f, 2.3f, 2.4f, 2.5f, 2.6f, 2.7f, 2.8f}; Graph g; std::ofstream outfile("graphdata.m"); outfile << '{'; bool outputComma = false; for (int numVertices = 200; numVertices <= 1000; numVertices += 100) { 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 for (int degreeSample = 0; degreeSample < 500; ++degreeSample) { // Generate a graph // might require multiple tries for (int i = 1; ; ++i) { std::generate(ds.begin(), ds.end(), [°Dist, &rng] { return degDist(rng); }); 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; constexpr int mixingTime = 40000; constexpr int measureTime = 20000; constexpr int measureSkip = 200; // Take a sample every ... steps constexpr int measurements = (measureTime - 1) / measureSkip + 1; int movesDone = 0; int triangles[measurements]; for (int i = 0; i < mixingTime; ++i) { if (chain.doMove()) ++movesDone; } for (int i = 0; i < measureTime; ++i) { if (chain.doMove()) ++movesDone; if (i % measureSkip == 0) triangles[i / measureSkip] = chain.g.countTriangles(); } std::cout << movesDone << '/' << mixingTime + measureTime << " moves succeeded." << std::endl; if (outputComma) outfile << ','; outputComma = true; std::sort(ds.begin(), ds.end()); outfile << '{' << '{' << numVertices << ',' << tau << '}'; outfile << ',' << triangles << ',' << ds << '}' << std::flush; } } } outfile << '}'; return 0; }