size_t scn::MRTofRandomWalk(UGraph::pGraph graph) { size_t total_steps = 0; vector<size_t> neighbors; srand(size_t(time(00))); //#pragma omp parallel for shared(total_steps) private(neighbors) for(size_t source = 0; source < graph->GetNumberOfNodes(); source++) { // if(omp_get_thread_num() == 0) // cout<<"Random walk on "<<source<<"/"<<graph->GetNumberOfNodes() / omp_get_num_procs()<<endl; size_t next = source; size_t steps = 0; do { neighbors.assign(graph->find(next)->begin(), graph->find(next)->end()); next = neighbors[rand() % neighbors.size()]; steps++; }while(next != source); //#pragma omp critical { total_steps += steps; } } return static_cast<double>(total_steps) / static_cast<double>(graph->GetNumberOfNodes()); }
void scn::GetClusteringCoeffDist(vector<pair<double, double>> &distribution, UGraph::pGraph graph, double slide) { assert(slide >= 0 && slide <= 1); if(slide == 0) { unordered_map <double,double> cc_dist; for(auto node = graph->begin(); node != graph->end(); node++) { cc_dist[GetClusteringCoeff(graph,*node)]++; } for(auto iter = cc_dist.begin(); iter != cc_dist.end(); iter++) { iter->second /= graph->GetNumberOfNodes(); } distribution.assign(cc_dist.begin(), cc_dist.end()); sort(distribution.begin(), distribution.end()); } else { unordered_map<size_t, double> cc_dist; for(auto node = graph->begin(); node != graph->end(); node++) { cc_dist[static_cast<size_t>(GetClusteringCoeff(graph, *node) / slide)]++; } distribution.assign(cc_dist.begin(), cc_dist.end()); sort(distribution.begin(), distribution.end()); for(auto iter = distribution.begin(); iter != distribution.end(); iter++) { iter->first = iter->first * slide + slide / 2; if(iter->first > 1) iter->first = 1; iter->second /= graph->GetNumberOfNodes(); } } }
Matrix scn::GetGeodesicMatrix(UGraph::pGraph graph) { Matrix result(graph->GetNumberOfNodes(), graph->GetNumberOfNodes()); std::unordered_map<size_t,size_t> distance; //auto& distance = distance_sssp; size_t diameter = 0; for(auto node = graph->begin(); node != graph->end(); node++) { RunSPFA(graph,*node,distance); for(auto iter = distance.begin(); iter != distance.end(); iter++) { result(*node, iter->first) = iter->second; if(iter->second > diameter) { diameter = iter->second; } } } //result.Print("Matrix:"); for(size_t i = 0; i < result.GetHeight(); i++) { result(i, i) = - valarray<double>(result.row(i)).sum(); } result /= static_cast<double>(diameter); return result; }
double scn::GetAverageSearchInfo(UGraph::pGraph graph) { double sum = 0; for(auto node1 = graph->begin(); node1 != graph->end(); node1++) { for(auto node2 = graph->begin(); node2 != graph->end(); node2++) { if(node1 == node2) continue; sum += GetSearchInfo(graph,*node1, *node2); } } return sum / static_cast<double>(graph->GetNumberOfNodes() * graph->GetNumberOfNodes()); }
void scn::WriteToNetFile(char* path, UNetwork<>::pNetwork &network) { using std::endl; std::ofstream outfile(path,ios_base::trunc); UGraph::pGraph graph = network->GetTopology(); outfile<<"*Vertices "<<graph->GetNumberOfNodes()<<endl; //write node for(auto node = graph->begin(); node != graph->end(); node++) { auto position = network->GetNodePosition(*node); outfile<<*node + 1<<" "<<*node + 1<<" "<<position[0]<<" " <<position[1]<<" "<<position[2]<<endl; } outfile<<"*Arcs"<<endl; outfile<<"*Edges"<<endl; //write edge for(auto node = graph->begin(); node != graph->end(); node++) { for(auto other = node->begin(); other != node->end(); other++) { if(*other < *node) { outfile<<*node + 1<<" "<<*other + 1<<" 1"<<endl; } } } outfile.close(); }
QUNetwork::QUNetwork(UGraph::pGraph &graph) :UNetwork(graph) { CreateScene(graph->GetNumberOfNodes()); //create draw node for(auto node = graph->begin(); node != graph->end(); node++) { pNode data = new QNodeItem(this); data->indexOfNode = *node; data->SetText(QString("%1").arg(*node)); SetNodeData(node, data); } //create position CreateCirclePosition(); //add draw edge pEdge data; for(auto node = graph->begin(); node != graph->end(); node++) { for(auto other = node->begin(); other != node->end(); other++) { data = new QEdgeItem(GetNodeData(node)->pos(), GetNodeData(*other)->pos()); SetEdgeData(node, *other, data); } } }
double scn::ComputeAverageDegree(UGraph::pGraph graph) { double sum = 0; for(auto node = graph->begin(); node != graph->end(); node++) { sum += node->GetDegree(); } return sum / graph->GetNumberOfNodes(); }
double scn::GetHideInfo(UGraph::pGraph graph,size_t indexOfNode) { double sum = 0; for(auto node = graph->begin(); node != graph->end(); node++) { if(*node == indexOfNode) continue; sum += GetSearchInfo(graph,*node, indexOfNode); } return sum / static_cast<double>(graph->GetNumberOfNodes()); }
double scn::GetCyclicCoeff(UGraph::pGraph graph,size_t indexOfNode) { //IndexList edges; std::pair<IndexList, IndexList> result; std::unordered_map<size_t,size_t> distance; //auto& distance = distance_sssp; distance.clear(); if(indexOfNode != UGraph::NaF) {//one vertex result = graph->RemoveNode(indexOfNode); IndexList& edges = result.first; double sum = 0; for(auto head = edges.begin(); head != edges.end(); head++) { RunSPFA(graph,*head,distance); for(auto tail = head + 1; tail != edges.end(); tail++) { sum += 1.0 / static_cast<double>(distance[*tail] + 2); } } ///restore graph->AddEdge(graph->AddNode(indexOfNode), edges); return 2 * sum / static_cast<double>(edges.size() * (edges.size() - 1)); } else {//the whole network //copy node list IndexList nodes = graph->CopyIndexOfNodes(); double total_sum = 0; for(auto node = nodes.begin(); node != nodes.end(); node++) { result = graph->RemoveNode(*node); IndexList& edges = result.first; double sum = 0; for(auto head = edges.begin(); head != edges.end(); head++) { RunSPFA(graph,*head,distance); for(auto tail = head + 1; tail != edges.end(); tail++) { sum += 1.0 / static_cast<double>(distance[*tail] + 2); } } ///restore, add node first, then add list of edges of this node graph->AddEdge(graph->AddNode(*node), edges); //accumulate total_sum += 2 * sum / static_cast<double>(edges.size() * (edges.size() - 1)); } return total_sum / static_cast<double>(graph->GetNumberOfNodes()); } }
void scn::RunDjikstra(UGraph::pGraph graph,size_t indexOfSource,std::unordered_map<size_t,size_t> &distance) { //auto& distance = distance_sssp;//using distance_sssp eariler assert(graph->HasNode(indexOfSource)); //init //distance.reserve(graph->GetNumberOfNodes()); for(auto node = graph->begin(); node != graph->end(); node++) { distance[*node] = Graph::NaF; } distance[indexOfSource] = 0; list<size_t> queue; //fill index of nodes into queue for(size_t i = 0; i < graph->GetNumberOfNodes(); i++) { queue.push_back(i); } //begin size_t next_distance; while(!queue.empty()) { //get min one auto min = min_element(queue.begin(), queue.end(), [&](const size_t &one, const size_t &two)->bool { if(distance[one] < distance[two]) return true; else return false; }); auto node = graph->find(*min); if(distance[*node] < Graph::NaF) next_distance = distance[*node] + 1; else next_distance = Graph::NaF; //relax neighbors for(auto other = node->begin(); other != node->end(); other++) { if(distance[*other] > next_distance) { distance[*other] = next_distance; } } queue.erase(min); } }
double scn::GetEntropyOfDegreeDist(UGraph::pGraph graph) { //get degree distribution std::unordered_map<size_t,size_t> distribution; for(auto node = graph->begin(); node != graph->end(); node++) { distribution[node->GetDegree()]++; } //compute the entropy double sum = 0; double pk = 0; for(auto iter = distribution.begin(); iter != distribution.end(); iter++) { pk = static_cast<double>(iter->second) / graph->GetNumberOfNodes(); sum -= pk * log(pk)/log(2.0); } return sum; }
double scn::GetClusteringCoeff(UGraph::pGraph graph,size_t indexOfNode) { if(indexOfNode == UGraph::NaF) {//the whole network double coefficient = 0; for(auto node = graph->begin(); node != graph->end(); node++) { size_t numberOfTriangles = 0; for(auto other1 = node->begin(); other1 != node->end(); other1++) { for(auto other2 = other1 + 1; other2 != node->end(); other2++) { if(graph->HasEdge(*other1, *other2)) numberOfTriangles++; } } if(node->GetDegree()>1) { coefficient += 2 * static_cast<double>(numberOfTriangles) / (node->GetDegree() * (node->GetDegree() - 1)); } } return coefficient / graph->GetNumberOfNodes(); } else {//one vertex auto node = graph->find(indexOfNode); double numberOfTriangles = 0; for(auto other1 = node->begin(); other1 != node->end(); other1++) { for(auto other2 = other1 + 1; other2 != node->end(); other2++) { if(graph->HasEdge(*other1, *other2)) numberOfTriangles++; } } if(node->GetDegree()>1) return 2 * numberOfTriangles / (node->GetDegree() * (node->GetDegree() - 1)); else return 0.0; } }
//注意:需要特征值计算,Fortran void scn::ComputeSpectralDensity(std::unordered_map<double,double> &result,UGraph::pGraph graph,double slide) { auto lambdas = ComputeSpectrum(graph); int start = floor(lambdas[0]); int end = ceil(lambdas[lambdas.size() - 1]); for(int i = 0; i < (end - start) / slide; i++) { result[double(start) + i * slide] = 0; } for(int ii=0;ii<lambdas.size();ii++) { result[floor(lambdas[ii] / slide) * slide]++; } //normalized for(auto iter = result.begin(); iter != result.end(); iter++) { iter->second /= graph->GetNumberOfNodes(); } //return result; }
double scn::GetGlobalEfficiency(UGraph::pGraph graph) { double sum = 0; std::unordered_map<size_t,size_t> distance; //auto& distance = distance_sssp; distance.clear(); for(auto node = graph->begin(); node != graph->end(); node++) { RunSPFA(graph,*node,distance); //add distance for(auto iter = distance.begin(); iter != distance.end(); iter++) { if(iter->first == *node) continue; sum += 1.0 / static_cast<double>(iter->second); } } double size = static_cast<double>(graph->GetNumberOfNodes()); return size * (size - 1) / sum; }
void scn::GetClusteringDegreeCorre(pair<double, vector<pair<size_t, double>>> &correlation,UGraph::pGraph graph) { unordered_map<size_t, double> degree_dist, degree_cc; //accumulate degree and clustering coefficient for(auto node = graph->begin(); node != graph->end(); node++) { degree_dist[node->GetDegree()]++; degree_cc[node->GetDegree()] += GetClusteringCoeff(graph,*node); } //get average double degree_average = 0;//1-order moment of degree double degree_sqr_average = 0;//2-order moment of degree for(auto iter = degree_dist.begin(); iter != degree_dist.end(); iter++) { //average clustering coefficient in each degree degree_cc[iter->first] /= iter->second; //probability of degree iter->second /= graph->GetNumberOfNodes(); //1-order moment of degree degree_average += iter->first * iter->second; //2-order moment of degree degree_sqr_average += iter->first * iter->first * iter->second; } //compute global clustering degree correlation double clustering_degree_corre = 0; for(auto iter = degree_dist.begin(); iter != degree_dist.end(); iter++) { clustering_degree_corre += iter->first * (iter->first - 1) * iter->second * degree_cc[iter->first]; } clustering_degree_corre /= (degree_sqr_average - degree_average); //sort and get result correlation.second.assign(degree_cc.begin(), degree_cc.end()); sort(correlation.second.begin(), correlation.second.end()); correlation.first=clustering_degree_corre; }