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;
}