void scn::GetPSDegreeCorrelation(vector<pair<size_t, double>> &correlation,UGraph::pGraph graph)
{
//get degree distribution
unordered_map<size_t,size_t> degree_dist;
for(auto node = graph->begin(); node != graph->end(); node++)
{
degree_dist[node->GetDegree()]++;
}
//compute degree correlation
unordered_map<size_t, double> degree_corre;
for(auto node = graph->begin(); node != graph->end(); node++)
{
double degree_sum = 0;
for(auto other = node->begin(); other != node->end(); other++)
{
degree_sum += (*graph)[*other]->GetDegree();
}
degree_corre[node->GetDegree()] += degree_sum /
static_cast<double>(node->GetDegree());
}
//normalize
for(auto iter = degree_corre.begin(); iter != degree_corre.end(); iter++)
{
iter->second /= degree_dist[iter->first];
}
correlation.assign(degree_corre.begin(), degree_corre.end());
sort(correlation.begin(), correlation.end());
}
double scn::GetAverageDistance(UGraph::pGraph graph)
{
size_t sum = 0;
size_t count = 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 except NaF
for(auto iter = distance.begin(); iter != distance.end(); iter++)
{
if(iter->first == *node)
continue;
if(iter->second < Graph::NaF)
{
sum += iter->second;
count++;
}
}
}
return double(sum) / count;
}
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::GetAverageDistanceByDjikstra(UGraph::pGraph graph)
{
std::unordered_map<size_t,size_t> distance;
size_t sum = 0;
size_t count = 0;
//auto& distance = distance_sssp;
distance.clear();
for(auto node = graph->begin(); node != graph->end(); node++)
{
RunDjikstra(graph,*node,distance);
//add distance except NaF
for(auto other = graph->begin(); other != graph->end(); other++)
{
if(node == other)
continue;
if(distance[*other] < Graph::NaF)
{
sum += distance[*other];
count++;
}
}
}
return double(sum) / count;
}
void scn::RunSPFA(UGraph::pGraph graph,size_t indexOfSource, std::unordered_map<size_t,size_t> &distance)
{
assert(graph->HasNode(indexOfSource));
// Map<size_t>& distance = distance_sssp;
//distance, stored the distance information of each node
//init
for(auto node = graph->begin(); node != graph->end(); node++)
{
distance[*node] = Graph::NaF;
}
distance[indexOfSource] = 0;
queue<size_t> queue_buffer;
unordered_set<size_t> in_queue;
queue_buffer.push(indexOfSource);//push source node
size_t front;
while(!queue_buffer.empty())
{
front = queue_buffer.front();
queue_buffer.pop();
in_queue.erase(front);
auto node = graph->find(front);
for(auto other = node->begin(); other != node->end(); other++)
{
if(in_queue.find(*other) == in_queue.end() &&
distance[front] + 1 < distance[*other])
{
distance[*other] = distance[front] + 1;
queue_buffer.push(*other);
in_queue.insert(*other);
}
}
}
}
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;
}
void scn::GetDiameterAndAverageDistance(size_t &Diamter,double &APL,UGraph::pGraph graph)
{
size_t sum = 0;
size_t count = 0;
size_t diameter = 0;
std::unordered_map<size_t,size_t> distance;
for(auto node = graph->begin(); node != graph->end(); node++)
{
RunSPFA(graph,*node,distance);
//add distance except NaF
for(auto iter = distance.begin(); iter != distance.end(); iter++)
{
if(iter->first == *node)
continue;
if(iter->second < Graph::NaF)
{
sum += iter->second;
count++;
if(iter->second > diameter)
diameter = iter->second;
}
}
}
//return make_pair(diameter, double(sum) / count);
Diamter=diameter;
APL=double(sum) / count;
}
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());
}
UGraph::pGraph scn::GenSmallWorldNetworkByNW(size_t numberOfNodes, size_t k,
double probability)
{
assert(2* k + 1 <= numberOfNodes);
assert(probability >= 0);
assert(probability <= 1);
//generate k-nearest network
UGraph::pGraph graph = GenKNearestNetwork(numberOfNodes, k);
//add edges randomly
size_t numberOfEdges = numberOfNodes * (numberOfNodes - 2 * k - 1) / 2 * probability;
size_t sum_edges = 0;
size_t one, two;
srand(size_t(time(00)));
do
{
one = rand() % numberOfNodes;
two = rand() % numberOfNodes;
if(!(one == two || graph->HasEdge(one, two)))
{
graph->AddEdge(one, two);
sum_edges++;
}
}while(sum_edges < numberOfEdges);
return graph;
}
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());
}
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);
}
}
//注意：需要特征值计算，Fortran
void scn::GetLambda2AndRatio(double &lambda2, double &ratio,UGraph::pGraph graph)
{
auto list = graph->GetLaplacianMatrix().GetEigenvalueList();
//return make_pair(list[list.size() - 2], list[0] / list[list.size() - 2]);
lambda2=list[list.size() - 2];
ratio=list[0] / list[list.size() - 2];
}
double scn::GetSearchInfo(UGraph::pGraph graph,size_t indexOfSource, size_t indexOfTarget)
{
assert(graph->HasNode(indexOfSource));
assert(graph->HasNode(indexOfTarget));
assert(indexOfSource != indexOfTarget);
std::unordered_map<size_t,size_t> distance;
//get shortest distance
//auto& distance = distance_sssp;
RunSPFA(graph,indexOfSource,distance);
double sum = 0;
//search in breadth-first way
queue<pair<size_t, double>> path_queue;//pair : indexOfNode,
//probability of path
path_queue.push(make_pair(indexOfTarget, 1.0));
while(!path_queue.empty())
{
auto current = path_queue.front();
auto node = (*graph)[current.first];
path_queue.pop();
for(auto other = node->begin(); other != node->end(); other++)
{//put all of previous-node in path into queue
if(distance[*other] == distance[*node] - 1)
{
if(distance[*other] == 0)
sum += current.second / static_cast<double>(node->GetDegree());
else
path_queue.push(make_pair(*other, current.second /
static_cast<double>((*graph)[*other]->GetDegree() - 1)));
}
}
}
return - log(sum)/log(2.0);
}
size_t scn::RandomWalkByURW(UGraph::pGraph graph,size_t indexOfSource, size_t indexOfTarget)
{
unordered_set<size_t> neighbors_of_target(graph->find(indexOfTarget)->begin(),
graph->find(indexOfTarget)->end());
vector<size_t> neighbors;
size_t steps = 0;
size_t next = indexOfSource;
srand(size_t(time(00)));
do
{
neighbors.assign(graph->find(next)->begin(), graph->find(next)->end());
next = neighbors[rand() % neighbors.size()];
steps++;
}while(neighbors_of_target.find(next) == neighbors_of_target.end());
return steps;
}
size_t scn::RandomWalkBySARW(UGraph::pGraph graph,size_t indexOfSource, size_t indexOfTarget)
{
unordered_set<size_t> neighbors_of_target(graph->find(indexOfTarget)->begin(),
graph->find(indexOfTarget)->end());
vector<size_t> neighbors;
size_t steps = 0;
size_t next = indexOfSource;
unordered_set<size_t> history;
stack<size_t> precessors;
history.insert(indexOfSource);
precessors.push(indexOfSource);
srand(size_t(time(00)));
// judge first
if(graph->HasEdge(indexOfSource, indexOfTarget))
return 1;
do
{
auto other = graph->find(next);
neighbors.clear();
for(auto iter = other->begin(); iter != other->end(); iter++)
{
if(history.find(*iter) == history.end())
neighbors.push_back(*iter);
}
if(neighbors.empty())
{
history.insert(*other);
precessors.pop();
next = precessors.top();
history.insert(next);
steps++;
continue;
}
do
{
next = neighbors[rand() % neighbors.size()];
}while(history.find(next) != history.end());
steps++;
history.insert(next);
precessors.push(next);
}while(neighbors_of_target.find(next) == neighbors_of_target.end());
return steps;
}
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;
}
void scn::GetDegreeDistribution(vector<pair<size_t, size_t>> &pairs,UGraph::pGraph graph)
{
std::unordered_map<size_t,size_t> distribution;
for(auto node = graph->begin(); node != graph->end(); node++)
{
distribution[node->GetDegree()]++;
}
//copy and sort
pairs.assign(distribution.begin(), distribution.end());
sort(pairs.begin(), pairs.end(), [&](const pair<size_t, size_t> &one,
const pair<size_t, size_t> &two)->bool
{
if(one.first < two.first)
return true;
else
return false;
});
}
double scn::GetBetweennessCentrality(UGraph::pGraph graph,size_t indexOfNode)
{
double sum = 0;
for(auto node1 = graph->begin(); node1 != graph->end(); node1++)
{
if(*node1 == indexOfNode)
continue;
for(auto node2 = graph->begin(); node2 != graph->end(); node2++)
{
if(*node2 == indexOfNode || node1 == node2)
continue;
//compute
auto result = GetNumberOfShortestPath(graph,*node1, *node2, indexOfNode);
sum += static_cast<double>(result.second) /
static_cast<double>(result.first);
}
}
return sum;
}
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;
}
size_t scn::GetDiameter(UGraph::pGraph graph)
{
//auto& distance = distance_sssp;
std::unordered_map<size_t,size_t> distance;
size_t diameter = 0;
distance.clear();
for(auto node = graph->begin(); node != graph->end(); node++)
{
RunSPFA(graph,*node,distance);
//search for the max distance except NaF
for(auto other = graph->begin(); other != graph->end(); other++)
{
if(distance[*other] > diameter && distance[*other] < Graph::NaF)
{
diameter = distance[*other];
}
}
}
return diameter;
}
double scn::GetPearsonCorrCoeff(UGraph::pGraph graph)
{
size_t sum = 0;
size_t product = 0;
size_t square_sum = 0;
for(auto i = graph->begin(); i != graph->end(); i++)
{
for(auto j = i + 1; j != graph->end(); j++)
{
if(graph->HasEdge(*i, *j))
{
sum += i->GetDegree() + j->GetDegree();
product += i->GetDegree() * j->GetDegree();
square_sum += i->GetDegree() * i->GetDegree() + j->GetDegree() * j->GetDegree();
}
}
}
double tmp = 1.0 / static_cast<double>(graph->GetNumberOfEdges());
return (tmp * product - (tmp * sum) * (tmp * sum) / 4) /
(tmp * square_sum / 2 - (tmp * sum) * (tmp * sum) / 4);
}
double scn::GetTransitivity(UGraph::pGraph graph)
{
size_t numberOfTriangles = 0;
size_t numberOfTriples = 0;
for(auto node = graph->begin(); node != graph->end(); node++)
{
for(auto other1 = node->begin(); other1 != node->end(); other1++)
{
for(auto other2= other1 + 1; other2 != node->end(); other2++)
{
if(graph->HasEdge(*other1, *other2))
{
numberOfTriangles++;
}
}
}
numberOfTriples += node->GetDegree() * (node->GetDegree() - 1) / 2;
}
return static_cast<double>(numberOfTriangles) /
static_cast<double>(numberOfTriples);
}
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();
}
}
}
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();
}
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::GetShortestDistanceDistribution(vector<pair<size_t, size_t>> &distribution,UGraph::pGraph graph)
{
std::unordered_map<size_t,size_t> distance;
std::unordered_map<size_t,size_t> tempdist;
for(auto node = graph->begin(); node != graph->end(); node++)
{
RunSPFA(graph,*node,distance);
//add distance except NaF
for(auto iter = distance.begin(); iter !=distance.end(); iter++)
{
if(iter->first == *node)
continue;
if(iter->second < Graph::NaF)
{
tempdist[iter->second]++;
}
}
}
distribution.assign(tempdist.begin(),tempdist.end());
sort(distribution.begin(), distribution.end());
}
double scn::GetRichClubCoeff(UGraph::pGraph graph,size_t degree)
{
IndexList setOfHighNode;//whose degree is greater than
//argument degree
for(auto node = graph->begin(); node != graph->end(); node++)
{
if(node->GetDegree() > degree)
{
setOfHighNode.push_back(*node);
}
}
double sum = 0;
for(auto one = setOfHighNode.begin(); one != setOfHighNode.end(); one++)
{
for(auto two = one + 1; two != setOfHighNode.end(); two++)
{
if(graph->HasEdge(*one, *two))
sum++;
}
}
return 2 * sum / static_cast<double>(setOfHighNode.size() * (setOfHighNode.size() - 1));
}
size_t scn::GetShortestDistance(UGraph::pGraph graph,size_t indexOfSource, size_t indexOfTarget)
{
assert(graph->HasNode(indexOfSource) && graph->HasNode(indexOfTarget));
//breadth-first search
queue<size_t> search_queue;
std::unordered_map<size_t,size_t> distance;
unordered_set<size_t> in_queue;
size_t front;
//initial
distance[indexOfSource] = 0;
search_queue.push(indexOfSource);
in_queue.insert(indexOfSource);
while(!search_queue.empty())
{
front = search_queue.front();
search_queue.pop();
in_queue.erase(front);
auto node = graph->find(front);
for(auto other = node->begin(); other != node->end(); other++)
{
if(*other == indexOfTarget)
return distance[*node] + 1;
if(in_queue.find(*other) == in_queue.end() &&
(distance.find(*other) == distance.end() || distance[front] + 1 < distance[*other]))
{
distance[*other] = distance[front] + 1;
search_queue.push(*other);
in_queue.insert(*other);
}
}
}
//if this point is reached, the indexOfTarget is an isolated node
return Graph::NaF;
}
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;
}