int erase_links(deque<set<int> > & E, const deque<deque<int> > & member_list, const bool excess, const bool defect, const double mixing_parameter) {
int num_nodes= member_list.size();
int eras_add_times=0;
if (excess) {
for (int i=0; i<num_nodes; i++) {
while ( (E[i].size()>1) && double(internal_kin(E, member_list, i))/E[i].size() < 1 - mixing_parameter) {
//---------------------------------------------------------------------------------
cout<<"degree sequence changed to respect the option -sup ... "<<++eras_add_times<<endl;
deque<int> deqar;
for (set<int>::iterator it_est=E[i].begin(); it_est!=E[i].end(); it_est++)
if (!they_are_mate(i, *it_est, member_list))
deqar.push_back(*it_est);
if(deqar.size()==E[i].size()) { // this shouldn't happen...
cerr<<"sorry, something went wrong: there is a node which does not respect the constraints. (option -sup)"<<endl;
return -1;
}
int random_mate=deqar[irand(deqar.size()-1)];
E[i].erase(random_mate);
E[random_mate].erase(i);
}
}
}
if (defect) {
for (int i=0; i<num_nodes; i++)
while ( (E[i].size()<E.size()) && double(internal_kin(E, member_list, i))/E[i].size() > 1 - mixing_parameter) {
//---------------------------------------------------------------------------------
cout<<"degree sequence changed to respect the option -inf ... "<<++eras_add_times<<endl;
int stopper_here=num_nodes;
int stopper_=0;
int random_mate=irand(num_nodes-1);
while ( ( (they_are_mate(i, random_mate, member_list)) || E[i].find(random_mate)!=E[i].end()) && (stopper_<stopper_here) ) {
random_mate=irand(num_nodes-1);
stopper_++;
}
if(stopper_==stopper_here) { // this shouldn't happen...
cerr<<"sorry, something went wrong: there is a node which does not respect the constraints. (option -inf)"<<endl;
return -1;
}
E[i].insert(random_mate);
E[random_mate].insert(i);
}
}
//------------------------------------ Erasing links ------------------------------------------------------
return 0;
}
int weights(deque<set<int> > & en, const deque<deque<int> > & member_list, const double beta, const double mu, deque<map <int, double > > & neigh_weigh) {
double tstrength=0;
for(int i=0; i<en.size(); i++)
tstrength+=pow(en[i].size(), beta);
double strs[en.size()]; // strength of the nodes
// build a matrix like this: deque < map <int, double > > each row corresponds to link - weights
for(int i=0; i<en.size(); i++) {
map<int, double> new_map;
neigh_weigh.push_back(new_map);
for (set<int>::iterator its=en[i].begin(); its!=en[i].end(); its++)
neigh_weigh[i].insert(make_pair(*its, 0.));
strs[i]=pow(double(en[i].size()), beta);
}
deque<double> s_in_out_id_row(3);
s_in_out_id_row[0]=0;
s_in_out_id_row[1]=0;
s_in_out_id_row[2]=0;
deque<deque<double> > wished; // 3 numbers for each node: internal, idle and extra strength. the sum of the three is strs[i]. wished is the theoretical, factual the factual one.
deque<deque<double> > factual;
for (int i=0; i<en.size(); i++) {
wished.push_back(s_in_out_id_row);
factual.push_back(s_in_out_id_row);
}
double tot_var=0;
for (int i=0; i<en.size(); i++) {
wished[i][0]=(1. -mu)*strs[i];
wished[i][1]=mu*strs[i];
factual[i][2]=strs[i];
tot_var+= wished[i][0] * wished[i][0] + wished[i][1] * wished[i][1] + strs[i] * strs[i];
}
deque<int> internal_kin_top;
for(int i=0; i<en.size(); i++)
internal_kin_top.push_back(internal_kin(en, member_list, i));
double precision = 1e-9;
double precision2 = 1e-2;
double not_better_than = pow(tstrength, 2) * precision;
//cout<<"tot_var "<<tot_var<<";\tnot better "<<not_better_than<<endl;
int step=0;
while (true) {
time_t t0=time(NULL);
double pre_var=tot_var;
for (int i=0; i<en.size(); i++)
propagate(neigh_weigh, member_list, wished, factual, i, tot_var, strs, internal_kin_top);
//check_weights(neigh_weigh, member_list, wished, factual, tot_var, strs);
double relative_improvement=double(pre_var - tot_var)/pre_var;
//cout<<"tot_var "<<tot_var<<"\trelative improvement: "<<relative_improvement<<endl;
if (tot_var<not_better_than)
break;
if (relative_improvement < precision2)
break;
time_t t1= time(NULL);
int deltat= t1 - t0;
/*
if(step%2==0 && deltat !=0)
cout<<"About "<<cast_int((log(not_better_than) -log(tot_var)) / log(1. - relative_improvement)) * deltat<<" secs..."<<endl;
*/
step++;
}
//check_weights(neigh_weigh, member_list, wished, factual, tot_var, strs);
return 0;
}
int print_network(deque<set<int> > & E, const deque<deque<int> > & member_list, const deque<deque<int> > & member_matrix, deque<int> & num_seq) {
int edges=0;
int num_nodes=member_list.size();
deque<double> double_mixing;
for (int i=0; i<E.size(); i++) {
double one_minus_mu = double(internal_kin(E, member_list, i))/E[i].size();
double_mixing.push_back(1.- one_minus_mu);
edges+=E[i].size();
}
//cout<<"\n----------------------------------------------------------"<<endl;
//cout<<endl;
double density=0;
double sparsity=0;
for (int i=0; i<member_matrix.size(); i++) {
double media_int=0;
double media_est=0;
for (int j=0; j<member_matrix[i].size(); j++) {
double kinj = double(internal_kin_only_one(E[member_matrix[i][j]], member_matrix[i]));
media_int+= kinj;
media_est+=E[member_matrix[i][j]].size() - double(internal_kin_only_one(E[member_matrix[i][j]], member_matrix[i]));
}
double pair_num=(member_matrix[i].size()*(member_matrix[i].size()-1));
double pair_num_e=((num_nodes-member_matrix[i].size())*(member_matrix[i].size()));
if(pair_num!=0)
density+=media_int/pair_num;
if(pair_num_e!=0)
sparsity+=media_est/pair_num_e;
}
density=density/member_matrix.size();
sparsity=sparsity/member_matrix.size();
ofstream out1("network.dat");
for (int u=0; u<E.size(); u++) {
set<int>::iterator itb=E[u].begin();
while (itb!=E[u].end())
out1<<u+1<<"\t"<<*(itb++)+1<<endl;
}
out1.close();
ofstream out2("community.dat");
for (int i=0; i<member_list.size(); i++) {
out2<<i+1<<"\t";
for (int j=0; j<member_list[i].size(); j++)
out2<<member_list[i][j]+1<<" ";
out2<<endl;
}
out2.close();
cout<<"\n\n---------------------------------------------------------------------------"<<endl;
cout<<"network of "<<num_nodes<<" vertices and "<<edges/2<<" edges"<<";\t average degree = "<<double(edges)/num_nodes<<endl;
cout<<"\naverage mixing parameter: "<<average_func(double_mixing)<<" +/- "<<sqrt(variance_func(double_mixing))<<endl;
cout<<"p_in: "<<density<<"\tp_out: "<<sparsity<<endl;
ofstream statout("statistics.dat");
deque<int> degree_seq;
for (int i=0; i<E.size(); i++)
degree_seq.push_back(E[i].size());
statout<<"degree distribution (probability density function of the degree in logarithmic bins) "<<endl;
log_histogram(degree_seq, statout, 10);
statout<<"\ndegree distribution (degree-occurrences) "<<endl;
int_histogram(degree_seq, statout);
statout<<endl<<"--------------------------------------"<<endl;
statout<<"community distribution (size-occurrences)"<<endl;
int_histogram(num_seq, statout);
statout<<endl<<"--------------------------------------"<<endl;
statout<<"mixing parameter"<<endl;
not_norm_histogram(double_mixing, statout, 20, 0, 0);
statout<<endl<<"--------------------------------------"<<endl;
statout.close();
cout<<endl<<endl;
return 0;
}
int print_network(deque<set<int> > & E, const deque<deque<int> > & member_list, const deque<deque<int> > & member_matrix,
deque<int> & num_seq, deque<map <int, double > > & neigh_weigh, double beta, double mu, double mu0) {
int edges=0;
int num_nodes=member_list.size();
deque<double> double_mixing;
for (int i=0; i<E.size(); i++) {
double one_minus_mu = double(internal_kin(E, member_list, i))/E[i].size();
double_mixing.push_back(1.- one_minus_mu);
edges+=E[i].size();
}
//cout<<"\n----------------------------------------------------------"<<endl;
//cout<<endl;
double density=0;
double sparsity=0;
for (int i=0; i<member_matrix.size(); i++) {
double media_int=0;
double media_est=0;
for (int j=0; j<member_matrix[i].size(); j++) {
double kinj = double(internal_kin_only_one(E[member_matrix[i][j]], member_matrix[i]));
media_int+= kinj;
media_est+=E[member_matrix[i][j]].size() - double(internal_kin_only_one(E[member_matrix[i][j]], member_matrix[i]));
}
double pair_num=(member_matrix[i].size()*(member_matrix[i].size()-1));
double pair_num_e=((num_nodes-member_matrix[i].size())*(member_matrix[i].size()));
if(pair_num!=0)
density+=media_int/pair_num;
if(pair_num_e!=0)
sparsity+=media_est/pair_num_e;
}
density=density/member_matrix.size();
sparsity=sparsity/member_matrix.size();
ofstream out1("network.dat");
for (int u=0; u<E.size(); u++) {
set<int>::iterator itb=E[u].begin();
while (itb!=E[u].end())
out1<<u+1<<"\t"<<*(itb++)+1<<"\t"<<neigh_weigh[u][*(itb)]<<endl;
}
ofstream out2("community.dat");
for (int i=0; i<member_list.size(); i++) {
out2<<i+1<<"\t";
for (int j=0; j<member_list[i].size(); j++)
out2<<member_list[i][j]+1<<" ";
out2<<endl;
}
cout<<"\n\n---------------------------------------------------------------------------"<<endl;
cout<<"network of "<<num_nodes<<" vertices and "<<edges/2<<" edges"<<";\t average degree = "<<double(edges)/num_nodes<<endl;
cout<<"\naverage mixing parameter (topology): "<< average_func(double_mixing)<<" +/- "<<sqrt(variance_func(double_mixing))<<endl;
cout<<"p_in: "<<density<<"\tp_out: "<<sparsity<<endl;
ofstream statout("statistics.dat");
deque<int> degree_seq;
for (int i=0; i<E.size(); i++)
degree_seq.push_back(E[i].size());
statout<<"degree distribution (probability density function of the degree in logarithmic bins) "<<endl;
log_histogram(degree_seq, statout, 10);
statout<<"\ndegree distribution (degree-occurrences) "<<endl;
int_histogram(degree_seq, statout);
statout<<endl<<"--------------------------------------"<<endl;
statout<<"community distribution (size-occurrences)"<<endl;
int_histogram(num_seq, statout);
statout<<endl<<"--------------------------------------"<<endl;
statout<<"mixing parameter (topology)"<<endl;
not_norm_histogram(double_mixing, statout, 20, 0, 0);
statout<<endl<<"--------------------------------------"<<endl;
//*
deque<double> inwij;
deque<double> outwij;
//deque<double> inkij;
//deque<double> outkij;
double csi=(1. - mu) / (1. - mu0);
double csi2=mu /mu0;
double tstrength=0;
deque<double> one_minus_mu2;
for(int i=0; i<neigh_weigh.size(); i++) {
double internal_strength_i=0;
double strength_i=0;
for(map<int, double>::iterator itm = neigh_weigh[i].begin(); itm!=neigh_weigh[i].end(); itm++) {
if(they_are_mate(i, itm->first, member_list)) {
inwij.push_back(itm->second);
//inkij.push_back(csi * pow(E[i].size(), beta-1));
internal_strength_i+=itm->second;
}
else {
outwij.push_back(itm->second);
//outkij.push_back(csi2 * pow(E[i].size(), beta-1));
}
tstrength+=itm->second;
strength_i+=itm->second;
}
one_minus_mu2.push_back(1 - internal_strength_i/strength_i);
}
//cout<<"average strength "<<tstrength / E.size()<<"\taverage internal strenght: "<<average_internal_strenght<<endl;
cout<<"\naverage mixing parameter (weights): "<<average_func(one_minus_mu2)<<" +/- "<<sqrt(variance_func(one_minus_mu2))<<endl;
statout<<"mixing parameter (weights)"<<endl;
not_norm_histogram(one_minus_mu2, statout, 20, 0, 0);
statout<<endl<<"--------------------------------------"<<endl;
//cout<<" expected internal "<<tstrength * (1 - mu) / E.size()<<endl;
//cout<<"internal links: "<<inwij.size()<<" external: "<<outwij.size()<<endl;
/*
ofstream hout1("inwij.dat");
not_norm_histogram(inwij, hout1, 20, 0, 0);
ofstream hout2("outwij.dat");
not_norm_histogram(outwij, hout2, 20, 0, 0);
ofstream hout3("corrin.dat");
not_norm_histogram_correlated(inkij, inwij, hout3, 20, 0, 0);
ofstream hout4("corrout.dat");
not_norm_histogram_correlated(outkij, outwij, hout4, 20, 0, 0);
//*/
//*/
cout<<"average weight of an internal link "<<average_func(inwij)<<" +/- "<<sqrt(variance_func(inwij))<<endl;
cout<<"average weight of an external link "<<average_func(outwij)<<" +/- "<<sqrt(variance_func(outwij))<<endl;
//cout<<"average weight of an internal link expected "<<tstrength / edges * (1. - mu) / (1. - mu0)<<endl;
//cout<<"average weight of an external link expected "<<tstrength / edges * (mu) / (mu0)<<endl;
statout<<"internal weights (weight-occurrences)"<<endl;
not_norm_histogram(inwij, statout, 20, 0, 0);
statout<<endl<<"--------------------------------------"<<endl;
statout<<"external weights (weight-occurrences)"<<endl;
not_norm_histogram(outwij, statout, 20, 0, 0);
cout<<endl<<endl;
return 0;
}
