graph_community.hh 26.6 KB
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// graph-tool -- a general graph modification and manipulation thingy
//
// Copyright (C) 2007  Tiago de Paula Peixoto <tiago@forked.de>
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 3
// of the License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.

#ifndef GRAPH_COMMUNITY_HH
#define GRAPH_COMMUNITY_HH

#include <boost/random.hpp>
#include <tr1/unordered_set>
#include <fstream>
#include <iomanip>

#include "graph_util.hh"
#include "graph_properties.hh"

namespace graph_tool
{

using namespace std;
using namespace boost;

using std::tr1::unordered_map;
using std::tr1::unordered_set;

typedef boost::mt19937 rng_t;

// computes the community structure through a spin glass system with
// simulated annealing

template <template <class G, class CommunityMap> class NNKS>
struct get_communities
{
    template <class Graph, class WeightMap, class CommunityMap>
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    void operator()(const Graph& g, WeightMap weights, CommunityMap s,
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                    double gamma, size_t n_iter, pair<double,double> Tinterval,
                    pair<size_t,bool> Nspins, size_t seed,
                    pair<bool,string> verbose) const
    {
        typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
        typedef typename graph_traits<Graph>::edge_descriptor edge_t;
        typedef typename property_traits<WeightMap>::key_type weight_key_t;
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        size_t N = HardNumVertices()(g);
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        stringstream out_str;
        ofstream out_file;
        if (verbose.second != "")
        {
            out_file.open(verbose.second.c_str());
            if (!out_file.is_open())
                throw GraphException("error opening file " + verbose.second +
                                     " for writing");
            out_file.exceptions (ifstream::eofbit | ifstream::failbit |
                                 ifstream::badbit);
        }

        double Tmin = Tinterval.first;
        double Tmax = Tinterval.second;

        rng_t rng(static_cast<rng_t::result_type>(seed));
        boost::uniform_real<double> uniform_p(0.0,1.0);

        if (Nspins.first == 0)
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            Nspins.first = HardNumVertices()(g);
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        unordered_map<size_t, size_t> Ns; // spin histogram
        // global energy term
        unordered_map<size_t, map<double, unordered_set<size_t> > > global_term;

        // init spins from [0,N-1] and global info
        uniform_int<size_t> sample_spin(0, Nspins.first-1);
        unordered_set<size_t> deg_set;
        typename graph_traits<Graph>::vertex_iterator v,v_end;
        for (tie(v,v_end) = vertices(g); v != v_end; ++v)
        {
            if (Nspins.second)
                s[*v] = sample_spin(rng);
            Ns[s[*v]]++;
            deg_set.insert(out_degree_no_loops(*v, g));
        }

        NNKS<Graph,CommunityMap> Nnnks(g, s); // this will retrieve the expected
                                              // number of neighbours with given
                                              // spin, in funcion of degree

        // setup global energy terms for all degrees and spins
        vector<size_t> degs;
        for (typeof(deg_set.begin()) iter = deg_set.begin();
             iter != deg_set.end(); ++iter)
            degs.push_back(*iter);
        for (size_t i = 0; i < degs.size(); ++i)
            for (size_t sp = 0; sp < Nspins.first; ++sp)
                global_term[degs[i]][gamma*Nnnks(degs[i],sp)].insert(sp);


        // define cooling rate so that temperature starts at Tmax at temp_count
        // == 0 and reaches Tmin at temp_count == n_iter - 1
        if (Tmin < numeric_limits<double>::epsilon())
            Tmin = numeric_limits<double>::epsilon();
        double cooling_rate = -(log(Tmin)-log(Tmax))/(n_iter-1);

        // start the annealing
        for (size_t temp_count = 0; temp_count < n_iter; ++temp_count)
        {
            double T = Tmax*exp(-cooling_rate*temp_count);

            bool steepest_descent = false; // flags if temperature is too low

            // calculate the cumulative probabilities of each spin energy level
            unordered_map<size_t, map<long double, pair<double, bool> > >
                cumm_prob;
            unordered_map<size_t, unordered_map<double, long double> >
                energy_to_prob;
            int i, NK = degs.size();
#ifdef USING_OPENMP
            for (i = 0; i < NK; ++i)
            {
                cumm_prob[degs[i]];
                energy_to_prob[degs[i]];
            }
#endif //USING_OPENMP
            #pragma omp parallel for default(shared) private(i)\
                schedule(dynamic)
            for (i = 0; i < NK; ++i)
            {
                long double prob = 0;
                for (typeof(global_term[degs[i]].begin()) iter =
                         global_term[degs[i]].begin();
                     iter != global_term[degs[i]].end(); ++iter)
                {
                    long double M = log(numeric_limits<long double>::max()/
                                        (Nspins.first*10));
                    long double this_prob =
                        exp((long double)(-iter->first - degs[i])/T + M)*
                        iter->second.size();

                    if (prob + this_prob != prob)
                    {
                        prob += this_prob;
                        cumm_prob[degs[i]][prob] = make_pair(iter->first, true);
                        energy_to_prob[degs[i]][iter->first] = prob;
                    }
                    else
                    {
                        energy_to_prob[degs[i]][iter->first] = 0;
                    }
                }
                if (prob == 0.0)
                {
                    #pragma omp critical
                    {
                        steepest_descent = true;
                    }
                }
            }

            // list of spins which were updated
            vector<pair<vertex_t,size_t> > spin_update;
            spin_update.reserve(N);

            // sample a new spin for every vertex
            int NV = num_vertices(g);
            #pragma omp parallel for default(shared) private(i) \
                firstprivate(global_term, cumm_prob) schedule(dynamic)
            for (i = 0; i < NV; ++i)
            {
                vertex_t v = vertex(i, g);
                if (v == graph_traits<Graph>::null_vertex())
                    continue;

                unordered_map<size_t, double> ns; // number of neighbours with
                                                  // spin 's' (weighted)

                // neighborhood spins info
                typename graph_traits<Graph>::out_edge_iterator e,e_end;
                for (tie(e,e_end) = out_edges(v,g); e != e_end; ++e)
                {
                    vertex_t t = target(*e,g);
                    if (t != v)
                        ns[s[t]] += get(weights, weight_key_t(*e));
                }

                size_t k = out_degree_no_loops(v,g);

                map<double,unordered_set<size_t> >& global_term_k =
                    global_term[k];
                map<long double,pair<double,bool> >& cumm_prob_k = cumm_prob[k];

                // update energy levels with local info
                unordered_set<double> modified_energies;
                for (typeof(ns.begin()) iter = ns.begin(); iter != ns.end();
                     ++iter)
                {
                    double old_E = gamma*Nnnks(k, iter->first);
                    double new_E = old_E - ns[iter->first];
                    global_term_k[old_E].erase(iter->first);
                    if (global_term_k[old_E].empty())
                        global_term_k.erase(old_E);
                    global_term_k[new_E].insert(iter->first);
                    modified_energies.insert(old_E);
                    modified_energies.insert(new_E);
                }

                // update probabilities
                size_t prob_mod_count = 0;
                for (typeof(modified_energies.begin()) iter =
                         modified_energies.begin();
                     iter != modified_energies.end(); ++iter)
                {
                    if (energy_to_prob[k].find(*iter) !=
                        energy_to_prob[k].end())
                        if (energy_to_prob[k][*iter] != 0.0)
                            cumm_prob_k[energy_to_prob[k][*iter]].second =
                                false;
                    if (global_term_k.find(*iter) != global_term_k.end())
                    {
                        long double M = log(numeric_limits<long double>::max()/
                                            (Nspins.first*10));
                        long double prob = exp((long double)(-*iter - k)/T + M)*
                            global_term_k[*iter].size();
                        if (cumm_prob_k.empty() ||
                            cumm_prob_k.rbegin()->first + prob !=
                            cumm_prob_k.rbegin()->first)
                        {
                            if (!cumm_prob_k.empty())
                                prob += cumm_prob_k.rbegin()->first;
                            cumm_prob_k.insert(cumm_prob_k.end(),
                                               make_pair(prob,
                                                         make_pair(*iter,
                                                                   true)));
                            prob_mod_count++;
                        }
                    }
                }

                // choose the new energy
                double E = numeric_limits<double>::max();
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                if ((prob_mod_count == 0 &&
                     !modified_energies.empty()) ||
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                    steepest_descent)
                {
                    // Temperature too low! The computer precision is not enough
                    // to calculate the probabilities correctly.  Switch to
                    // steepest descent mode....
                    steepest_descent = true;
                    E = global_term_k.begin()->first;
                }
                else
                {
                    // sample energy according to its probability
                    uniform_real<long double> prob_sample
                        (0.0, max(cumm_prob_k.rbegin()->first,
                                  numeric_limits<long double>::epsilon()));
                    bool accept = false;
                    while (!accept)
                    {
                        typeof(cumm_prob_k.begin()) upper;

                        #pragma omp critical
                        {
                            upper = cumm_prob_k.upper_bound(prob_sample(rng));
                        }

                        if (upper == cumm_prob_k.end())
                            upper--;
                        E = upper->second.first;
                        accept = upper->second.second;
                    }
                }

                //new spin (randomly chosen amongst those with equal energy)
                uniform_int<size_t> sample_spin(0,global_term_k[E].size()-1);
                typeof(global_term_k[E].begin()) iter =
                    global_term_k[E].begin();

                size_t spin_n;
                #pragma omp critical
                {
                    spin_n = sample_spin(rng);
                }
                advance(iter, spin_n);
                int a = *iter;

                // cleanup modified probabilities
                for (typeof(modified_energies.begin()) iter =
                         modified_energies.begin();
                     iter != modified_energies.end(); ++iter)
                {
                    if (energy_to_prob[k].find(*iter) !=
                        energy_to_prob[k].end())
                        if (energy_to_prob[k][*iter] != 0.0)
                            cumm_prob_k[energy_to_prob[k][*iter]].second = true;
                    if (prob_mod_count > 0)
                    {
                        cumm_prob_k.erase(cumm_prob_k.rbegin()->first);
                        prob_mod_count--;
                    }
                }

                // cleanup modified energy levels
                for (typeof(ns.begin()) iter = ns.begin(); iter != ns.end();
                     ++iter)
                {
                    double new_E = gamma*Nnnks(k, iter->first);
                    double old_E = new_E - ns[iter->first];
                    global_term_k[old_E].erase(iter->first);
                    if (global_term_k[old_E].empty())
                        global_term_k.erase(old_E);
                    global_term_k[new_E].insert(iter->first);
                }

                //update global info
                if (s[v] != a)
                {
                    #pragma omp critical
                    {
                        spin_update.push_back(make_pair(v, a));
                    }
                }
            }

            // flip spins and update Nnnks
            for (size_t u = 0; u < spin_update.size(); ++u)
            {
                vertex_t v = spin_update[u].first;
                size_t k = out_degree_no_loops(v, g);
                size_t a = spin_update[u].second;

                int i, NK = degs.size();
                #pragma omp parallel for default(shared) private(i) \
                    schedule(dynamic)
                for (i = 0; i < NK; ++i)
                {
                    size_t nk = degs[i];
                    double old_E = gamma*Nnnks(nk,s[v]);
                    double new_E = gamma*Nnnks(nk,a);
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                    map<double,unordered_set<size_t> >& global_term_k =
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                        global_term[nk];
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                    unordered_set<size_t>& global_term_k_old_E =
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                        global_term_k[old_E];
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                    unordered_set<size_t>& global_term_k_new_E =
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                        global_term_k[new_E];
                    global_term_k_old_E.erase(s[v]);
                    if (global_term_k_old_E.empty())
                        global_term_k.erase(old_E);
                    global_term_k_new_E.erase(a);
                    if (global_term_k_new_E.empty())
                        global_term_k.erase(new_E);
                }

                Nnnks.Update(k,s[v],a);
                Ns[s[v]]--;
                if (Ns[s[v]] == 0)
                    Ns.erase(s[v]);
                Ns[a]++;

                #pragma omp parallel for default(shared) private(i) \
                    schedule(dynamic)
                for (i = 0; i < NK; ++i)
                {
                    size_t nk = degs[i];
                    map<double,unordered_set<size_t> >& global_term_k =
                        global_term[nk];
                    double old_E = gamma*Nnnks(nk,s[v]);
                    double new_E = gamma*Nnnks(nk,a);
                    global_term_k[old_E].insert(s[v]);
                    global_term_k[new_E].insert(a);
                }

                // update spin
                s[v] = a;
            }

            if (verbose.first)
            {
                for (size_t j = 0; j < out_str.str().length(); ++j)
                    cout << "\b";
                out_str.str("");
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                out_str << setw(lexical_cast<string>(n_iter).size())
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                        << temp_count << " of " << n_iter
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                        << " (" << setw(2) << (temp_count+1)*100/n_iter
                        << "%) " << "temperature: " << setw(14)
                        << setprecision(10) << T << " spins: "
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                        << Ns.size() << " energy levels: ";
                size_t n_energy = 0;
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                for (typeof(global_term.begin()) iter = global_term.begin();
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                     iter != global_term.end(); ++iter)
                    n_energy += iter->second.size();
                out_str << setw(lexical_cast<string>
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                                (Nspins.first*degs.size()).size())
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                        << n_energy << "  ";
                if (steepest_descent)
                    out_str << " (steepest descent)";
                cout << out_str.str() << flush;
            }
            if (verbose.second != "")
            {
                try
                {
                    size_t n_energy = 0;
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                    for (typeof(global_term.begin()) iter =
                             global_term.begin(); iter != global_term.end();
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                         ++iter)
                        n_energy += iter->second.size();
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                    out_file << temp_count << "\t" << setprecision(10)
                             << T << "\t" << Ns.size() << "\t" << n_energy
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                             << endl;
                }
                catch (ifstream::failure e)
                {
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                    throw GraphException("error writing to file " +
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                                         verbose.second + ": " + e.what());
                }
            }
        }


        // get final energy
        double E = 0.0;
        unordered_map<size_t,vector<vertex_t> > spin_groups;
        for (tie(v,v_end) = vertices(g); v != v_end; ++v)
        {
            typename graph_traits<Graph>::out_edge_iterator e, e_end;
            for (tie(e,e_end) = out_edges(*v,g); e != e_end; ++e)
            {
                vertex_t t = target(*e,g);
                if (s[t] == s[*v])
                    E -= get(weights, weight_key_t(*e));
            }
            E += gamma*Nnnks(out_degree_no_loops(*v,g), s[*v]);
        }

        if (verbose.first)
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            cout << " total energy: " << scientific << setprecision(20)
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                 << E << endl;

        // rename spins, starting from zero
        unordered_map<size_t,size_t> spins;
        for (tie(v,v_end) = vertices(g); v != v_end; ++v)
        {
            if (spins.find(s[*v]) == spins.end())
                spins[s[*v]] = spins.size() - 1;
            s[*v] = spins[s[*v]];
        }

    }
};

template <class Graph, class CommunityMap>
class NNKSErdosReyni
{
public:
    NNKSErdosReyni(const Graph &g, CommunityMap s)
    {
        size_t N = 0;
        double _avg_k = 0.0;
        typename graph_traits<Graph>::vertex_iterator v,v_end;
        for (tie(v,v_end) = vertices(g); v != v_end; ++v)
        {
            size_t k = out_degree_no_loops(*v,g);
            _avg_k += k;
            N++;
            _Ns[s[*v]]++;
        }
        _p = _avg_k/(N*N);
    }

    void Update(size_t k, size_t old_s, size_t s)
    {
        _Ns[old_s]--;
        if (_Ns[old_s] == 0)
            _Ns.erase(old_s);
        _Ns[s]++;
    }

    double operator()(size_t k, size_t s) const
    {
        size_t ns = 0;
        typeof(_Ns.begin()) iter = _Ns.find(s);
        if (iter != _Ns.end())
            ns = iter->second;
        return _p*ns;
    }

private:
    double _p;
    unordered_map<size_t,size_t> _Ns;
};

template <class Graph, class CommunityMap>
class NNKSUncorr
{
public:
    NNKSUncorr(const Graph &g, CommunityMap s): _g(g), _K(0)
    {
        typename graph_traits<Graph>::vertex_iterator v,v_end;
        for (tie(v,v_end) = vertices(_g); v != v_end; ++v)
        {
            size_t k = out_degree_no_loops(*v, _g);
            _K += k;
            _Ks[s[*v]] += k;
        }
    }

    void Update(size_t k, size_t old_s, size_t s)
    {
        _Ks[old_s] -= k;
        if (_Ks[old_s] == 0)
            _Ks.erase(old_s);
        _Ks[s] += k;
    }

    double operator()(size_t k, size_t s) const
    {
        size_t ks = 0;
        typeof(_Ks.begin()) iter = _Ks.find(s);
        if (iter != _Ks.end())
            ks = iter->second;
        return k*ks/double(_K);
    }

private:
    const Graph& _g;
    size_t _K;
    unordered_map<size_t,size_t> _Ks;
};

template <class Graph, class CommunityMap>
class NNKSCorr
{
public:
    NNKSCorr(const Graph &g, CommunityMap s): _g(g)
    {
        unordered_set<size_t> spins;

        typename graph_traits<Graph>::vertex_iterator v,v_end;
        for (tie(v,v_end) = vertices(_g); v != v_end; ++v)
        {
            size_t k = out_degree_no_loops(*v, _g);
            _Nk[k]++;
            _Nks[k][s[*v]]++;
            spins.insert(s[*v]);
        }

        size_t E = 0;
        typename graph_traits<Graph>::edge_iterator e,e_end;
        for (tie(e,e_end) = edges(_g); e != e_end; ++e)
        {
            typename graph_traits<Graph>::vertex_descriptor s, t;

            s = source(*e,g);
            t = target(*e,g);
            if (s != t)
            {
                size_t k1 = out_degree_no_loops(s, g);
                size_t k2 = out_degree_no_loops(t, g);
                _Pkk[k1][k2]++;
                _Pkk[k2][k1]++;
                E++;
            }
        }

        for (typeof(_Pkk.begin()) iter1 = _Pkk.begin(); iter1 != _Pkk.end();
             ++iter1)
        {
            double sum = 0;
            for (typeof(iter1->second.begin()) iter2 = iter1->second.begin();
                 iter2 != iter1->second.end(); ++iter2)
                sum += iter2->second;
            for (typeof(iter1->second.begin()) iter2 = iter1->second.begin();
                 iter2 != iter1->second.end(); ++iter2)
                iter2->second /= sum;
        }

        for (typeof(_Nk.begin()) k_iter = _Nk.begin(); k_iter != _Nk.end();
             ++k_iter)
        {
            size_t k1 = k_iter->first;
            _degs.push_back(k1);
            for (typeof(spins.begin()) s_iter = spins.begin();
                 s_iter != spins.end(); ++s_iter)
                for (typeof(_Nk.begin()) k_iter2 = _Nk.begin();
                     k_iter2 != _Nk.end(); ++k_iter2)
                {
                    size_t k2 = k_iter2->first;
                    if (_Nks[k2].find(*s_iter) != _Nks[k2].end())
                        _NNks[k1][*s_iter] +=
                            k1*_Pkk[k1][k2] * _Nks[k2][*s_iter]/double(_Nk[k2]);
                }
        }
    }

    void Update(size_t k, size_t old_s, size_t s)
    {
        int i, NK = _degs.size();
        #pragma omp parallel for default(shared) private(i) schedule(dynamic)
        for (i = 0; i < NK; ++i)
        {
            size_t k1 = _degs[i], k2 = k;
            if (_Pkk.find(k1) == _Pkk.end())
                continue;
            if (_Pkk.find(k1)->second.find(k2) == _Pkk.find(k1)->second.end())
                continue;
            unordered_map<size_t,double>& NNks_k1 = _NNks[k1];
            double Pk1k2 = _Pkk[k1][k2];
            unordered_map<size_t,size_t>& Nksk2 = _Nks[k2];
            double Nk2 = _Nk[k2];
            NNks_k1[old_s] -=  k1*Pk1k2 * Nksk2[old_s]/Nk2;
            if (NNks_k1[old_s] == 0.0)
                NNks_k1.erase(old_s);
            if (Nksk2.find(s) != Nksk2.end())
                NNks_k1[s] -=  k1*Pk1k2 * Nksk2[s]/Nk2;
            if (NNks_k1[s] == 0.0)
                NNks_k1.erase(s);
        }

        _Nks[k][old_s]--;
        if (_Nks[k][old_s] == 0)
            _Nks[k].erase(old_s);
        _Nks[k][s]++;

        #pragma omp parallel for default(shared) private(i) schedule(dynamic)
        for (i = 0; i < NK; ++i)
        {
            size_t k1 = _degs[i], k2 = k;
            if (_Pkk.find(k1) == _Pkk.end())
                continue;
            if (_Pkk.find(k1)->second.find(k2) == _Pkk.find(k1)->second.end())
                continue;
            unordered_map<size_t,double>& NNks_k1 = _NNks[k1];
            double Pk1k2 = _Pkk[k1][k2];
            unordered_map<size_t,size_t>& Nksk2 = _Nks[k2];
            double Nk2 = _Nk[k2];
            NNks_k1[old_s] +=  k1*Pk1k2 * Nksk2[old_s]/Nk2;
            if (NNks_k1[old_s] == 0.0)
                NNks_k1.erase(old_s);
            NNks_k1[s] +=  k1*Pk1k2 * Nksk2[s]/Nk2;
        }

    }

    double operator()(size_t k, size_t s) const
    {
        const typeof(_NNks[k])& nnks = _NNks.find(k)->second;
        const typeof(nnks.begin()) iter = nnks.find(s);
        if (iter != nnks.end())
            return iter->second;
        return 0.0;
    }

private:
    const Graph& _g;
    vector<size_t> _degs;
    unordered_map<size_t,size_t> _Nk;
    unordered_map<size_t,unordered_map<size_t,double> > _Pkk;
    unordered_map<size_t,unordered_map<size_t,size_t> > _Nks;
    unordered_map<size_t,unordered_map<size_t,double> > _NNks;
};

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enum comm_corr_t
{
    ERDOS_REYNI,
    UNCORRELATED,
    CORRELATED
};
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struct get_communities_selector
{
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    get_communities_selector(comm_corr_t corr):_corr(corr) {}
    comm_corr_t _corr;
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    template <class Graph, class WeightMap, class CommunityMap>
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    void operator()(const Graph& g, WeightMap weights, CommunityMap s, double gamma,
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                    size_t n_iter, pair<double,double> Tinterval,
                    pair<size_t,bool> Nspins, size_t seed,
                    pair<bool,string> verbose) const
    {
        switch (_corr)
        {
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        case ERDOS_REYNI:
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            get_communities<NNKSErdosReyni>()(g, weights, s, gamma, n_iter,
                                              Tinterval, Nspins, seed, verbose);
            break;
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        case UNCORRELATED:
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            get_communities<NNKSUncorr>()(g, weights, s, gamma, n_iter,
                                          Tinterval, Nspins, seed, verbose);
            break;
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        case CORRELATED:
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            get_communities<NNKSCorr>()(g, weights, s, gamma, n_iter,
                                        Tinterval, Nspins, seed, verbose);
            break;
        }
    }
};

// get Newman's modularity of a given community partition
struct get_modularity
{
    template <class Graph, class WeightMap, class CommunityMap>
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    void operator()(const Graph& g, WeightMap weights, CommunityMap s,
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                    double& modularity) const
    {
        typedef typename property_traits<WeightMap>::key_type weight_key_t;

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        modularity = 0.0;
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        size_t E = 0;
        double W = 0;

        typename graph_traits<Graph>::edge_iterator e, e_end;
        for (tie(e,e_end) = edges(g); e != e_end; ++e)
            if (target(*e,g) != source(*e,g))
            {
                W += get(weights, *e);
                E++;
                if (get(s, target(*e,g)) == get(s, source(*e,g)))
                    modularity += 2*get(weights, weight_key_t(*e));
            }

        unordered_map<size_t, size_t> Ks;

        typename graph_traits<Graph>::vertex_iterator v, v_end;
        for (tie(v,v_end) = vertices(g); v != v_end; ++v)
            Ks[get(s, *v)] += out_degree_no_loops(*v, g);
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        for (typeof(Ks.begin()) iter = Ks.begin(); iter != Ks.end(); ++iter)
            modularity -= (iter->second*iter->second)/double(2*E);

        modularity /= 2*W;
    }
};

} // graph_tool namespace

#endif //GRAPH_COMMUNITY_HH