graph_motifs.hh 13.1 KB
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// graph-tool -- a general graph modification and manipulation thingy
//
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// Copyright (C) 2007-2010 Tiago de Paula Peixoto <tiago@forked.de>
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//
// 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_MOTIFS_HH
#define GRAPH_MOTIFS_HH

#include <boost/functional/hash.hpp>
#include <boost/graph/copy.hpp>
#include <boost/graph/isomorphism.hpp>
#include <tr1/unordered_map>
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#include <tr1/random>
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#include <algorithm>

namespace graph_tool
{

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typedef tr1::mt19937 rng_t;
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template <class Value>
void insert_sorted(vector<Value>& v, const Value& val)
{
    typeof(v.begin()) iter = lower_bound(v.begin(), v.end(), val);
    if (iter != v.end() && *iter == val)
        return; // no repetitions
    v.insert(iter, val);
}

template <class Value>
bool has_val(vector<Value>& v, const Value& val)
{
    typeof(v.begin()) iter = lower_bound(v.begin(), v.end(), val);
    if (iter == v.end())
        return false;
    return *iter == val;
}

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// gets all the subgraphs starting from vertex v and store it in subgraphs.
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template <class Graph, class Sampler>
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void get_subgraphs(Graph& g, typename graph_traits<Graph>::vertex_descriptor v,
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                   size_t n,
                   vector<vector<typename graph_traits<Graph>::vertex_descriptor> >& subgraphs,
                   Sampler sampler)
{
    typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;

    // extension and subgraph stack
    vector<vector<vertex_t> > ext_stack(1);
    vector<vector<vertex_t> > sub_stack(1);
    vector<vector<vertex_t> > sub_neighbours_stack(1);

    sub_stack[0].push_back(v);
    typename graph_traits<Graph>::out_edge_iterator e, e_end;
    for (tie(e, e_end) = out_edges(v, g); e != e_end; ++e)
    {
        typename graph_traits<Graph>::vertex_descriptor u = target(*e, g);
        if (u > v && !has_val(ext_stack[0], u))
        {
            insert_sorted(ext_stack[0], u);
            insert_sorted(sub_neighbours_stack[0],u);
        }
    }

    while (!sub_stack.empty())
    {
        vector<vertex_t>& ext = ext_stack.back();
        vector<vertex_t>& sub = sub_stack.back();
        vector<vertex_t>& sub_neighbours = sub_neighbours_stack.back();

        if (sub.size() == n)
        {
            // found a subgraph of the desired size; put it in the list and go
            // back a level
            subgraphs.push_back(sub);
            sub_stack.pop_back();
            ext_stack.pop_back();
            sub_neighbours_stack.pop_back();
            continue;
        }

        if (ext.empty())
        {
            // no where else to go
            ext_stack.pop_back();
            sub_stack.pop_back();
            sub_neighbours_stack.pop_back();
            continue;
        }
        else
        {
            // extend subgraph
            vector<vertex_t> new_ext, new_sub = sub,
                new_sub_neighbours = sub_neighbours;

            // remove w from ext
            vertex_t w = ext.back();
            ext.pop_back();

            // insert w in subgraph
            insert_sorted(new_sub, w);

            // update new_ext
            new_ext = ext;
            for (tie(e, e_end) = out_edges(w, g); e != e_end; ++e)
            {
                vertex_t u = target(*e,g);
                if (u > v)
                {
                    if (!has_val(sub_neighbours, u))
                        insert_sorted(new_ext, u);
                    insert_sorted(new_sub_neighbours, u);
                }
            }

            sampler(new_ext, ext_stack.size());

            ext_stack.push_back(new_ext);
            sub_stack.push_back(new_sub);
            sub_neighbours_stack.push_back(new_sub_neighbours);
        }
    }
}

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// sampling selectors

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struct sample_all
{
    template <class val_type>
    void operator()(vector<val_type>&, size_t) {}
};

struct sample_some
{
    sample_some(vector<double>& p, rng_t& rng): _p(&p), _rng(&rng) {}
    sample_some() {}

    template <class val_type>
    void operator()(vector<val_type>& extend, size_t d)
    {
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        typedef tr1::uniform_real<double> rdist_t;
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        tr1::variate_generator<rng_t&, rdist_t> random(*_rng, rdist_t());
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        double pd = (*_p)[d+1];
        size_t nc = extend.size();
        double u = nc*pd - floor(nc*pd);
        size_t n;
        double r;
        {
            #pragma omp critical
            r = random();
        }
        if (r < u)
            n = ceil(nc*pd);
        else
            n = floor(nc*pd);

        if (n == extend.size())
            return;
        if (n == 0)
        {
            extend.clear();
            return;
        }

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        typedef tr1::uniform_int<size_t> idist_t;
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        for (size_t i = 0; i < n; ++i)
        {
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            tr1::variate_generator<rng_t&, idist_t>
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                random_v(*_rng, idist_t(0, extend.size()-i-1));
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            size_t j;
            {
                #pragma omp critical
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                j = i + random_v();
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            }
            swap(extend[i], extend[j]);
        }
        extend.resize(n);
    }

    vector<double>* _p;
    rng_t* _rng;
};


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// build the actual induced subgraph from the vertex list
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template <class Graph, class GraphSG>
void make_subgraph
    (vector<typename graph_traits<Graph>::vertex_descriptor>& vlist,
     Graph& g, GraphSG& sub)
{
    for (size_t i = 0; i < vlist.size(); ++i)
        add_vertex(sub);
    for (size_t i = 0; i < vlist.size(); ++i)
    {
        typename graph_traits<Graph>::vertex_descriptor ov = vlist[i], ot;
        typename graph_traits<GraphSG>::vertex_descriptor nv = vertex(i,sub);
        typename graph_traits<Graph>::out_edge_iterator e, e_end;
        for (tie(e, e_end) = out_edges(ov, g); e != e_end; ++e)
        {
            ot = target(*e, g);
            typeof(vlist.begin()) viter =
                lower_bound(vlist.begin(), vlist.end(), ot);
            size_t ot_index = viter - vlist.begin();
            if (viter != vlist.end() && vlist[ot_index] == ot &&
                (is_directed::apply<Graph>::type::value || ot < ov))
                add_edge(nv, vertex(ot_index, sub), sub);
        }
    }
}

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// compare two graphs for labeled exactness (not isomorphism)
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template <class Graph>
bool graph_cmp(Graph& g1, Graph& g2)
{
    if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2))
        return false;

    typename graph_traits<Graph>::vertex_iterator v1, v1_end;
    typename graph_traits<Graph>::vertex_iterator v2, v2_end;
    tie(v2, v2_end) = vertices(g2);
    for (tie(v1, v1_end) = vertices(g1); v1 != v1_end; ++v1)
    {
        if (out_degree(*v1, g1) != out_degree(*v2, g2))
            return false;
        if (in_degreeS()(*v1, g1) != in_degreeS()(*v2, g2))
            return false;

        vector<typename graph_traits<Graph>::vertex_iterator> out1, out2;
        typename graph_traits<Graph>::out_edge_iterator e, e_end;
        for (tie(e, e_end) = out_edges(*v1, g1); e != e_end; ++e)
            out1.push_back(target(*e, g1));
        for (tie(e, e_end) = out_edges(*v2, g2); e != e_end; ++e)
            out2.push_back(target(*e, g2));
        sort(out1.begin(), out1.end());
        sort(out2.begin(), out2.end());
        if (out1 != out2)
            return false;
    }
    return true;
}

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// short hand for both types of subgraphs
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typedef adjacency_list<vecS,vecS,bidirectionalS> d_graph_t;
typedef adjacency_list<vecS,vecS,undirectedS> u_graph_t;

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// we need this wrap to use the UndirectedAdaptor only on directed graphs
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struct wrap_undirected
{
    template <class Graph>
    struct apply
    {
        typedef typename mpl::if_<typename is_directed::apply<Graph>::type,
                                  UndirectedAdaptor<Graph>,
                                  Graph&>::type type;
    };
};

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// get the signature of the graph: sorted degree sequence
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template <class Graph>
void get_sig(Graph& g, vector<size_t>& sig)
{
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    sig.clear();
    size_t N = num_vertices(g);
    if (N > 0)
        sig.resize(is_directed::apply<Graph>::type::value ? 2 * N : N);
    for (size_t i = 0; i < N; ++i)
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    {
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        typename graph_traits<Graph>::vertex_descriptor v = vertex(i, g);
        sig[i] = out_degree(v, g);
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        if(is_directed::apply<Graph>::type::value)
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            sig[i + N] = in_degreeS()(v, g);
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    }
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    sort(sig.begin(), sig.end());
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}

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// gets (or samples) all the subgraphs in graph g
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struct get_all_motifs
{
    template <class Graph, class Sampler>
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    void operator()(Graph& g, size_t k, boost::any& list,
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                    vector<size_t>& hist, Sampler sampler, double p,
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                    bool comp_iso, bool fill_list, rng_t& rng) const
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    {
        typedef typename mpl::if_<typename is_directed::apply<Graph>::type,
                                  d_graph_t,
                                  u_graph_t>::type graph_sg_t;

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        // the main subgraph lists
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        vector<graph_sg_t>& subgraph_list =
            any_cast<vector<graph_sg_t>&>(list);

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        // this hashes subgraphs according to their signature
        tr1::unordered_map<vector<size_t>,
                           vector<pair<size_t, graph_sg_t> >,
                           hash<vector<size_t> > > sub_list;
        vector<size_t> sig; // current signature

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        for (size_t i = 0; i < subgraph_list.size(); ++i)
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        {
            get_sig(subgraph_list[i], sig);
            sub_list[sig].push_back(make_pair(i,subgraph_list[i]));
        }
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        // the subgraph count
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        hist.resize(subgraph_list.size());

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        typedef tr1::uniform_real<double> rdist_t;
        tr1::variate_generator<rng_t&, rdist_t> random(rng, rdist_t());

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        // the set of vertices V to be sampled (filled only if p < 1)
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        vector<size_t> V;
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        if (p < 1)
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        {
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            typename graph_traits<Graph>::vertex_iterator v, v_end;
            for (tie(v, v_end) = vertices(g); v != v_end; ++v)
                V.push_back(*v);

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            size_t n;
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            if (random() < p)
                n = ceil(V.size()*p);
            else
                n = floor(V.size()*p);

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            typedef tr1::uniform_int<size_t> idist_t;
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            for (size_t i = 0; i < n; ++i)
            {
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                tr1::variate_generator<rng_t&, idist_t>
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                    random_v(rng, idist_t(0, V.size()-i-1));

                size_t j = i + random_v();
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                swap(V[i], V[j]);
            }
            V.resize(n);
        }

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        int i, N = (p < 1) ? V.size() : num_vertices(g);
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        #pragma omp parallel for default(shared) private(i, sig) \
            schedule(dynamic)
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        for (i = 0; i < N; ++i)
        {
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            vector<vector<typename graph_traits<Graph>::vertex_descriptor> >
                subgraphs;
            typename graph_traits<Graph>::vertex_descriptor v =
                (p < 1) ? V[i] : vertex(i, g);
            if (v == graph_traits<Graph>::null_vertex())
                continue;
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            typename wrap_undirected::apply<Graph>::type ug(g);
            get_subgraphs(ug, v, k, subgraphs, sampler);

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            #pragma omp critical

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            for (size_t j = 0; j < subgraphs.size(); ++j)
            {
                graph_sg_t sub;
                make_subgraph(subgraphs[j], g, sub);
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                get_sig(sub, sig);
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                typeof(sub_list.begin()) iter = sub_list.find(sig);
                if(iter == sub_list.end())
                {
                    if (!fill_list)
                        continue; // avoid inserting an element in sub_list
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                    sub_list[sig].clear();
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                }

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                bool found = false;
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                typeof(sub_list.begin()) sl = sub_list.find(sig);
                if (sl != sub_list.end())
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                {
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                    for (size_t l = 0; l < sl->second.size(); ++l)
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                    {
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                        graph_sg_t& motif = sl->second[l].second;
                        if (comp_iso)
                        {
                            if (isomorphism(motif, sub))
                                found = true;
                        }
                        else
                        {
                            if (graph_cmp(motif, sub))
                                found = true;
                        }
                        if (found)
                        {
                            hist[sl->second[l].first]++;
                            break;
                        }
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                    }
                }

                if (found == false && fill_list)
                {
                    subgraph_list.push_back(sub);
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                    sub_list[sig].push_back(make_pair(subgraph_list.size() - 1,
                                                      sub));
                    hist.push_back(1);
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                }
            }
        }
    }
};

} //graph-tool namespace

#endif // GRAPH_MOTIFS_HH