graph_motifs.hh 13.3 KB
Newer Older
1
2
// graph-tool -- a general graph modification and manipulation thingy
//
3
// Copyright (C) 2007-2010 Tiago de Paula Peixoto <tiago@forked.de>
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
//
// 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/graph/copy.hpp>
#include <boost/graph/isomorphism.hpp>
23
24
25
26
27
28
29
30
#if (GCC_VERSION >= 40400)
#   include <tr1/unordered_set>
#   include <tr1/random>
#else
#   include <boost/tr1/unordered_set.hpp>
#   include <boost/tr1/random.hpp>
#endif
#include <boost/functional/hash.hpp>
31
32
33
34
35
#include <algorithm>

namespace graph_tool
{

36
typedef tr1::mt19937 rng_t;
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55

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;
}

56
// gets all the subgraphs starting from vertex v and store it in subgraphs.
57
template <class Graph, class Sampler>
58
void get_subgraphs(Graph& g, typename graph_traits<Graph>::vertex_descriptor v,
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
                   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);
        }
    }
}

142
143
// sampling selectors

144
145
146
147
148
149
150
151
152
153
154
155
156
157
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)
    {
158
        typedef tr1::uniform_real<double> rdist_t;
159
        tr1::variate_generator<rng_t&, rdist_t> random(*_rng, rdist_t());
160

161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
        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;
        }

183
        typedef tr1::uniform_int<size_t> idist_t;
184
185
        for (size_t i = 0; i < n; ++i)
        {
186
            tr1::variate_generator<rng_t&, idist_t>
187
                random_v(*_rng, idist_t(0, extend.size()-i-1));
188
189
190
            size_t j;
            {
                #pragma omp critical
191
                j = i + random_v();
192
193
194
195
196
197
198
199
200
201
202
            }
            swap(extend[i], extend[j]);
        }
        extend.resize(n);
    }

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


203
// build the actual induced subgraph from the vertex list
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
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);
        }
    }
}

229
// compare two graphs for labeled exactness (not isomorphism)
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
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;
}

260
// short hand for both types of subgraphs
261
262
263
typedef adjacency_list<vecS,vecS,bidirectionalS> d_graph_t;
typedef adjacency_list<vecS,vecS,undirectedS> u_graph_t;

264
// we need this wrap to use the UndirectedAdaptor only on directed graphs
265
266
267
268
269
270
271
272
273
274
275
struct wrap_undirected
{
    template <class Graph>
    struct apply
    {
        typedef typename mpl::if_<typename is_directed::apply<Graph>::type,
                                  UndirectedAdaptor<Graph>,
                                  Graph&>::type type;
    };
};

Tiago Peixoto's avatar
Tiago Peixoto committed
276
// get the signature of the graph: sorted degree sequence
277
278
279
template <class Graph>
void get_sig(Graph& g, vector<size_t>& sig)
{
Tiago Peixoto's avatar
Tiago Peixoto committed
280
281
282
283
284
    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)
285
    {
Tiago Peixoto's avatar
Tiago Peixoto committed
286
287
        typename graph_traits<Graph>::vertex_descriptor v = vertex(i, g);
        sig[i] = out_degree(v, g);
288
        if(is_directed::apply<Graph>::type::value)
Tiago Peixoto's avatar
Tiago Peixoto committed
289
            sig[i + N] = in_degreeS()(v, g);
290
    }
Tiago Peixoto's avatar
Tiago Peixoto committed
291
    sort(sig.begin(), sig.end());
292
293
}

294
// gets (or samples) all the subgraphs in graph g
295
296
297
struct get_all_motifs
{
    template <class Graph, class Sampler>
298
    void operator()(Graph& g, size_t k, boost::any& list,
299
                    vector<size_t>& hist, Sampler sampler, double p,
300
                    bool comp_iso, bool fill_list, rng_t& rng) const
301
302
303
304
305
    {
        typedef typename mpl::if_<typename is_directed::apply<Graph>::type,
                                  d_graph_t,
                                  u_graph_t>::type graph_sg_t;

306
        // the main subgraph lists
307
308
309
        vector<graph_sg_t>& subgraph_list =
            any_cast<vector<graph_sg_t>&>(list);

310
311
312
313
314
315
        // 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

316
        for (size_t i = 0; i < subgraph_list.size(); ++i)
317
318
319
320
        {
            get_sig(subgraph_list[i], sig);
            sub_list[sig].push_back(make_pair(i,subgraph_list[i]));
        }
321
322

        // the subgraph count
323
324
        hist.resize(subgraph_list.size());

325
326
327
        typedef tr1::uniform_real<double> rdist_t;
        tr1::variate_generator<rng_t&, rdist_t> random(rng, rdist_t());

328
        // the set of vertices V to be sampled (filled only if p < 1)
329
        vector<size_t> V;
330
        if (p < 1)
331
        {
332
333
334
335
            typename graph_traits<Graph>::vertex_iterator v, v_end;
            for (tie(v, v_end) = vertices(g); v != v_end; ++v)
                V.push_back(*v);

336
            size_t n;
337
338
339
340
341
            if (random() < p)
                n = ceil(V.size()*p);
            else
                n = floor(V.size()*p);

342
            typedef tr1::uniform_int<size_t> idist_t;
343
344
            for (size_t i = 0; i < n; ++i)
            {
345
                tr1::variate_generator<rng_t&, idist_t>
346
347
348
                    random_v(rng, idist_t(0, V.size()-i-1));

                size_t j = i + random_v();
349
350
351
352
353
                swap(V[i], V[j]);
            }
            V.resize(n);
        }

354
        int i, N = (p < 1) ? V.size() : num_vertices(g);
355
356
        #pragma omp parallel for default(shared) private(i, sig) \
            schedule(dynamic)
357
358
        for (i = 0; i < N; ++i)
        {
359
360
361
362
363
364
            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;
365
366
367
368

            typename wrap_undirected::apply<Graph>::type ug(g);
            get_subgraphs(ug, v, k, subgraphs, sampler);

Tiago Peixoto's avatar
Tiago Peixoto committed
369
370
            #pragma omp critical

371
372
373
374
            for (size_t j = 0; j < subgraphs.size(); ++j)
            {
                graph_sg_t sub;
                make_subgraph(subgraphs[j], g, sub);
375
                get_sig(sub, sig);
376

377
378
379
380
381
                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
Tiago Peixoto's avatar
Tiago Peixoto committed
382
                    sub_list[sig].clear();
383
384
                }

385
                bool found = false;
Tiago Peixoto's avatar
Tiago Peixoto committed
386
387
                typeof(sub_list.begin()) sl = sub_list.find(sig);
                if (sl != sub_list.end())
388
                {
Tiago Peixoto's avatar
Tiago Peixoto committed
389
                    for (size_t l = 0; l < sl->second.size(); ++l)
390
                    {
Tiago Peixoto's avatar
Tiago Peixoto committed
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
                        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;
                        }
407
408
409
410
411
412
                    }
                }

                if (found == false && fill_list)
                {
                    subgraph_list.push_back(sub);
Tiago Peixoto's avatar
Tiago Peixoto committed
413
414
415
                    sub_list[sig].push_back(make_pair(subgraph_list.size() - 1,
                                                      sub));
                    hist.push_back(1);
416
417
418
419
420
421
422
423
424
                }
            }
        }
    }
};

} //graph-tool namespace

#endif // GRAPH_MOTIFS_HH