graph_adjacency.hh 23.8 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
// graph-tool -- a general graph modification and manipulation thingy
//
// Copyright (C) 2006-2013 Tiago de Paula Peixoto <tiago@skewed.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/>.

18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
#ifndef GRAPH_ADJACENCY_HH
#define GRAPH_ADJACENCY_HH

#include <vector>
#include <deque>
#include <utility>
#include <numeric>
#include <iostream>
#include <boost/iterator.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/range/irange.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/properties.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <boost/iterator/iterator_facade.hpp>

34
35
#include "transform_iterator.hh"

36
37
38
39
#include "tr1_include.hh"

#include TR1_HEADER(tuple)

40

41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
namespace boost
{

// ========================================================================
// Forward declarations
// ========================================================================

template <class Vertex>
class adj_list;

// forward declaration of manipulation functions
template <class Vertex>
std::pair<typename adj_list<Vertex>::vertex_iterator,
          typename adj_list<Vertex>::vertex_iterator>
vertices(const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::edge_iterator,
          typename adj_list<Vertex>::edge_iterator>
edges(const adj_list<Vertex>& g);

template <class Vertex>
63
std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
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
edge(Vertex s, Vertex t, const adj_list<Vertex>& g);

template <class Vertex>
size_t out_degree(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
size_t in_degree(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::out_edge_iterator,
          typename adj_list<Vertex>::out_edge_iterator>
out_edges(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::in_edge_iterator,
          typename adj_list<Vertex>::in_edge_iterator>
in_edges(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::adjacency_iterator,
          typename adj_list<Vertex>::adjacency_iterator>
adjacent_vertices(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
size_t num_vertices(const adj_list<Vertex>& g);

template <class Vertex>
size_t num_edges(const adj_list<Vertex>& g);

template <class Vertex>
Vertex add_vertex(adj_list<Vertex>& g);

template <class Vertex>
void clear_vertex(Vertex v, adj_list<Vertex>& g);

template <class Vertex>
void remove_vertex(Vertex v, adj_list<Vertex>& g);

102
103
104
template <class Vertex>
void remove_vertex_fast(Vertex v, adj_list<Vertex>& g);

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
142
143
144
145
146
147
148
149
150
151
152
template <class Vertex>
std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
add_edge(Vertex s, Vertex t, adj_list<Vertex>& g);

template <class Vertex>
void remove_edge(Vertex s, Vertex t, adj_list<Vertex>& g);

template <class Vertex>
void remove_edge(const typename adj_list<Vertex>::edge_descriptor& e,
                 adj_list<Vertex>& g);

// ========================================================================
// adj_list<Vertex>
// ========================================================================
//
// adj_list is a very simple adjacency list implementation for bidirectional
// graphs based on std::vector, meant to be reasonably efficient both
// memory-wise and computationally. It maintains a list of in and out-edges for
// each vertex, and each edge has a built-in index (which is replicated in both
// lists). For each edge, a total of 4 integers is necessary: the source and
// target vertices, in the in_edges and out_edges lists, respectively, and the
// (same) edge index in both lists. The integer type is given by the Vertex
// template parameter. It achieves about half as much memory as
// boost::adjacency_list with an edge index property map and the same integer
// type.

// The complexity guarantees and iterator invalidation rules are the same as
// boost::adjacency_list with vector storage selectors for both vertex and edge
// lists.

template <class Vertex = size_t>
class adj_list
{
public:
    struct graph_tag {};
    typedef Vertex vertex_t;
    typedef std::tr1::tuple<vertex_t, vertex_t, vertex_t> edge_descriptor;
    typedef std::vector<std::pair<vertex_t, vertex_t> > edge_list_t;
    typedef typename integer_range<Vertex>::iterator vertex_iterator;

    struct get_vertex
    {
        get_vertex() {}
        typedef Vertex result_type;
        Vertex operator()(const std::pair<vertex_t, vertex_t>& v) const
        { return v.first; }
    };

153
    typedef transform_random_access_iterator<get_vertex, typename edge_list_t::const_iterator>
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
        adjacency_iterator;

    struct make_out_edge
    {
        make_out_edge(vertex_t src): _src(src) {}
        make_out_edge() {}
        vertex_t _src;
        typedef edge_descriptor result_type;
        edge_descriptor operator()(const std::pair<vertex_t, vertex_t>& v) const
        { return std::tr1::make_tuple(_src, v.first, v.second); }
    };

    struct make_in_edge
    {
        make_in_edge(vertex_t tgt): _tgt(tgt) {}
        make_in_edge() {}
        vertex_t _tgt;
        typedef edge_descriptor result_type;
        edge_descriptor operator()(const std::pair<vertex_t, vertex_t>& v) const
        { return std::tr1::make_tuple(v.first, _tgt, v.second); }
    };

176
    typedef transform_random_access_iterator<make_out_edge, typename edge_list_t::const_iterator>
177
        out_edge_iterator;
178
    typedef transform_random_access_iterator<make_in_edge, typename edge_list_t::const_iterator>
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
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
229
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
        in_edge_iterator;

    class edge_iterator:
        public boost::iterator_facade<edge_iterator,
                                      edge_descriptor,
                                      boost::forward_traversal_tag,
                                      edge_descriptor>
    {
    public:
        edge_iterator() {}
        explicit edge_iterator(const typename std::vector<edge_list_t>::const_iterator& vi_begin,
                               const typename std::vector<edge_list_t>::const_iterator& vi_end,
                               const typename std::vector<edge_list_t>::const_iterator& vi,
                               const typename edge_list_t::const_iterator& ei)
            : _vi_begin(vi_begin), _vi_end(vi_end), _vi(vi), _ei(ei)
        {
            // move position to first edge
            skip();
        }

    private:
        friend class boost::iterator_core_access;

        void skip()
        {
            //skip empty vertices
            while (_vi != _vi_end && _ei == _vi->end())
            {
                ++_vi;
                if (_vi != _vi_end)
                    _ei = _vi->begin();
            }
        }

        void increment()
        {
            ++_ei;
            skip();
        }

        bool equal(edge_iterator const& other) const
        {
            if (_vi_begin == _vi_end)
                return _vi == other._vi;
            return _vi == other._vi && _ei == other._ei;
        }

        edge_descriptor dereference() const
        {
            return std::tr1::make_tuple(vertex_t(_vi - _vi_begin),
                                        _ei->first, _ei->second);
        }

        typename std::vector<edge_list_t>::const_iterator _vi_begin;
        typename std::vector<edge_list_t>::const_iterator _vi_end;
        typename std::vector<edge_list_t>::const_iterator _vi;
        typename edge_list_t::const_iterator _ei;
    };

    void reindex_edges()
    {
        _free_indexes.clear();
        _last_idx = 0;
        _in_edges.clear();
        _in_edges.resize(_out_edges.size());
        for (size_t i = 0; i < _out_edges.size(); ++i)
            for (size_t j = 0; j < _out_edges[i].size(); ++j)
            {
                Vertex v = _out_edges[i][j].first;
                _out_edges[i][j].second = _last_idx;
                _in_edges[v].push_back(std::make_pair(Vertex(i),
                                                      _last_idx));
                _last_idx++;
            }
    }

    size_t get_last_index() const {return _last_idx;}

257
258
    static Vertex null_vertex() { return std::numeric_limits<Vertex>::max(); }

259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
private:
    typedef std::vector<edge_list_t> vertex_list_t;
    vertex_list_t _out_edges;
    vertex_list_t _in_edges;
    size_t _n_edges;
    size_t _last_idx;
    std::deque<size_t> _free_indexes; // indexes of deleted edges to be used up
                                      // for new edges to avoid very large
                                      // indexes, and unnecessary property map
                                      // memory use

    // manipulation functions
    friend std::pair<vertex_iterator, vertex_iterator>
    vertices<>(const adj_list<Vertex>& g);

    friend std::pair<edge_iterator, edge_iterator>
    edges<>(const adj_list<Vertex>& g);

277
    friend std::pair<edge_descriptor, bool>
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
    edge<>(Vertex s, Vertex t, const adj_list<Vertex>& g);

    friend size_t out_degree<>(Vertex v, const adj_list<Vertex>& g);

    friend size_t in_degree<>(Vertex v, const adj_list<Vertex>& g);

    friend std::pair<out_edge_iterator, out_edge_iterator>
    out_edges<>(Vertex v, const adj_list<Vertex>& g);

    friend std::pair<in_edge_iterator, in_edge_iterator>
    in_edges<>(Vertex v, const adj_list<Vertex>& g);

    friend std::pair<adjacency_iterator, adjacency_iterator>
    adjacent_vertices<>(Vertex v, const adj_list<Vertex>& g);

    friend size_t num_vertices<>(const adj_list<Vertex>& g);

    friend size_t num_edges<>(const adj_list<Vertex>& g);

    friend Vertex add_vertex<>(adj_list<Vertex>& g);

    friend void clear_vertex<>(Vertex v, adj_list<Vertex>& g);

    friend void remove_vertex<>(Vertex v, adj_list<Vertex>& g);

303
304
    friend void remove_vertex_fast<>(Vertex v, adj_list<Vertex>& g);

305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
    friend std::pair<edge_descriptor, bool>
    add_edge<>(Vertex s, Vertex t, adj_list<Vertex>& g);

    friend void remove_edge<>(Vertex s, Vertex t, adj_list<Vertex>& g);

    friend void remove_edge<>(const edge_descriptor& e, adj_list<Vertex>& g);
};

//========================================================================
// Graph traits and BGL scaffolding
//========================================================================

struct adj_list_traversal_tag
    : public vertex_list_graph_tag,
      public edge_list_graph_tag,
      public adjacency_graph_tag,
      public bidirectional_graph_tag { };

template <class Vertex>
struct graph_traits<adj_list<Vertex> >
{
    typedef Vertex vertex_descriptor;
    typedef typename adj_list<Vertex>::edge_descriptor edge_descriptor;
    typedef typename adj_list<Vertex>::edge_iterator edge_iterator;
    typedef typename adj_list<Vertex>::adjacency_iterator adjacency_iterator;

    typedef typename adj_list<Vertex>::out_edge_iterator out_edge_iterator;
    typedef typename adj_list<Vertex>::in_edge_iterator in_edge_iterator;

    typedef typename adj_list<Vertex>::vertex_iterator vertex_iterator;

    typedef bidirectional_tag directed_category;
    typedef allow_parallel_edge_tag edge_parallel_category;
    typedef adj_list_traversal_tag traversal_category;

    typedef Vertex vertices_size_type;
    typedef Vertex edges_size_type;
    typedef size_t degree_size_type;

344
    static Vertex null_vertex() { return adj_list<Vertex>::null_vertex(); }
345
346
347
348
349
350
351
private:
    BOOST_STATIC_ASSERT((is_convertible<typename std::iterator_traits<out_edge_iterator>::iterator_category,
                                        std::random_access_iterator_tag>::value));
    BOOST_STATIC_ASSERT((is_convertible<typename std::iterator_traits<in_edge_iterator>::iterator_category,
                                        std::random_access_iterator_tag>::value));
    BOOST_STATIC_ASSERT((is_convertible<typename std::iterator_traits<adjacency_iterator>::iterator_category,
                                        std::random_access_iterator_tag>::value));
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
};

template <class Vertex>
struct graph_traits<const adj_list<Vertex> >
    : public graph_traits<adj_list<Vertex> >
{
};


template <class Vertex>
struct edge_property_type<adj_list<Vertex> >
{
    typedef void type;
};

template <class Vertex>
struct vertex_property_type<adj_list<Vertex> >
{
    typedef void type;
};

template <class Vertex>
struct graph_property_type<adj_list<Vertex> >
{
    typedef void type;
};

//========================================================================
// Graph access and manipulation functions
//========================================================================

template <class Vertex>
inline std::pair<typename adj_list<Vertex>::vertex_iterator,
                 typename adj_list<Vertex>::vertex_iterator>
vertices(const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::vertex_iterator vi_t;
    return std::make_pair(vi_t(0), vi_t(g._out_edges.size()));
}


template <class Vertex>
inline std::pair<typename adj_list<Vertex>::edge_iterator,
                 typename adj_list<Vertex>::edge_iterator>
edges(const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::edge_list_t::const_iterator ei_t;
    typedef typename adj_list<Vertex>::vertex_list_t::const_iterator vi_t;
    ei_t ei_begin = g._out_edges.empty() ? ei_t() : g._out_edges[0].begin();
    vi_t last_vi = g._out_edges.end();
    if (!g._out_edges.empty())
        --last_vi;
    ei_t ei_end = g._out_edges.empty() ? ei_t() : last_vi->end();
    typename adj_list<Vertex>::edge_iterator ebegin(g._out_edges.begin(),
                                                    g._out_edges.end(),
                                                    g._out_edges.begin(),
                                                    ei_begin);
    typename adj_list<Vertex>::edge_iterator eend(g._out_edges.begin(),
                                                  g._out_edges.end(),
                                                  last_vi,
                                                  ei_end);
    return std::make_pair(ebegin, eend);
}

template <class Vertex>
inline Vertex vertex(size_t i, const adj_list<Vertex>&)
{
    return i;
}

template <class Vertex>
423
inline std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
424
425
edge(Vertex s, Vertex t, const adj_list<Vertex>& g)
{
426
    const typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[s];
427
428
429
    for (size_t i = 0; i < oes.size(); ++i)
        if (oes[i].first == t)
            return std::make_pair(std::tr1::make_tuple(s, t, oes[i].second), true);
430
    Vertex v = graph_traits<adj_list<Vertex> >::null_vertex();
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
    return std::make_pair(std::tr1::make_tuple(v, v, v), false);
}

template <class Vertex>
inline size_t out_degree(Vertex v, const adj_list<Vertex>& g)
{
    return g._out_edges[v].size();
}

template <class Vertex>
inline size_t in_degree(Vertex v, const adj_list<Vertex>& g)
{
    return g._in_edges[v].size();
}

template <class Vertex>
inline size_t degree(Vertex v, const adj_list<Vertex>& g)
{
    return in_degree(v, g) + out_degree(v, g);
}

template <class Vertex>
inline std::pair<typename adj_list<Vertex>::out_edge_iterator,
                 typename adj_list<Vertex>::out_edge_iterator>
out_edges(Vertex v, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::out_edge_iterator ei_t;
    typedef typename adj_list<Vertex>::make_out_edge mk_edge;
    return std::make_pair(ei_t(g._out_edges[v].begin(), mk_edge(v)),
                          ei_t(g._out_edges[v].end(), mk_edge(v)));
}

template <class Vertex>
inline std::pair<typename adj_list<Vertex>::in_edge_iterator,
                 typename adj_list<Vertex>::in_edge_iterator>
in_edges(Vertex v, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::in_edge_iterator ei_t;
    typedef typename adj_list<Vertex>::make_in_edge mk_edge;
    return std::make_pair(ei_t(g._in_edges[v].begin(), mk_edge(v)),
                          ei_t(g._in_edges[v].end(), mk_edge(v)));
}

template <class Vertex>
inline std::pair<typename adj_list<Vertex>::adjacency_iterator,
                 typename adj_list<Vertex>::adjacency_iterator>
adjacent_vertices(Vertex v, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::adjacency_iterator ai_t;
    return std::make_pair(ai_t(g._out_edges[v].begin()),
                          ai_t(g._out_edges[v].end()));
}

template <class Vertex>
inline size_t num_vertices(const adj_list<Vertex>& g)
{
    return g._out_edges.size();
}

template <class Vertex>
inline size_t num_edges(const adj_list<Vertex>& g)
{
    return g._n_edges;
}

template <class Vertex>
inline Vertex add_vertex(adj_list<Vertex>& g)
{
    size_t n = g._out_edges.size();
    g._out_edges.resize(n + 1);
    g._in_edges.resize(n + 1);
    return n;
}

template <class Vertex>
inline void clear_vertex(Vertex v, adj_list<Vertex>& g)
{
    typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[v];
    for (size_t i = 0; i < oes.size(); ++i)
    {
        Vertex t = oes[i].first;
        typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[t];
        for (size_t j = 0; j < ies.size(); ++j)
        {
            if (ies[j].first == v)
            {
                g._free_indexes.push_back(ies[j].second);
                ies.erase(ies.begin() + j);
            }
        }
    }
    g._n_edges -= oes.size();
    oes.clear();

    typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[v];
    for (size_t i = 0; i < oes.size(); ++i)
    {
        Vertex s = ies[i].first;
        typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[s];
        for (size_t j = 0; j < oes.size(); ++j)
        {
            if (oes[j].first == v)
            {
                g._free_indexes.push_back(oes[j].second);
                oes.erase(oes.begin() + j);
            }
        }
    }
    g._n_edges -= ies.size();
    ies.clear();
}

543
// O(V + E)
544
545
546
547
548
549
template <class Vertex>
inline void remove_vertex(Vertex v, adj_list<Vertex>& g)
{
    clear_vertex(v, g);
    g._out_edges.erase(g._out_edges.begin() + v);
    g._in_edges.erase(g._in_edges.begin() + v);
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565

    int i, N = g._out_edges.size();
    #pragma omp parallel for default(shared) private(i)
    for (i = 0; i < N; ++i)
    {
        for (size_t j = 0; j < g._out_edges[i].size(); ++j)
        {
            if (g._out_edges[i][j].first > v)
                g._out_edges[i][j].first--;
        }
        for (size_t j = 0; j < g._in_edges[i].size(); ++j)
        {
            if (g._in_edges[i][j].first > v)
                g._in_edges[i][j].first--;
        }
    }
566
567
}

568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
// O(k + k_last)
template <class Vertex>
inline void remove_vertex_fast(Vertex v, adj_list<Vertex>& g)
{
    clear_vertex(v, g);
    Vertex back = g._out_edges.size() - 1;

    if (v < back)
    {
        g._out_edges[v].swap(g._out_edges[back]);
        g._in_edges[v].swap(g._in_edges[back]);

        for (size_t i = 0; i < g._out_edges[v].size(); ++i)
        {
            Vertex u = g._out_edges[v][i].first;
            if (u == back)
            {
                g._out_edges[v][i].first = v;
            }
            else
            {
                for (size_t j = 0; j < g._in_edges[u].size(); ++j)
                    if (g._in_edges[u][j].first == back)
                        g._in_edges[u][j].first = v;
            }
        }

        for (size_t i = 0; i < g._in_edges[v].size(); ++i)
        {
            Vertex u = g._in_edges[v][i].first;
            if (u == back)
            {
                g._out_edges[v][i].first = v;
            }
            else
            {
                for (size_t j = 0; j < g._out_edges[u].size(); ++j)
                    if (g._out_edges[u][j].first == back)
                        g._out_edges[u][j].first = v;
            }
        }
    }

    g._out_edges.pop_back();
    g._in_edges.pop_back();
}
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689

template <class Vertex>
inline typename std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
add_edge(Vertex s, Vertex t, adj_list<Vertex>& g)
{
    Vertex idx;
    if (g._free_indexes.empty())
    {
        idx = g._last_idx++;
    }
    else
    {
        idx = g._free_indexes.front();
        g._free_indexes.pop_front();
    }

    g._out_edges[s].push_back(std::make_pair(t, idx));
    g._in_edges[t].push_back(std::make_pair(s, idx));
    g._n_edges++;

    return std::make_pair(std::tr1::make_tuple(s, t, idx), true);
}

template <class Vertex>
inline void remove_edge(Vertex s, Vertex t,
                        adj_list<Vertex>& g)
{
    typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[s];
    for (size_t i = 0; i < oes.size(); ++i)
    {
        if (t == oes[i].first)
        {
            g._free_indexes.push_back(oes[i].second);
            oes.erase(oes.begin() + i);
            g._n_edges--;
        }
    }

    typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[t];
    for (size_t i = 0; i < ies.size(); ++i)
    {
        if (s == ies[i].first)
            ies.erase(ies.begin() + i);
    }
}

template <class Vertex>
inline void remove_edge(const typename adj_list<Vertex>::edge_descriptor& e,
                        adj_list<Vertex>& g)
{
    Vertex s = get<0>(e);
    Vertex t = get<1>(e);
    Vertex idx = get<2>(e);
    typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[s];
    for (size_t i = 0; i < oes.size(); ++i)
    {
        if (t == oes[i].first && idx == oes[i].second)
        {
            oes.erase(oes.begin() + i);
            break;
        }
    }

    typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[t];
    for (size_t i = 0; i < ies.size(); ++i)
    {
        if (s == ies[i].first && idx == ies[i].second)
        {
            ies.erase(ies.begin() + i);
            break;
        }
    }
    g._free_indexes.push_back(idx);
    g._n_edges--;
}

690

691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
template <class Vertex>
inline Vertex source(const typename adj_list<Vertex>::edge_descriptor& e,
                     const adj_list<Vertex>&)
{
    return get<0>(e);
}

template <class Vertex>
inline Vertex target(const typename adj_list<Vertex>::edge_descriptor& e,
                     const adj_list<Vertex>&)
{
    return get<1>(e);

}

//========================================================================
// Vertex and edge index property maps
//========================================================================

template <class Vertex>
struct property_map<adj_list<Vertex>, vertex_index_t>
{
    typedef identity_property_map type;
    typedef type const_type;
};

template <class Vertex>
struct property_map<const adj_list<Vertex>, vertex_index_t>
{
    typedef identity_property_map type;
    typedef type const_type;
};

template <class Vertex>
inline identity_property_map
get(vertex_index_t, adj_list<Vertex>&)
{
    return identity_property_map();
}

template <class Vertex>
inline identity_property_map
get(vertex_index_t, const adj_list<Vertex>&)
{
    return identity_property_map();
}

struct get_edge_index
{
    typedef size_t result_type;
    template <class Vertex>
    size_t operator()(const typename adj_list<Vertex>::edge_descriptor& e) const
    {
        return get<2>(e);
    }
};

template<class Vertex>
class adj_edge_index_property_map:
    public put_get_helper<Vertex, adj_edge_index_property_map<Vertex> >
{
public:
    typedef typename adj_list<Vertex>::edge_descriptor key_type;
    typedef Vertex reference;
    typedef Vertex value_type;
    typedef boost::readable_property_map_tag category;

    reference operator[](const key_type& k) const {return get<2>(k);}
};

template <class Vertex>
struct property_map<adj_list<Vertex>, edge_index_t>
{
    typedef adj_edge_index_property_map<Vertex> type;
    typedef type const_type;

};

template <class Vertex>
inline adj_edge_index_property_map<Vertex>
get(edge_index_t, const adj_list<Vertex>&)
{
    return adj_edge_index_property_map<Vertex>();
}

} // namespace boost

#endif //GRAPH_ADJACENCY_HH