Пример #1
0
igraph_vector_t * ggen_analyze_longest_antichain(igraph_t *g)
{
	/* The following steps are implemented :
	 *  - Convert our DAG to a specific bipartite graph B
	 *  - solve maximum matching on B
	 *  - conver maximum matching to min vectex cover
	 *  - convert min vertex cover to antichain on G
	 */
	int err;
	unsigned long i,vg,found,added;
	igraph_t b,gstar;
	igraph_vector_t edges,*res = NULL;
	igraph_vector_t c,s,t,todo,n,next,l,r;
	igraph_eit_t eit;
	igraph_es_t es;
	igraph_integer_t from,to;
	igraph_vit_t vit;
	igraph_vs_t vs;
	igraph_real_t value;

	if(g == NULL)
		return NULL;

	/* before creating the bipartite graph, we need all relations
	 * between any two vertices : the transitive closure of g */
	err = igraph_copy(&gstar,g);
	if(err) return NULL;

	err = ggen_transform_transitive_closure(&gstar);
	if(err) goto error;

	/* Bipartite convertion : let G = (S,C),
	 * we build B = (U,V,E) with
	 *	- U = V = S (each vertex is present twice)
	 *	- (u,v) \in E iff :
	 *		- u \in U
	 *		- v \in V
	 *		- u < v in C (warning, this means that we take
	 *		transitive closure into account, not just the
	 *		original edges)
	 * We will also need two additional nodes further in the code.
	 */
	vg = igraph_vcount(g);
	err = igraph_empty(&b,vg*2,1);
	if(err) goto error;

	/* id and id+vg will be a vertex in U and its copy in V,
	 * iterate over gstar edges to create edges in b
	 */
	err = igraph_vector_init(&edges,igraph_ecount(&gstar));
	if(err) goto d_b;
	igraph_vector_clear(&edges);

	err = igraph_eit_create(&gstar,igraph_ess_all(IGRAPH_EDGEORDER_ID),&eit);
	if(err) goto d_edges;

	for(IGRAPH_EIT_RESET(eit); !IGRAPH_EIT_END(eit); IGRAPH_EIT_NEXT(eit))
	{
		err = igraph_edge(&gstar,IGRAPH_EIT_GET(eit),&from,&to);
		if(err)
		{
			igraph_eit_destroy(&eit);
			goto d_edges;
		}
		to += vg;
		igraph_vector_push_back(&edges,(igraph_real_t)from);
		igraph_vector_push_back(&edges,(igraph_real_t)to);
	}
	igraph_eit_destroy(&eit);
	err = igraph_add_edges(&b,&edges,NULL);
	if(err) goto d_edges;

	/* maximum matching on b */
	igraph_vector_clear(&edges);
	err = bipartite_maximum_matching(&b,&edges);
	if(err) goto d_edges;

	/* Let M be the max matching, and N be E - M
	 * Define T as all unmatched vectices from U as well as all vertices
	 * reachable from those by going left-to-right along N and right-to-left along
	 * M.
	 * Define L = U - T, R = V \inter T
	 * C:= L + R
	 * C is a minimum vertex cover
	 */
	err = igraph_vector_init_seq(&n,0,igraph_ecount(&b)-1);
	if(err) goto d_edges;

	err = vector_diff(&n,&edges);
	if(err) goto d_n;

	err = igraph_vector_init(&c,vg);
	if(err) goto d_n;
	igraph_vector_clear(&c);

	/* matched vertices : S */
	err = igraph_vector_init(&s,vg);
	if(err) goto d_c;
	igraph_vector_clear(&s);

	for(i = 0; i < igraph_vector_size(&edges); i++)
	{
		err = igraph_edge(&b,VECTOR(edges)[i],&from,&to);
		if(err) goto d_s;

		igraph_vector_push_back(&s,from);
	}
	/* we may have inserted the same vertex multiple times */
	err = vector_uniq(&s);
	if(err) goto d_s;

	/* unmatched */
	err = igraph_vector_init_seq(&t,0,vg-1);
	if(err) goto d_s;

	err = vector_diff(&t,&s);
	if(err) goto d_t;

	/* alternating paths
	 */
	err = igraph_vector_copy(&todo,&t);
	if(err) goto d_t;

	err = igraph_vector_init(&next,vg);
	if(err) goto d_todo;
	igraph_vector_clear(&next);
	do {
		vector_uniq(&todo);
		added = 0;
		for(i = 0; i < igraph_vector_size(&todo); i++)
		{
			if(VECTOR(todo)[i] < vg)
			{
				/* scan edges */
				err = igraph_es_adj(&es,VECTOR(todo)[i],IGRAPH_OUT);
				if(err) goto d_next;
				err = igraph_eit_create(&b,es,&eit);
				if(err)
				{
					igraph_es_destroy(&es);
					goto d_next;
				}
				for(IGRAPH_EIT_RESET(eit); !IGRAPH_EIT_END(eit); IGRAPH_EIT_NEXT(eit))
				{
					if(igraph_vector_binsearch(&n,IGRAPH_EIT_GET(eit),NULL))
					{
						err = igraph_edge(&b,IGRAPH_EIT_GET(eit),&from,&to);
						if(err)
						{
							igraph_eit_destroy(&eit);
							igraph_es_destroy(&es);
							goto d_next;
						}
						if(!igraph_vector_binsearch(&t,to,NULL))
						{
							igraph_vector_push_back(&next,to);
							added = 1;
						}
					}
				}
			}
			else
			{
				/* scan edges */
				err = igraph_es_adj(&es,VECTOR(todo)[i],IGRAPH_IN);
				if(err) goto d_next;
				err = igraph_eit_create(&b,es,&eit);
				if(err)
				{
					igraph_es_destroy(&es);
					goto d_next;
				}
				for(IGRAPH_EIT_RESET(eit); !IGRAPH_EIT_END(eit); IGRAPH_EIT_NEXT(eit))
				{
					if(igraph_vector_binsearch(&edges,IGRAPH_EIT_GET(eit),NULL))
					{
						err = igraph_edge(&b,IGRAPH_EIT_GET(eit),&from,&to);
						if(err)
						{
							igraph_eit_destroy(&eit);
							igraph_es_destroy(&es);
							goto d_next;
						}
						if(!igraph_vector_binsearch(&t,to,NULL))
						{
							igraph_vector_push_back(&next,from);
							added = 1;
						}
					}
				}
			}
			igraph_es_destroy(&es);
			igraph_eit_destroy(&eit);
		}
		igraph_vector_append(&t,&todo);
		igraph_vector_clear(&todo);
		igraph_vector_append(&todo,&next);
		igraph_vector_clear(&next);
	} while(added);

	err = igraph_vector_init_seq(&l,0,vg-1);
	if(err) goto d_t;

	err = vector_diff(&l,&t);
	if(err) goto d_l;

	err = igraph_vector_update(&c,&l);
	if(err) goto d_l;

	err = igraph_vector_init(&r,vg);
	if(err) goto d_l;
	igraph_vector_clear(&r);

	/* compute V \inter T */
	for(i = 0; i < igraph_vector_size(&t); i++)
	{
		if(VECTOR(t)[i] >= vg)
			igraph_vector_push_back(&r,VECTOR(t)[i]);
	}

	igraph_vector_add_constant(&r,(igraph_real_t)-vg);
	err = vector_union(&c,&r);
	if(err) goto d_r;

	/* our antichain is U - C */
	res = malloc(sizeof(igraph_vector_t));
	if(res == NULL) goto d_r;

	err = igraph_vector_init_seq(res,0,vg-1);
	if(err) goto f_res;

	err = vector_diff(res,&c);
	if(err) goto d_res;

	goto ret;
d_res:
	igraph_vector_destroy(res);
f_res:
	free(res);
	res = NULL;
ret:
d_r:
	igraph_vector_destroy(&r);
d_l:
	igraph_vector_destroy(&l);
d_next:
	igraph_vector_destroy(&next);
d_todo:
	igraph_vector_destroy(&todo);
d_t:
	igraph_vector_destroy(&t);
d_s:
	igraph_vector_destroy(&s);
d_c:
	igraph_vector_destroy(&c);
d_n:
	igraph_vector_destroy(&n);
d_edges:
	igraph_vector_destroy(&edges);
d_b:
	igraph_destroy(&b);
error:
	igraph_destroy(&gstar);
	return res;
}
Пример #2
0
int main() {

  igraph_t g;
  FILE *karate, *neural;
  igraph_real_t res;
  igraph_vector_t types;
  igraph_vector_t degree, outdegree, indegree;

  igraph_real_t football_types[] = { 
    7,0,2,3,7,3,2,8,8,7,3,10,6,2,6,2,7,9,6,1,9,8,8,7,10,0,6,9,
    11,1,1,6,2,0,6,1,5,0,6,2,3,7,5,6,4,0,11,2,4,11,10,8,3,11,6,
    1,9,4,11,10,2,6,9,10,2,9,4,11,8,10,9,6,3,11,3,4,9,8,8,1,5,3,
    5,11,3,6,4,9,11,0,5,4,4,7,1,9,9,10,3,6,2,1,3,0,7,0,2,3,8,0,
    4,8,4,9,11 };

  karate=fopen("karate.gml", "r");
  igraph_read_graph_gml(&g, karate);
  fclose(karate);
  
  igraph_vector_init(&types, 0);
  igraph_degree(&g, &types, igraph_vss_all(), IGRAPH_ALL, /*loops=*/ 1);

  igraph_assortativity_nominal(&g, &types, &res, /*directed=*/ 0);
  printf("%.5f\n", res);
  
  igraph_destroy(&g);

  /*---------------------*/

  neural=fopen("celegansneural.gml", "r");
  igraph_read_graph_gml(&g, neural);
  fclose(neural);
  
  igraph_degree(&g, &types, igraph_vss_all(), IGRAPH_ALL, /*loops=*/ 1);

  igraph_assortativity_nominal(&g, &types, &res, /*directed=*/ 1);
  printf("%.5f\n", res);  
  igraph_assortativity_nominal(&g, &types, &res, /*directed=*/ 0);
  printf("%.5f\n", res);  

  igraph_destroy(&g);
  igraph_vector_destroy(&types);

  /*---------------------*/
  
  karate=fopen("karate.gml", "r");
  igraph_read_graph_gml(&g, karate);
  fclose(karate);
  
  igraph_vector_init(&degree, 0);
  igraph_degree(&g, &degree, igraph_vss_all(), IGRAPH_ALL, /*loops=*/ 1);
  igraph_vector_add_constant(&degree, -1);

  igraph_assortativity(&g, &degree, 0, &res, /*directed=*/ 0);
  printf("%.5f\n", res);
  
  igraph_destroy(&g);

  /*---------------------*/

  neural=fopen("celegansneural.gml", "r");
  igraph_read_graph_gml(&g, neural);
  fclose(neural);
  
  igraph_degree(&g, &degree, igraph_vss_all(), IGRAPH_ALL, /*loops=*/ 1);
  igraph_vector_add_constant(&degree, -1);

  igraph_assortativity(&g, &degree, 0, &res, /*directed=*/ 1);
  printf("%.5f\n", res);  
  igraph_assortativity(&g, &degree, 0, &res, /*directed=*/ 0);
  printf("%.5f\n", res);  

  igraph_vector_destroy(&degree);

  /*---------------------*/
  
  igraph_vector_init(&indegree, 0);
  igraph_vector_init(&outdegree, 0);
  igraph_degree(&g, &indegree, igraph_vss_all(), IGRAPH_IN, /*loops=*/ 1);
  igraph_degree(&g, &outdegree, igraph_vss_all(), IGRAPH_OUT, /*loops=*/ 1);
  igraph_vector_add_constant(&indegree, -1);
  igraph_vector_add_constant(&outdegree, -1);
  
  igraph_assortativity(&g, &outdegree, &indegree, &res, /*directed=*/ 1);
  printf("%.5f\n", res);

  igraph_vector_destroy(&indegree);
  igraph_vector_destroy(&outdegree);

  /*---------------------*/
  
  igraph_assortativity_degree(&g, &res, /*directed=*/ 1);
  printf("%.5f\n", res);

  igraph_destroy(&g);  

  /*---------------------*/

  karate=fopen("karate.gml", "r");
  igraph_read_graph_gml(&g, karate);
  fclose(karate);
  
  igraph_assortativity_degree(&g, &res, /*directed=*/ 1);
  printf("%.5f\n", res);
  
  igraph_destroy(&g);

  /*---------------------*/
  
  igraph_small(&g, sizeof(football_types)/sizeof(igraph_real_t), 
	       IGRAPH_UNDIRECTED,
	       0,1,2,3,0,4,4,5,3,5,2,6,6,7,7,8,8,9,0,9,4,9,5,10,10,11,5,11,
	       3,11,12,13,2,13,2,14,12,14,14,15,13,15,2,15,4,16,9,16,0,16,
	       16,17,12,17,12,18,18,19,17,20,20,21,8,21,7,21,9,22,7,22,21,
	       22,8,22,22,23,9,23,4,23,16,23,0,23,11,24,24,25,1,25,3,26,12,
	       26,14,26,26,27,17,27,1,27,17,27,4,28,11,28,24,28,19,29,29,
	       30,19,30,18,31,31,32,21,32,15,32,13,32,6,32,0,33,1,33,25,33,
	       19,33,31,34,26,34,12,34,18,34,34,35,0,35,29,35,19,35,30,35,
	       18,36,12,36,20,36,19,36,36,37,1,37,25,37,33,37,18,38,16,38,
	       28,38,26,38,14,38,12,38,38,39,6,39,32,39,13,39,15,39,7,40,3,
	       40,40,41,8,41,4,41,23,41,9,41,0,41,16,41,34,42,29,42,18,42,
	       26,42,42,43,36,43,26,43,31,43,38,43,12,43,14,43,19,44,35,44,
	       30,44,44,45,13,45,33,45,1,45,37,45,25,45,21,46,46,47,22,47,
	       6,47,15,47,2,47,39,47,32,47,44,48,48,49,32,49,46,49,30,50,
	       24,50,11,50,28,50,50,51,40,51,8,51,22,51,21,51,3,52,40,52,5,
	       52,52,53,25,53,48,53,49,53,46,53,39,54,31,54,38,54,14,54,34,
	       54,18,54,54,55,31,55,6,55,35,55,29,55,19,55,30,55,27,56,56,
	       57,1,57,42,57,44,57,48,57,3,58,6,58,17,58,36,58,36,59,58,59,
	       59,60,10,60,39,60,6,60,47,60,13,60,15,60,2,60,43,61,47,61,
	       54,61,18,61,26,61,31,61,34,61,61,62,20,62,45,62,17,62,27,62,
	       56,62,27,63,58,63,59,63,42,63,63,64,9,64,32,64,60,64,2,64,6,
	       64,47,64,13,64,0,65,27,65,17,65,63,65,56,65,20,65,65,66,59,
	       66,24,66,44,66,48,66,16,67,41,67,46,67,53,67,49,67,67,68,15,
	       68,50,68,21,68,51,68,7,68,22,68,8,68,4,69,24,69,28,69,50,69,
	       11,69,69,70,43,70,65,70,20,70,56,70,62,70,27,70,60,71,18,71,
	       14,71,34,71,54,71,38,71,61,71,31,71,71,72,2,72,10,72,3,72,
	       40,72,52,72,7,73,49,73,53,73,67,73,46,73,73,74,2,74,72,74,5,
	       74,10,74,52,74,3,74,40,74,20,75,66,75,48,75,57,75,44,75,75,
	       76,27,76,59,76,20,76,70,76,66,76,56,76,62,76,73,77,22,77,7,
	       77,51,77,21,77,8,77,77,78,23,78,50,78,28,78,22,78,8,78,68,
	       78,7,78,51,78,31,79,43,79,30,79,19,79,29,79,35,79,55,79,79,
	       80,37,80,29,80,16,81,5,81,40,81,10,81,72,81,3,81,81,82,74,
	       82,39,82,77,82,80,82,30,82,29,82,7,82,53,83,81,83,69,83,73,
	       83,46,83,67,83,49,83,83,84,24,84,49,84,52,84,3,84,74,84,10,
	       84,81,84,5,84,3,84,6,85,14,85,38,85,43,85,80,85,12,85,26,85,
	       31,85,44,86,53,86,75,86,57,86,48,86,80,86,66,86,86,87,17,87,
	       62,87,56,87,24,87,20,87,65,87,49,88,58,88,83,88,69,88,46,88,
	       53,88,73,88,67,88,88,89,1,89,37,89,25,89,33,89,55,89,45,89,
	       5,90,8,90,23,90,0,90,11,90,50,90,24,90,69,90,28,90,29,91,48,
	       91,66,91,69,91,44,91,86,91,57,91,80,91,91,92,35,92,15,92,86,
	       92,48,92,57,92,61,92,66,92,75,92,0,93,23,93,80,93,16,93,4,
	       93,82,93,91,93,41,93,9,93,34,94,19,94,55,94,79,94,80,94,29,
	       94,30,94,82,94,35,94,70,95,69,95,76,95,62,95,56,95,27,95,17,
	       95,87,95,37,95,48,96,17,96,76,96,27,96,56,96,65,96,20,96,87,
	       96,5,97,86,97,58,97,11,97,59,97,63,97,97,98,77,98,48,98,84,
	       98,40,98,10,98,5,98,52,98,81,98,89,99,34,99,14,99,85,99,54,
	       99,18,99,31,99,61,99,71,99,14,99,99,100,82,100,13,100,2,100,
	       15,100,32,100,64,100,47,100,39,100,6,100,51,101,30,101,94,
	       101,1,101,79,101,58,101,19,101,55,101,35,101,29,101,100,102,
	       74,102,52,102,98,102,72,102,40,102,10,102,3,102,102,103,33,
	       103,45,103,25,103,89,103,37,103,1,103,70,103,72,104,11,104,
	       0,104,93,104,67,104,41,104,16,104,87,104,23,104,4,104,9,104,
	       89,105,103,105,33,105,62,105,37,105,45,105,1,105,80,105,25,
	       105,25,106,56,106,92,106,2,106,13,106,32,106,60,106,6,106,
	       64,106,15,106,39,106,88,107,75,107,98,107,102,107,72,107,40,
	       107,81,107,5,107,10,107,84,107,4,108,9,108,7,108,51,108,77,
	       108,21,108,78,108,22,108,68,108,79,109,30,109,63,109,1,109,
	       33,109,103,109,105,109,45,109,25,109,89,109,37,109,67,110,
	       13,110,24,110,80,110,88,110,49,110,73,110,46,110,83,110,53,
	       110,23,111,64,111,46,111,78,111,8,111,21,111,51,111,7,111,
	       108,111,68,111,77,111,52,112,96,112,97,112,57,112,66,112,63,
	       112,44,112,92,112,75,112,91,112,28,113,20,113,95,113,59,113,
	       70,113,17,113,87,113,76,113,65,113,96,113,83,114,88,114,110,
	       114,53,114,49,114,73,114,46,114,67,114,58,114,15,114,104,114,
	       -1);
  igraph_simplify(&g, /*multiple=*/ 1, /*loops=*/ 1, /*edge_comb=*/ 0);
  igraph_vector_view(&types, football_types, 
		     sizeof(football_types) / sizeof(igraph_real_t));
  igraph_assortativity_nominal(&g, &types, &res, /*directed=*/ 0);
  printf("%.5f\n", res);
  
  igraph_destroy(&g);
  
  return 0;
}