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;
}
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(°ree, 0);
igraph_degree(&g, °ree, igraph_vss_all(), IGRAPH_ALL, /*loops=*/ 1);
igraph_vector_add_constant(°ree, -1);
igraph_assortativity(&g, °ree, 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, °ree, igraph_vss_all(), IGRAPH_ALL, /*loops=*/ 1);
igraph_vector_add_constant(°ree, -1);
igraph_assortativity(&g, °ree, 0, &res, /*directed=*/ 1);
printf("%.5f\n", res);
igraph_assortativity(&g, °ree, 0, &res, /*directed=*/ 0);
printf("%.5f\n", res);
igraph_vector_destroy(°ree);
/*---------------------*/
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;
}
