For using the igraph C library
igraph_disjoint_union
— Creates the union of two disjoint graphs.igraph_disjoint_union_many
— The disjoint union of many graphs.igraph_join
— Creates the join of two disjoint graphs.igraph_union
— Calculates the union of two graphs.igraph_union_many
— Creates the union of many graphs.igraph_intersection
— Collect the common edges from two graphs.igraph_intersection_many
— The intersection of more than two graphs.
igraph_error_t igraph_disjoint_union(igraph_t *res, const igraph_t *left, const igraph_t *right);
First the vertices of the second graph will be relabeled with new vertex IDs to have two disjoint sets of vertex IDs, then the union of the two graphs will be formed. If the two graphs have V1 and V2 vertices and E1 and E2 edges respectively then the new graph will have V1+V2 vertices and E1+E2 edges.
The vertex and edge ordering of the graphs will be preserved. In other words, the vertex and edge IDs of the first graph map to identical values in the new graph, while the vertex and edge IDs of the second graph map to IDs incremented by the vertex and edge count of the first graph.
Both graphs need to have the same directedness, i.e. either both directed or both undirected.
The current version of this function cannot handle graph, vertex and edge attributes, they will be lost.
Arguments:

Pointer to an uninitialized graph object, the result will stored here. 

The first graph. 

The second graph. 
Returns:
Error code. 
See also:

Time complexity: O(V1+V2+E1+E2).
Example 28.1. File examples/simple/igraph_disjoint_union.c
#include <igraph.h> #include <stdio.h> int main(void) { igraph_t left, right, uni; igraph_vector_ptr_t glist; igraph_integer_t i, n; igraph_small(&left, 4, IGRAPH_UNDIRECTED, 0,1, 1,2, 2,2, 2,3, 1); igraph_small(&right, 5, IGRAPH_UNDIRECTED, 0,1, 1,2, 2,2, 2,4, 1); igraph_disjoint_union(&uni, &left, &right); igraph_write_graph_edgelist(&uni, stdout); printf("\n"); igraph_destroy(&left); igraph_destroy(&right); igraph_destroy(&uni); /* Empty graph list; the result is the directed null graph. */ igraph_vector_ptr_init(&glist, 0); igraph_disjoint_union_many(&uni, &glist); if (!igraph_is_directed(&uni)  igraph_vcount(&uni) != 0) { return 1; } igraph_vector_ptr_destroy(&glist); igraph_destroy(&uni); /* Nonempty graph list. */ igraph_vector_ptr_init(&glist, 10); n = igraph_vector_ptr_size(&glist); for (i = 0; i < n; i++) { VECTOR(glist)[i] = calloc(1, sizeof(igraph_t)); igraph_small(VECTOR(glist)[i], 2, IGRAPH_DIRECTED, 0,1, 1,0, 1); } if (!igraph_is_directed(&uni)) { return 2; } igraph_disjoint_union_many(&uni, &glist); igraph_write_graph_edgelist(&uni, stdout); printf("\n"); /* Destroy and free the graph list. */ n = igraph_vector_ptr_size(&glist); for (i = 0; i < n; i++) { igraph_destroy(VECTOR(glist)[i]); free(VECTOR(glist)[i]); } igraph_vector_ptr_destroy(&glist); igraph_destroy(&uni); return 0; }
igraph_error_t igraph_disjoint_union_many(igraph_t *res, const igraph_vector_ptr_t *graphs);
First the vertices in the graphs will be relabeled with new vertex IDs to have pairwise disjoint vertex ID sets and then the union of the graphs is formed. The number of vertices and edges in the result is the total number of vertices and edges in the graphs.
The vertex and edge ordering of the input graphs is preserved in the output graph.
All graphs need to have the same directedness, i.e. either all directed or all undirected. If the graph list has length zero, the result will be a directed graph with no vertices.
The current version of this function cannot handle graph, vertex and edge attributes, they will be lost.
Arguments:

Pointer to an uninitialized graph object, the result of the operation will be stored here. 

Pointer vector, contains pointers to initialized graph objects. 
Returns:
Error code. 
See also:

Time complexity: O(V+E), the number of vertices plus the number of edges in the result.
igraph_error_t igraph_join(igraph_t *res, const igraph_t *left, const igraph_t *right);
This function is experimental and its signature is not considered final yet. We reserve the right to change the function signature without changing the major version of igraph. Use it at your own risk.
First the vertices of the second graph will be relabeled with new vertex IDs to have two disjoint sets of vertex IDs, then the union of the two graphs will be formed. Finally, the vertces from the first graph will have edges added to each vertex from the second. If the two graphs have V1 and V2 vertices and E1 and E2 edges respectively then the new graph will have V1+V2 vertices and E1+E2+V1*V2 edges.
The vertex ordering of the graphs will be preserved. In other words, the vertex IDs of the first graph map to identical values in the new graph, while the vertex IDs of the second graph map to IDs incremented by the vertex count of the first graph. The new edges will be grouped with the other edges that share a from vertex.
Both graphs need to have the same directedness, i.e. either both directed or both undirected. If both graphs are directed, then for each vertex v, u in graphs G1, G2 we add edges (v, u), (u, v) to maintain completeness.
The current version of this function cannot handle graph, vertex and edge attributes, they will be lost.
Arguments:

Pointer to an uninitialized graph object, the result will be stored here. 

The first graph. 

The second graph. 
Returns:
Error code. 
Time complexity: O(V1*V2+E1+E2).
igraph_error_t igraph_union( igraph_t *res, const igraph_t *left, const igraph_t *right, igraph_vector_int_t *edge_map1, igraph_vector_int_t *edge_map2);
The number of vertices in the result is that of the larger graph from the two arguments. The result graph contains edges which are present in at least one of the operand graphs.
The directedness of the operand graphs must be the same.
Edge multiplicities are handled by taking the larger of the two multiplicities in the input graphs. In other words, if the first graph has N edges between a vertex pair (u, v) and the second graph has M edges, the result graph will have max(N, M) edges between them.
Arguments:

Pointer to an uninitialized graph object, the result will be stored here. 

The first graph. 

The second graph. 

Pointer to an initialized vector or a null pointer.
If not a null pointer, it will contain a mapping from the edges
of the first argument graph ( 

The same as 
Returns:
Error code. 
See also:

Time complexity: O(V+E), V is the number of vertices, E the number of edges in the result graph.
Example 28.2. File examples/simple/igraph_union.c
#include <igraph.h> #include <stdio.h> int main(void) { igraph_t left, right, uni; igraph_vector_int_t edge_map1, edge_map2; igraph_vector_int_init(&edge_map1, 0); igraph_vector_int_init(&edge_map2, 0); igraph_small(&left, 4, IGRAPH_DIRECTED, 0,1, 1,2, 2,2, 2,3, 2,3, 3,2, 1); igraph_small(&right, 6, IGRAPH_DIRECTED, 0,1, 1,2, 2,2, 2,3, 5,2, 1); igraph_union(&uni, &left, &right, &edge_map1, &edge_map2); igraph_write_graph_edgelist(&uni, stdout); igraph_vector_int_print(&edge_map1); igraph_vector_int_print(&edge_map2); igraph_destroy(&uni); igraph_destroy(&left); igraph_destroy(&right); igraph_vector_int_destroy(&edge_map2); igraph_vector_int_destroy(&edge_map1); return 0; }
igraph_error_t igraph_union_many( igraph_t *res, const igraph_vector_ptr_t *graphs, igraph_vector_int_list_t *edgemaps );
The result graph will contain as many vertices as the largest graph among the arguments does, and an edge will be included in it if it is part of at least one operand graph.
The number of vertices in the result graph will be the maximum number of vertices in the argument graphs.
The directedness of the argument graphs must be the same. If the graph list has length zero, the result will be a directed graph with no vertices.
Edge multiplicities are handled by taking the maximum multiplicity of the all multiplicities for the same vertex pair (u, v) in the input graphs; this will be the multiplicity of (u, v) in the result graph.
Arguments:

Pointer to an uninitialized graph object, this will contain the result. 

Pointer vector, contains pointers to the operands of the union operator, graph objects of course. 

If not a null pointer, then it must be an initialized
list of integer vectors, and the mappings of edges from the graphs to
the result graph will be stored here, in the same order as

Returns:
Error code. 
See also:

Time complexity: O(V+E), V is the number of vertices in largest graph and E is the number of edges in the result graph.
igraph_error_t igraph_intersection( igraph_t *res, const igraph_t *left, const igraph_t *right, igraph_vector_int_t *edge_map1, igraph_vector_int_t *edge_map2);
The result graph contains only edges present both in the first and the second graph. The number of vertices in the result graph is the same as the larger from the two arguments.
The directedness of the operand graphs must be the same.
Edge multiplicities are handled by taking the smaller of the two multiplicities in the input graphs. In other words, if the first graph has N edges between a vertex pair (u, v) and the second graph has M edges, the result graph will have min(N, M) edges between them.
Arguments:

Pointer to an uninitialized graph object. This will contain the result of the operation. 

The first operand, a graph object. 

The second operand, a graph object. 

Null pointer, or an initialized vector.
If the latter, then a mapping from the edges of the result graph, to
the edges of the 

Null pointer, or an initialized vector. The same
as 
Returns:
Error code. 
See also:

Time complexity: O(V+E), V is the number of nodes, E is the number of edges in the smaller graph of the two. (The one containing less vertices is considered smaller.)
Example 28.3. File examples/simple/igraph_intersection.c
#include <igraph.h> void print_vector(igraph_vector_t *v) { igraph_integer_t i, l = igraph_vector_size(v); for (i = 0; i < l; i++) { printf(" %" IGRAPH_PRId "", (igraph_integer_t) VECTOR(*v)[i]); } printf("\n"); } int main(void) { igraph_t left, right, isec; igraph_vector_int_t v; igraph_vector_ptr_t glist; igraph_t g1, g2, g3; igraph_vector_int_t edge_map1, edge_map2; igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 3, 1); igraph_create(&left, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 1, 0, 5, 4, 1, 2, 3, 2, 1); igraph_create(&right, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init(&edge_map1, 0); igraph_vector_int_init(&edge_map2, 0); igraph_intersection(&isec, &left, &right, &edge_map1, &edge_map2); igraph_vector_int_init(&v, 0); igraph_get_edgelist(&isec, &v, 0); printf("\n"); igraph_vector_int_print(&v); igraph_vector_int_print(&edge_map1); igraph_vector_int_print(&edge_map2); printf("\n"); igraph_vector_int_destroy(&v); igraph_destroy(&left); igraph_destroy(&right); igraph_destroy(&isec); igraph_vector_int_destroy(&edge_map1); igraph_vector_int_destroy(&edge_map2); /* empty graph list */ igraph_vector_ptr_init(&glist, 0); igraph_intersection_many(&isec, &glist, 0); if (igraph_vcount(&isec) != 0  !igraph_is_directed(&isec)) { return 1; } igraph_destroy(&isec); igraph_vector_ptr_destroy(&glist); /* graph list with an empty graph */ igraph_vector_ptr_init(&glist, 3); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 3, 1); igraph_create(&g1, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 3, 1); igraph_create(&g2, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_empty(&g3, 10, IGRAPH_DIRECTED); VECTOR(glist)[0] = &g1; VECTOR(glist)[1] = &g2; VECTOR(glist)[2] = &g3; igraph_intersection_many(&isec, &glist, 0); if (igraph_ecount(&isec) != 0  igraph_vcount(&isec) != 10) { return 2; } igraph_destroy(&g1); igraph_destroy(&g2); igraph_destroy(&g3); igraph_destroy(&isec); igraph_vector_ptr_destroy(&glist); /* "proper" graph list */ igraph_vector_ptr_init(&glist, 3); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 3, 1); igraph_create(&g1, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 3, 3, 2, 4, 5, 6, 5, 1); igraph_create(&g2, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 2, 3, 1, 0, 1, 2, 3, 2, 4, 5, 6, 5, 2, 3, 1); igraph_create(&g3, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); VECTOR(glist)[0] = &g1; VECTOR(glist)[1] = &g2; VECTOR(glist)[2] = &g3; igraph_intersection_many(&isec, &glist, 0); igraph_write_graph_edgelist(&isec, stdout); igraph_destroy(&g1); igraph_destroy(&g2); igraph_destroy(&g3); igraph_destroy(&isec); igraph_vector_ptr_destroy(&glist); return 0; }
igraph_error_t igraph_intersection_many( igraph_t *res, const igraph_vector_ptr_t *graphs, igraph_vector_int_list_t *edgemaps );
This function calculates the intersection of the graphs stored in
the graphs
argument. Only those edges will be included in the
result graph which are part of every graph in graphs
.
The number of vertices in the result graph will be the maximum number of vertices in the argument graphs.
The directedness of the argument graphs must be the same. If the graph list has length zero, the result will be a directed graph with no vertices.
Edge multiplicities are handled by taking the minimum multiplicity of the all multiplicities for the same vertex pair (u, v) in the input graphs; this will be the multiplicity of (u, v) in the result graph.
Arguments:

Pointer to an uninitialized graph object, the result of the operation will be stored here. 

Pointer vector, contains pointers to graphs objects, the operands of the intersection operator. 

If not a null pointer, then it must be an initialized
list of integer vectors, and the mappings of edges from the graphs to
the result graph will be stored here, in the same order as

Returns:
Error code. 
See also:

Time complexity: O(V+E), V is the number of vertices, E is the number of edges in the smallest graph (i.e. the graph having the less vertices).
igraph_error_t igraph_difference(igraph_t *res, const igraph_t *orig, const igraph_t *sub);
The number of vertices in the result is the number of vertices in
the original graph, i.e. the left, first operand. In the results
graph only edges will be included from orig
which are not
present in sub
.
Arguments:

Pointer to an uninitialized graph object, the result will be stored here. 

The left operand of the operator, a graph object. 

The right operand of the operator, a graph object. 
Returns:
Error code. 
See also:

Time complexity: O(V+E), V is the number vertices in the smaller graph, E is the number of edges in the result graph.
Example 28.4. File examples/simple/igraph_difference.c
#include <igraph.h> int main(void) { igraph_t orig, sub, diff; igraph_vector_int_t v; /* Subtract from itself */ printf("subtract itself\n"); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 1, 4, 5, 1); igraph_create(&orig, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_difference(&diff, &orig, &orig); igraph_write_graph_edgelist(&diff, stdout); if (igraph_ecount(&diff) != 0  igraph_vcount(&diff) != igraph_vcount(&orig)) { return 1; } igraph_destroy(&orig); igraph_destroy(&diff); /* Same for undirected graph */ printf("subtract itself, undirected\n"); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 1, 4, 5, 1); igraph_create(&orig, &v, 0, IGRAPH_UNDIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 1, 0, 1, 2, 2, 1, 4, 5, 1); igraph_create(&sub, &v, 0, IGRAPH_UNDIRECTED); igraph_vector_int_destroy(&v); igraph_difference(&diff, &orig, &sub); igraph_write_graph_edgelist(&diff, stdout); if (igraph_ecount(&diff) != 0  igraph_vcount(&diff) != igraph_vcount(&orig)) { return 2; } igraph_destroy(&orig); igraph_destroy(&sub); igraph_destroy(&diff); /* Subtract the empty graph */ printf("subtract empty\n"); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 1, 4, 5, 1); igraph_create(&orig, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_empty(&sub, 3, IGRAPH_DIRECTED); igraph_difference(&diff, &orig, &sub); igraph_write_graph_edgelist(&diff, stdout); if (igraph_ecount(&diff) != igraph_ecount(&orig)  igraph_vcount(&diff) != igraph_vcount(&orig)) { return 3; } igraph_destroy(&orig); igraph_destroy(&sub); igraph_destroy(&diff); /* A `real' example */ printf("real example\n"); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 1, 4, 5, 8, 9, 1); igraph_create(&orig, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 0, 1, 5, 4, 2, 1, 6, 7, 1); igraph_create(&sub, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_difference(&diff, &orig, &sub); igraph_write_graph_edgelist(&diff, stdout); igraph_destroy(&diff); igraph_destroy(&orig); igraph_destroy(&sub); /* undirected version */ printf("real example, undirected\n"); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 1, 4, 5, 8, 9, 8, 10, 8, 13, 8, 11, 8, 12, 1); igraph_create(&orig, &v, 0, IGRAPH_UNDIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 0, 1, 5, 4, 2, 1, 6, 7, 8, 10, 8, 13, 1); igraph_create(&sub, &v, 0, IGRAPH_UNDIRECTED); igraph_vector_int_destroy(&v); igraph_difference(&diff, &orig, &sub); igraph_write_graph_edgelist(&diff, stdout); igraph_destroy(&diff); igraph_destroy(&orig); igraph_destroy(&sub); /* undirected version with loop edge, tests Github issue #597 */ printf("Github issue #597, undirected\n"); igraph_vector_int_init_int_end(&v, 1, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 0, 1); igraph_create(&orig, &v, 0, IGRAPH_UNDIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1); igraph_create(&sub, &v, 0, IGRAPH_UNDIRECTED); igraph_vector_int_destroy(&v); igraph_difference(&diff, &orig, &sub); igraph_write_graph_edgelist(&diff, stdout); igraph_destroy(&diff); igraph_destroy(&orig); igraph_destroy(&sub); return 0; }
igraph_error_t igraph_complementer(igraph_t *res, const igraph_t *graph, igraph_bool_t loops);
The complementer graph means that all edges which are not part of the original graph will be included in the result.
Arguments:

Pointer to an uninitialized graph object. 

The original graph. 

Whether to add loop edges to the complementer graph. 
Returns:
Error code. 
See also:
Time complexity: O(V+E1+E2), V is the number of vertices in the graph, E1 is the number of edges in the original and E2 in the complementer graph.
Example 28.5. File examples/simple/igraph_complementer.c
#include <igraph.h> int main(void) { igraph_t g1, g2; /* complementer of the empty graph */ igraph_empty(&g1, 5, IGRAPH_DIRECTED); igraph_complementer(&g2, &g1, IGRAPH_LOOPS); igraph_write_graph_edgelist(&g2, stdout); igraph_destroy(&g1); igraph_destroy(&g2); printf("\n"); /* the same without loops */ igraph_empty(&g1, 5, IGRAPH_DIRECTED); igraph_complementer(&g2, &g1, IGRAPH_NO_LOOPS); igraph_write_graph_edgelist(&g2, stdout); igraph_destroy(&g1); igraph_destroy(&g2); printf("\n"); /* complementer of the full graph */ igraph_full(&g1, 5, IGRAPH_DIRECTED, IGRAPH_LOOPS); igraph_complementer(&g2, &g1, IGRAPH_LOOPS); if (igraph_ecount(&g2) != 0) { return 1; } igraph_destroy(&g1); igraph_destroy(&g2); printf("\n"); /* complementer of the full graph, results loops only */ igraph_full(&g1, 5, IGRAPH_DIRECTED, IGRAPH_NO_LOOPS); igraph_complementer(&g2, &g1, IGRAPH_LOOPS); igraph_write_graph_edgelist(&g2, stdout); igraph_destroy(&g1); igraph_destroy(&g2); printf("\n"); /************** * undirected * *************/ /* complementer of the empty graph */ igraph_empty(&g1, 5, IGRAPH_UNDIRECTED); igraph_complementer(&g2, &g1, IGRAPH_LOOPS); igraph_write_graph_edgelist(&g2, stdout); igraph_destroy(&g1); igraph_destroy(&g2); printf("\n"); /* the same without loops */ igraph_empty(&g1, 5, IGRAPH_UNDIRECTED); igraph_complementer(&g2, &g1, IGRAPH_NO_LOOPS); igraph_write_graph_edgelist(&g2, stdout); igraph_destroy(&g1); igraph_destroy(&g2); printf("\n"); /* complementer of the full graph */ igraph_full(&g1, 5, IGRAPH_UNDIRECTED, IGRAPH_LOOPS); igraph_complementer(&g2, &g1, IGRAPH_LOOPS); if (igraph_ecount(&g2) != 0) { return 1; } igraph_destroy(&g1); igraph_destroy(&g2); printf("\n"); /* complementer of the full graph, results loops only */ igraph_full(&g1, 5, IGRAPH_UNDIRECTED, IGRAPH_NO_LOOPS); igraph_complementer(&g2, &g1, IGRAPH_LOOPS); igraph_write_graph_edgelist(&g2, stdout); igraph_destroy(&g1); igraph_destroy(&g2); return 0; }
igraph_error_t igraph_compose(igraph_t *res, const igraph_t *g1, const igraph_t *g2, igraph_vector_int_t *edge_map1, igraph_vector_int_t *edge_map2);
The composition of graphs contains the same number of vertices as the bigger graph of the two operands. It contains an (i,j) edge if and only if there is a k vertex, such that the first graph contains an (i,k) edge and the second graph a (k,j) edge.
This is of course exactly the composition of two binary relations.
The two graphs must have the same directedness, otherwise the function returns with an error. Note that for undirected graphs the two relations are by definition symmetric.
Arguments:

Pointer to an uninitialized graph object, the result will be stored here. 

The firs operand, a graph object. 

The second operand, another graph object. 

If not a null pointer, then it must be a pointer to an initialized vector, and a mapping from the edges of the result graph to the edges of the first graph is stored here. 

If not a null pointer, then it must be a pointer to an initialized vector, and a mapping from the edges of the result graph to the edges of the second graph is stored here. 
Returns:
Error code. 
Time complexity: O(V*d1*d2), V is the number of vertices in the first graph, d1 and d2 the average degree in the first and second graphs.
Example 28.6. File examples/simple/igraph_compose.c
#include <igraph.h> int main(void) { igraph_t g1, g2, res; igraph_vector_int_t v; igraph_vector_int_t map1, map2; igraph_vector_int_init(&map1, 0); igraph_vector_int_init(&map2, 0); /* composition with the empty graph */ igraph_empty(&g1, 5, IGRAPH_DIRECTED); igraph_full(&g2, 5, IGRAPH_DIRECTED, IGRAPH_NO_LOOPS); igraph_compose(&res, &g1, &g2, &map1, &map2); if (igraph_ecount(&res) != 0) { return 1; } if (igraph_vector_int_size(&map1) != 0  igraph_vector_int_size(&map2) != 0) { return 11; } igraph_destroy(&res); igraph_compose(&res, &g2, &g1, &map1, &map2); if (igraph_ecount(&res) != 0) { return 2; } if (igraph_vector_int_size(&map1) != 0  igraph_vector_int_size(&map2) != 0) { return 12; } igraph_destroy(&res); igraph_destroy(&g1); igraph_destroy(&g2); /* same but undirected */ igraph_empty(&g1, 5, IGRAPH_UNDIRECTED); igraph_full(&g2, 5, IGRAPH_UNDIRECTED, IGRAPH_NO_LOOPS); igraph_compose(&res, &g1, &g2, &map1, &map2); if (igraph_ecount(&res) != 0) { return 1; } if (igraph_vector_int_size(&map1) != 0  igraph_vector_int_size(&map2) != 0) { return 11; } igraph_destroy(&res); igraph_compose(&res, &g2, &g1, &map1, &map2); if (igraph_ecount(&res) != 0) { return 2; } if (igraph_vector_int_size(&map1) != 0  igraph_vector_int_size(&map2) != 0) { return 12; } igraph_destroy(&res); igraph_destroy(&g1); igraph_destroy(&g2); /* proper directed graph */ igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 5, 6, 1); igraph_create(&g1, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 0, 1, 2, 4, 5, 6, 1); igraph_create(&g2, &v, 0, IGRAPH_DIRECTED); igraph_vector_int_destroy(&v); igraph_compose(&res, &g1, &g2, &map1, &map2); igraph_write_graph_edgelist(&res, stdout); igraph_vector_int_print(&map1); igraph_vector_int_print(&map2); igraph_destroy(&res); igraph_destroy(&g1); igraph_destroy(&g2); /* undirected graph */ igraph_vector_int_init_int_end(&v, 1, 0, 1, 1, 2, 5, 6, 1); igraph_create(&g1, &v, 0, IGRAPH_UNDIRECTED); igraph_vector_int_destroy(&v); igraph_vector_int_init_int_end(&v, 1, 0, 1, 0, 4, 5, 6, 1); igraph_create(&g2, &v, 0, IGRAPH_UNDIRECTED); igraph_vector_int_destroy(&v); igraph_compose(&res, &g1, &g2, &map1, &map2); igraph_write_graph_edgelist(&res, stdout); igraph_vector_int_print(&map1); igraph_vector_int_print(&map2); igraph_destroy(&res); igraph_destroy(&g1); igraph_destroy(&g2); igraph_vector_int_destroy(&map2); igraph_vector_int_destroy(&map1); return 0; }
igraph_connect_neighborhood
— Connects each vertex to its neighborhood.igraph_contract_vertices
— Replace multiple vertices with a single one.igraph_graph_power
— The kth power of a graph.igraph_induced_subgraph
— Creates a subgraph induced by the specified vertices.igraph_induced_subgraph_map
— Creates an induced subraph and returns the mapping from the original.igraph_induced_subgraph_edges
— The edges contained within an induced subgraph.igraph_linegraph
— Create the line graph of a graph.igraph_simplify
— Removes loop and/or multiple edges from the graph.igraph_subgraph_from_edges
— Creates a subgraph with the specified edges and their endpoints.igraph_reverse_edges
— Reverses some edges of a directed graph.
igraph_error_t igraph_connect_neighborhood(igraph_t *graph, igraph_integer_t order, igraph_neimode_t mode);
This function adds new edges to the input graph. Each vertex is connected
to all vertices reachable by at most order
steps from it
(unless a connection already existed).
Note that the input graph is modified in place, no
new graph is created. Call igraph_copy()
if you want to keep
the original graph as well.
For undirected graphs reachability is always
symmetric: if vertex A can be reached from vertex B in at
most order
steps, then the opposite is also true. Only one
undirected (A,B) edge will be added in this case.
Arguments:

The input graph. It will be modified inplace. 

Integer constant, it gives the distance within which the vertices will be connected to the source vertex. 

Constant, it specifies how the neighborhood search is
performed for directed graphs. If 
Returns:
Error code. 
See also:

Time complexity: O(V*d^k), V is the number of vertices in the
graph, d is the average degree and k is the order
argument.
igraph_error_t igraph_contract_vertices(igraph_t *graph, const igraph_vector_int_t *mapping, const igraph_attribute_combination_t *vertex_comb);
This function modifies the graph by merging several vertices
into one. The vertices in the modified graph correspond
to groups of vertices in the input graph. No edges are removed,
thus the modified graph will typically have selfloops
(corresponding to ingroup edges) and multiedges
(corresponding to multiple connections between two groups).
Use igraph_simplify()
to eliminate selfloops and
merge multiedges.
Arguments:

The input graph. It will be modified inplace. 

A vector giving the mapping. For each vertex in the original graph, it should contain its desired ID in the result graph. In order not to create "orphan vertices" that have no corresponding vertices in the original graph, ensure that the IDs are consecutive integers starting from zero. 

What to do with the vertex attributes.

Returns:
Error code. 
Time complexity: O(V+E), linear in the number or vertices plus edges.
Example 28.7. File examples/simple/igraph_contract_vertices.c
#include <igraph.h> /* Create the condensation of a directed graph. * See https://en.wikipedia.org/wiki/Strongly_connected_component#Definitions * This example demonstrates how to write a basic igraph function, complete * with error handling. */ igraph_error_t condensation(const igraph_t *graph, igraph_t *cond) { igraph_vector_int_t membership; /* Data structures such as vector must be initialized in igraph before use. */ IGRAPH_CHECK(igraph_vector_int_init(&membership, 0)); /* Adding the initialized vector to the "finally" stack ensures that it will * be automatically destroyed if an error occurs. */ IGRAPH_FINALLY(igraph_vector_int_destroy, &membership); /* Functions that return an error code can be wrapped in IGRAPH_CHECK to pass that error * up to the caller. */ IGRAPH_CHECK(igraph_connected_components(graph, &membership, /* csize */ NULL, /* no */ NULL, IGRAPH_STRONG)); /* To compute the condensation, we simply contract strongly connected components. * Since igraph_contract_vertices() modifies graphs inplace, we make a copy first. */ IGRAPH_CHECK(igraph_copy(cond, graph)); /* Since we are not done creating the condensation yet, we add 'cond' to the * "finally" stack, so that it will be destroyed if an error occurs. */ IGRAPH_FINALLY(igraph_destroy, cond); /* Contract strongly connected components. */ IGRAPH_CHECK(igraph_contract_vertices(cond, &membership, NULL)); /* igraph_contract_vertices() preserves all edges, some of which become * parallel edges or selfloops after the contraction. We simplify these. */ IGRAPH_CHECK(igraph_simplify(cond, /* remove_multiple */ true, /* remove_loops */ true, NULL)); /* Data structures that are no longer needed must be explicitly destroyed. * If they were added to the "finally" stack, they must be removed explicitly, * in the opposite order to how they were added. IGRAPH_FINALLY_CLEAN removes * the indicated number of entries from the "finally" stack. We remove * 'membership' because it was destroyed, and 'cond' because the responsibility * to destroy it is now with the caller. */ igraph_vector_int_destroy(&membership); IGRAPH_FINALLY_CLEAN(2); return IGRAPH_SUCCESS; /* return with no error */ } int main(void) { igraph_t graph, cond; /* Create a random directed graph with mean degree 2 and compute its condensation. */ igraph_erdos_renyi_game_gnm(&graph, 100, 200, IGRAPH_DIRECTED, IGRAPH_NO_LOOPS); condensation(&graph, &cond); printf("Number of vertices in the condensation: %" IGRAPH_PRId "\n", igraph_vcount(&cond)); igraph_write_graph_edgelist(&cond, stdout); /* Destroy data structures that are no longer needed. */ igraph_destroy(&graph); igraph_destroy(&cond); return 0; }
igraph_error_t igraph_graph_power(const igraph_t *graph, igraph_t *res, igraph_integer_t order, igraph_bool_t directed);
This function is experimental and its signature is not considered final yet. We reserve the right to change the function signature without changing the major version of igraph. Use it at your own risk.
The kth power of a graph G is a simple graph where vertex u
is connected to
v
by a single edge if v
is reachable from u
in G within at most k steps.
By convention, the zeroth power of a graph has no edges. The first power is
identical to the original graph, except that multiple edges and selfloops
are removed.
Graph power is usually defined only for undirected graphs. igraph extends the concept
to directed graphs. To ignore edge directions in the input, set the directed
parameter to false
. In this case, the result will be an undirected graph.
Graph and vertex attributes are preserved, but edge attributes are discarded.
Arguments:

The input graph. 

The graph power of the given 

Nonnegative integer, the power to raise the graph to.
In other words, vertices within a distance 

Logical, whether to take edge directions into account. 
Returns:
Error code. 
See also:

Time complexity: O(V*d^k), V is the number of vertices in the
graph, d is the average degree and k is the order
argument.
igraph_error_t igraph_induced_subgraph(const igraph_t *graph, igraph_t *res, const igraph_vs_t vids, igraph_subgraph_implementation_t impl);
This function collects the specified vertices and all edges between
them to a new graph. As vertex IDs are always contiguos integers starting
at zero, the IDs in the created subgraph will be different from the IDs in
the original graph. To get the mappings between them, use
igraph_induced_subgraph_map()
Arguments:

The graph object. 

The subgraph, another graph object will be stored here,
do not initialize this object before calling this
function, and call 

A vertex selector describing which vertices to keep. A vertex may appear more than once in the selector, but it will be considered only once (i.e. it is not possible to duplicate a vertex by adding its ID more than once to the selector). The order in which the vertices appear in the vertex selector is ignored; the returned subgraph will always contain the vertices of the original graph in increasing order of vertex IDs. 

This parameter selects which implementation should we
use when constructing the new graph. Basically there are two
possibilities: 
Returns:
Error code:

Time complexity: O(V+E), V and E are the number of vertices and edges in the original graph.
See also:

igraph_error_t igraph_induced_subgraph_map(const igraph_t *graph, igraph_t *res, const igraph_vs_t vids, igraph_subgraph_implementation_t impl, igraph_vector_int_t *map, igraph_vector_int_t *invmap);
This function collects the specified vertices and all edges between
them to a new graph. As vertex IDs are always contiguos integers starting
at zero, the IDs in the created subgraph will be different from the IDs in
the original graph. The mapping between the vertex IDs in the graph and the
extracted subgraphs are returned in map
and invmap
.
Arguments:

The graph object. 

The subgraph, another graph object will be stored here,
do not initialize this object before calling this
function, and call 

A vertex selector describing which vertices to keep. 

This parameter selects which implementation should be
used when constructing the new graph. Basically there are two
possibilities: 

Returns a map of the vertices in 

Returns a map of the vertices in 
Returns:
Error code:

Time complexity: O(V+E), V and E are the number of vertices and edges in the original graph.
See also:

igraph_error_t igraph_induced_subgraph_edges(const igraph_t *graph, igraph_vs_t vids, igraph_vector_int_t *edges);
This function finds the IDs of those edges which connect vertices from
a given list, passed in the vids
parameter.
Arguments:

The graph. 

A vertex selector specifying the vertices that make up the subgraph. 

Integer vector. The IDs of edges within the subgraph induces by

Returns:
Error code. 
Time complexity: O(mv log(nv)) where nv is the number of vertices in vids
and mv is the sum of degrees of vertices in vids
.
igraph_error_t igraph_linegraph(const igraph_t *graph, igraph_t *linegraph);
The line graph L(G) of a G undirected graph is defined as follows. L(G) has one vertex for each edge in G and two different vertices in L(G) are connected by an edge if their corresponding edges share an end point. In a multigraph, if two end points are shared, two edges are created. The single vertex of an undirected selfloop is counted as two end points.
The line graph L(G) of a G directed graph is slightly different: L(G) has one vertex for each edge in G and two vertices in L(G) are connected by a directed edge if the target of the first vertex's corresponding edge is the same as the source of the second vertex's corresponding edge.
Selfloops are considered selfadjacent, thus their corresponding vertex in the line graph will also a have a single selfloop, in both undirected and directed graphs.
Edge i in the original graph will correspond to vertex i in the line graph.
The first version of this function was contributed by Vincent Matossian, thanks.
Arguments:

The input graph, may be directed or undirected. 

Pointer to an uninitialized graph object, the result is stored here. 
Returns:
Error code. 
Time complexity: O(V+E), the number of edges plus the number of vertices.
igraph_error_t igraph_simplify(igraph_t *graph, igraph_bool_t remove_multiple, igraph_bool_t remove_loops, const igraph_attribute_combination_t *edge_comb);
This function merges parallel edges and removes selfloops, according
to the multiple
and loops
parameters. Note that this function
may change the edge order, even if the input was already a simple graph.
Arguments:

The graph object. 

Logical, if true, multiple edges will be removed. 

Logical, if true, loops (self edges) will be removed. 

What to do with the edge attributes. 
Returns:
Error code:

Time complexity: O(V+E).
Example 28.8. File examples/simple/igraph_simplify.c
#include <igraph.h> int main(void) { igraph_t g; /* Multiple edges */ igraph_small(&g, 0, IGRAPH_DIRECTED, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1); igraph_simplify(&g, true, true, /*edge_comb=*/ NULL); igraph_write_graph_edgelist(&g, stdout); igraph_destroy(&g); igraph_small(&g, 0, IGRAPH_UNDIRECTED, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1); igraph_simplify(&g, true, true, /*edge_comb=*/ NULL); if (igraph_ecount(&g) != 1) { return 1; } igraph_destroy(&g); /* Loop edges*/ igraph_small(&g, 0, IGRAPH_DIRECTED, 0, 0, 1, 1, 2, 2, 1, 2, 1); igraph_simplify(&g, true, true, /*edge_comb=*/ NULL); igraph_write_graph_edgelist(&g, stdout); igraph_destroy(&g); igraph_small(&g, 0, IGRAPH_UNDIRECTED, 0, 0, 1, 1, 2, 2, 1, 2, 1); igraph_simplify(&g, true, true, /*edge_comb=*/ NULL); igraph_write_graph_edgelist(&g, stdout); igraph_destroy(&g); /* Loop & multiple edges */ igraph_small(&g, 0, IGRAPH_DIRECTED, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1); igraph_simplify(&g, /* remove_multiple */ true, /* remove_loops */ false, /*edge_comb=*/ NULL); igraph_write_graph_edgelist(&g, stdout); igraph_destroy(&g); igraph_small(&g, 0, IGRAPH_UNDIRECTED, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1); igraph_simplify(&g, /* remove_multiple */ true, /* remove_loops */ false, /*edge_comb=*/ NULL); igraph_write_graph_edgelist(&g, stdout); igraph_destroy(&g); igraph_small(&g, 0, IGRAPH_DIRECTED, 2, 2, 2, 2, 2, 2, 3, 2, 1); igraph_simplify(&g, /* remove_multiple */ false, /* remove_loops */ true, /*edge_comb=*/ NULL); igraph_write_graph_edgelist(&g, stdout); igraph_destroy(&g); igraph_small(&g, 0, IGRAPH_UNDIRECTED, 3, 3, 3, 3, 3, 4, 1); igraph_simplify(&g, /* remove_multiple */ false, /* remove_loops */ true, /*edge_comb=*/ NULL); igraph_write_graph_edgelist(&g, stdout); igraph_destroy(&g); igraph_small(&g, 0, IGRAPH_DIRECTED, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 1); igraph_simplify(&g, true, true, /*edge_comb=*/ NULL); igraph_write_graph_edgelist(&g, stdout); igraph_destroy(&g); igraph_small(&g, 0, IGRAPH_UNDIRECTED, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 3, 2, 1); igraph_simplify(&g, true, true, /*edge_comb=*/ NULL); if (igraph_ecount(&g) != 1) { return 2; } igraph_destroy(&g); return 0; }
igraph_error_t igraph_subgraph_from_edges( const igraph_t *graph, igraph_t *res, const igraph_es_t eids, igraph_bool_t delete_vertices );
This function collects the specified edges and their endpoints to a new
graph. As the edge IDs in a graph are always contiguous integers starting at
zero, the edge IDs in the extracted subgraph will be different from those
in the original graph. Vertex IDs will also be reassigned if
delete_vertices
is set to true
. Attributes are preserved.
Arguments:

The graph object. 

The subgraph, another graph object will be stored here,
do not initialize this object before calling this
function, and call 

An edge selector describing which edges to keep. 

Whether to delete the vertices not incident on any
of the specified edges as well. If 
Returns:
Error code:

Time complexity: O(V+E), V and E are the number of vertices and edges in the original graph.
See also:

igraph_error_t igraph_reverse_edges(igraph_t *graph, const igraph_es_t eids);
This function reverses some edges of a directed graph. The modification is done in place. All attributes, as well as the ordering of edges and vertices are preserved.
Note that is rarely necessary to reverse all edges, as almost all functions that
handle directed graphs take a mode
argument that can be set to IGRAPH_IN
to
effectively treat edges as reversed.
Arguments:

The graph whose edges will be reversed. 

The edges to be reversed.
Pass 
Returns:
Error code. 
Time complexity: O(1) if all edges are reversed, otherwise O(E) where E is the number of edges in the graph.
igraph_error_t igraph_subgraph_edges( const igraph_t *graph, igraph_t *res, const igraph_es_t eids, igraph_bool_t delete_vertices );
Deprecated since version 0.10.3. Please do not use this function in new
code; use igraph_subgraph_from_edges()
instead.
← Chapter 27. Embedding of graphs  Chapter 29. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs → 