igraph Reference Manual

For using the igraph C library

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Chapter 4. About igraph graphs, the basic interface

1. The igraph data model

The igraph library can handle directed and undirected graphs. The igraph graphs are multisets of ordered (if directed) or unordered (if undirected) labeled pairs. The labels of the pairs plus the number of vertices always starts with zero and ends with the number of edges minus one. In addition to that a table of metadata is also attached to every graph, its most important entries are the number of vertices in the graph and whether the graph is directed or undirected.

Like the edges, the igraph vertices are also labeled by numbers between zero and the number of vertices minus one. So, to summarize, a directed graph can be imagined like this:

  ( vertices: 6,
    directed: yes,
    {
     (0,2),
     (2,2),
     (2,3),
     (3,3),
     (3,4),
     (3,4),
     (4,1)
    }
  )

Here the edges are ordered pairs or vertex IDs, and the graph is a multiset of edges plus some meta-data.

An undirected graph is like this:

  ( vertices: 6,
    directed: no,
    {
     {0,2},
     {2},
     {2,3},
     {3},
     {3,4},
     {3,4},
     {4,1}
    }
  )

Here an edge is a set of one or two vertex IDs, two for most of the time, except for loop edges. A graph is a multiset of edges plus meta data, just like in the directed case.

It is possible to convert a directed graph to an undirected one, see the igraph_to_directed() and igraph_to_undirected() functions.

Note that igraph has some limited support for graphs with multiple edges. The support means that multiple edges can be stored in igraph graphs, but for most functions (like igraph_betweenness()) it is not checked that they work well on graphs with multiple edges. To eliminate multiple edges from a graph, you can use igraph_simplify().

2. The basic interface

This is the very minimal API in igraph. All the other functions use this minimal set for creating and manipulating graphs.

This is a very important principle since it makes possible to implement other data representations by implementing only this minimal set.

2.1. Graph constructors and destructors

2.1.1. igraph_empty — Creates an empty graph with some vertices and no edges.

igraph_error_t igraph_empty(igraph_t *graph, igraph_integer_t n, igraph_bool_t directed);

The most basic constructor, all the other constructors should call this to create a minimal graph object. Our use of the term "empty graph" in the above description should be distinguished from the mathematical definition of the empty or null graph. Strictly speaking, the empty or null graph in graph theory is the graph with no vertices and no edges. However by "empty graph" as used in igraph we mean a graph having zero or more vertices, but no edges.

Arguments: 

graph:

Pointer to a not-yet initialized graph object.

n:

The number of vertices in the graph, a non-negative integer number is expected.

directed:

Boolean; whether the graph is directed or not. Supported values are:

IGRAPH_DIRECTED

The graph will be directed.

IGRAPH_UNDIRECTED

The graph will be undirected.

Returns: 

Error code: IGRAPH_EINVAL: invalid number of vertices.

Time complexity: O(|V|) for a graph with |V| vertices (and no edges).

Example 4.1.  File examples/simple/igraph_empty.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard st, Cambridge MA, 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

int main() {

    igraph_t g;
    int ret;

    /* empty directed graph, zero vertices */
    igraph_empty(&g, 0, 1);
    if (igraph_vcount(&g) != 0) {
        return 1;
    }
    if (igraph_ecount(&g) != 0) {
        return 2;
    }
    igraph_destroy(&g);

    /* empty undirected graph, zero vertices */
    igraph_empty(&g, 0, 0);
    if (igraph_vcount(&g) != 0) {
        return 3;
    }
    if (igraph_ecount(&g) != 0) {
        return 4;
    }
    igraph_destroy(&g);

    /* empty directed graph, 20 vertices */
    igraph_empty(&g, 20, 1);
    if (igraph_vcount(&g) != 20) {
        return 5;
    }
    if (igraph_ecount(&g) != 0) {
        return 6;
    }
    igraph_destroy(&g);

    /* empty undirected graph, 30 vertices */
    igraph_empty(&g, 30, 0);
    if (igraph_vcount(&g) != 30) {
        return 7;
    }
    if (igraph_ecount(&g) != 0) {
        return 8;
    }
    igraph_destroy(&g);

    /* error: negative number of vertices */
    igraph_set_error_handler(igraph_error_handler_ignore);
    ret = igraph_empty(&g, -1, 0);
    if (ret != IGRAPH_EINVAL) {
        return 9;
    }

    return 0;
}


2.1.2. igraph_empty_attrs — Creates an empty graph with some vertices, no edges and some graph attributes.

igraph_error_t igraph_empty_attrs(igraph_t *graph, igraph_integer_t n, igraph_bool_t directed, void* attr);

Use this instead of igraph_empty() if you wish to add some graph attributes right after initialization. This function is currently not very interesting for the ordinary user. Just supply 0 here or use igraph_empty().

Arguments: 

graph:

Pointer to a not-yet initialized graph object.

n:

The number of vertices in the graph; a non-negative integer number is expected.

directed:

Boolean; whether the graph is directed or not. Supported values are:

IGRAPH_DIRECTED

Create a directed graph.

IGRAPH_UNDIRECTED

Create an undirected graph.

attr:

The attributes.

Returns: 

Error code: IGRAPH_EINVAL: invalid number of vertices.

Time complexity: O(|V|) for a graph with |V| vertices (and no edges).

2.1.3. igraph_copy — Creates an exact (deep) copy of a graph.

igraph_error_t igraph_copy(igraph_t *to, const igraph_t *from);

This function deeply copies a graph object to create an exact replica of it. The new replica should be destroyed by calling igraph_destroy() on it when not needed any more.

You can also create a shallow copy of a graph by simply using the standard assignment operator, but be careful and do not destroy a shallow replica. To avoid this mistake, creating shallow copies is not recommended.

Arguments: 

to:

Pointer to an uninitialized graph object.

from:

Pointer to the graph object to copy.

Returns: 

Error code.

Time complexity: O(|V|+|E|) for a graph with |V| vertices and |E| edges.

Example 4.2.  File examples/simple/igraph_copy.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard street, Cambridge, MA 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

int main() {

    igraph_t g1, g2;
    igraph_vector_int_t v1, v2;

    igraph_vector_int_init(&v1, 8);
    VECTOR(v1)[0] = 0;
    VECTOR(v1)[1] = 1;
    VECTOR(v1)[2] = 1;
    VECTOR(v1)[3] = 2;
    VECTOR(v1)[4] = 2;
    VECTOR(v1)[5] = 3;
    VECTOR(v1)[6] = 2;
    VECTOR(v1)[7] = 2;

    igraph_create(&g1, &v1, 0, 0);
    igraph_copy(&g2, &g1);

    igraph_vector_int_init(&v2, 0);
    igraph_get_edgelist(&g2, &v2, 0);
    if (!igraph_vector_int_all_e(&v1, &v2)) {
        return 1;
    }

    igraph_vector_int_destroy(&v1);
    igraph_vector_int_destroy(&v2);
    igraph_destroy(&g1);
    igraph_destroy(&g2);

    return 0;
}


2.1.4. igraph_destroy — Frees the memory allocated for a graph object.

void igraph_destroy(igraph_t *graph);

This function should be called for every graph object exactly once.

This function invalidates all iterators (of course), but the iterators of a graph should be destroyed before the graph itself anyway.

Arguments: 

graph:

Pointer to the graph to free.

Time complexity: operating system specific.

2.2. Basic query operations

2.2.1. igraph_vcount — The number of vertices in a graph.

igraph_integer_t igraph_vcount(const igraph_t *graph);

Arguments: 

graph:

The graph.

Returns: 

Number of vertices.

Time complexity: O(1)

2.2.2. igraph_ecount — The number of edges in a graph.

igraph_integer_t igraph_ecount(const igraph_t *graph);

Arguments: 

graph:

The graph.

Returns: 

Number of edges.

Time complexity: O(1)

2.2.3. igraph_edge — Gives the head and tail vertices of an edge.

igraph_error_t igraph_edge(const igraph_t *graph, igraph_integer_t eid,
                igraph_integer_t *from, igraph_integer_t *to);

Arguments: 

graph:

The graph object.

eid:

The edge ID.

from:

Pointer to an igraph_integer_t. The tail (head) of the edge will be placed here for undirected (directed) graphs.

to:

Pointer to an igraph_integer_t. The head (tail) of the edge will be placed here for undirected (directed) graphs.

Returns: 

Error code. The current implementation always returns with success.

See also: 

igraph_get_eid() for the opposite operation; igraph_edges() to get the endpoints of several edges; IGRAPH_TO(), IGRAPH_FROM() and IGRAPH_OTHER() for a faster but non-error-checked version.

Added in version 0.2.

Time complexity: O(1).

2.2.4. igraph_edges — Gives the head and tail vertices of a series of edges.

igraph_error_t igraph_edges(const igraph_t *graph, igraph_es_t eids,
                 igraph_vector_int_t *edges);

Arguments: 

graph:

The graph object.

eids:

Edge selector, the series of edges.

edges:

Pointer to an initialized vector. The start and endpoints of each edge will be placed here.

Returns: 

Error code.

See also: 

igraph_get_edgelist() to get the endpoints of all edges; igraph_get_eids() and igraph_get_eids_multi() for the opposite operation; igraph_edge() for getting the endpoints of a single edge; IGRAPH_TO(), IGRAPH_FROM() and IGRAPH_OTHER() for a faster but non-error-checked method.

Time complexity: O(k) where k is the number of edges in the selector.

2.2.5. IGRAPH_FROM — The source vertex of an edge.

#define IGRAPH_FROM(graph,eid)

Faster than igraph_edge(), but no error checking is done: eid is assumed to be valid.

Arguments: 

graph:

The graph.

eid:

The edge ID.

Returns: 

The source vertex of the edge.

See also: 

igraph_edge() if error checking is desired.

2.2.6. IGRAPH_TO — The target vertex of an edge.

#define IGRAPH_TO(graph,eid)

Faster than igraph_edge(), but no error checking is done: eid is assumed to be valid.

Arguments: 

graph:

The graph object.

eid:

The edge ID.

Returns: 

The target vertex of the edge.

See also: 

igraph_edge() if error checking is desired.

2.2.7. IGRAPH_OTHER — The other endpoint of an edge.

#define IGRAPH_OTHER(graph,eid,vid)

Typically used with undirected edges when one endpoint of the edge is known, and the other endpoint is needed. No error checking is done: eid and vid are assumed to be valid.

Arguments: 

graph:

The graph object.

eid:

The edge ID.

vid:

The vertex ID of one endpoint of an edge.

Returns: 

The other endpoint of the edge.

See also: 

IGRAPH_TO() and IGRAPH_FROM() to get the source and target of directed edges.

2.2.8. igraph_get_eid — Get the edge ID from the end points of an edge.

igraph_error_t igraph_get_eid(const igraph_t *graph, igraph_integer_t *eid,
                   igraph_integer_t pfrom, igraph_integer_t pto,
                   igraph_bool_t directed, igraph_bool_t error);

For undirected graphs pfrom and pto are exchangeable.

Arguments: 

graph:

The graph object.

eid:

Pointer to an integer, the edge ID will be stored here.

pfrom:

The starting point of the edge.

pto:

The end point of the edge.

directed:

Logical constant, whether to search for directed edges in a directed graph. Ignored for undirected graphs.

error:

Logical scalar, whether to report an error if the edge was not found. If it is false, then -1 will be assigned to eid.

Returns: 

Error code.

See also: 

igraph_edge() for the opposite operation.

Time complexity: O(log (d)), where d is smaller of the out-degree of pfrom and in-degree of pto if directed is true. If directed is false, then it is O(log(d)+log(d2)), where d is the same as before and d2 is the minimum of the out-degree of pto and the in-degree of pfrom.

Example 4.3.  File examples/simple/igraph_get_eid.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard st, Cambridge MA, 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

int main() {
    igraph_t g;
    igraph_integer_t eid;
    igraph_vector_int_t hist;
    igraph_integer_t i;
    igraph_error_t ret;

    /* DIRECTED */

    igraph_star(&g, 10, IGRAPH_STAR_OUT, 0);

    igraph_vector_int_init(&hist, 9);

    for (i = 1; i < 10; i++) {
        igraph_get_eid(&g, &eid, 0, i, IGRAPH_DIRECTED, /*error=*/ 1);
        VECTOR(hist)[ eid ] = 1;
    }

    igraph_vector_int_print(&hist);

    igraph_vector_int_destroy(&hist);
    igraph_destroy(&g);

    /* UNDIRECTED */

    igraph_star(&g, 10, IGRAPH_STAR_UNDIRECTED, 0);

    igraph_vector_int_init(&hist, 9);

    for (i = 1; i < 10; i++) {
        igraph_get_eid(&g, &eid, 0, i, IGRAPH_UNDIRECTED, /*error=*/ 1);
        VECTOR(hist)[ eid ] += 1;
        igraph_get_eid(&g, &eid, i, 0, IGRAPH_DIRECTED, /*error=*/ 1);
        VECTOR(hist)[ eid ] += 1;
    }
    igraph_vector_int_print(&hist);

    igraph_vector_int_destroy(&hist);
    igraph_destroy(&g);

    /* NON-EXISTENT EDGE */

    igraph_star(&g, 10, IGRAPH_STAR_UNDIRECTED, 0);

    igraph_set_error_handler(igraph_error_handler_ignore);

    ret = igraph_get_eid(&g, &eid, 5, 6, IGRAPH_UNDIRECTED, /*error=*/ 1);
    if (ret != IGRAPH_EINVAL) {
        return 1;
    }

    igraph_destroy(&g);

    return 0;
}

/* Stress test */

/* int main() { */

/*   igraph_t g; */
/*   igraph_integer_t i, n; */
/*   igraph_integer_t from, to, eid; */

/*   igraph_barabasi_game(&g, 10000, 100, 0, 0, 1); */
/*   n=igraph_ecount(&g); */
/*   for (i=0; i<n; i++) { */
/*     igraph_edge(&g, i, &from, &to); */
/*     igraph_get_eid(&g, &eid, from, to, 1, 1); */
/*     igraph_get_eid(&g, &eid, to, from, 0, 1); */
/*     igraph_get_eid(&g, &eid, from, to, 0, 1); */
/*   } */
/*   igraph_destroy(&g); */

/*   igraph_barabasi_game(&g, 10000, 100, 0, 0, 0); */
/*   n=igraph_ecount(&g); */
/*   for (i=0; i<n; i++) { */
/*     igraph_edge(&g, i, &from, &to); */
/*     igraph_get_eid(&g, &eid, from, to, 0, 1); */
/*     igraph_get_eid(&g, &eid, to, from, 0, 1); */
/*   } */
/*   igraph_destroy(&g); */

/*   igraph_erdos_renyi_game(&g, IGRAPH_ERDOS_RENYI_GNP, */
/*            2000, 100.0/2000, 0, 0); */
/*   n=igraph_ecount(&g); */
/*   for (i=0; i<n; i++) { */
/*     igraph_edge(&g, i, &from, &to); */
/*     igraph_get_eid(&g, &eid, from, to, 0, 1); */
/*     igraph_get_eid(&g, &eid, to, from, 0, 1); */
/*   } */
/*   igraph_destroy(&g); */

/*   igraph_full(&g, 500, 0, 0); */
/*   n=igraph_ecount(&g); */
/*   for (i=0; i<n; i++) { */
/*     igraph_edge(&g, i, &from, &to); */
/*     igraph_get_eid(&g, &eid, from, to, 0, 1); */
/*   } */
/*   igraph_destroy(&g); */

/*   igraph_star(&g, 20000, IGRAPH_STAR_OUT, 0); */
/*   n=igraph_ecount(&g); */
/*   for (i=0; i<n; i++) { */
/*     igraph_edge(&g, i, &from, &to); */
/*     igraph_get_eid(&g, &eid, from, to, 0, 1); */
/*   } */
/*   igraph_destroy(&g); */

/*   igraph_star(&g, 20000, IGRAPH_STAR_IN, 0); */
/*   n=igraph_ecount(&g); */
/*   for (i=0; i<n; i++) { */
/*     igraph_edge(&g, i, &from, &to); */
/*     igraph_get_eid(&g, &eid, from, to, 0, 1); */
/*   } */
/*   igraph_destroy(&g); */

/*   igraph_star(&g, 2000000, IGRAPH_STAR_UNDIRECTED, 1999999); */
/*   n=igraph_ecount(&g); */
/*   for (i=0; i<n; i++) { */
/*     igraph_edge(&g, i, &from, &to); */
/*     igraph_get_eid(&g, &eid, from, to, 0, 1); */
/*     igraph_get_eid(&g, &eid, to, from, 0, 1); */
/*   } */
/*   igraph_destroy(&g); */

/*   return 0; */
/* } */


Added in version 0.2.

2.2.9. igraph_get_eids — Return edge IDs based on the adjacent vertices.

igraph_error_t igraph_get_eids(const igraph_t *graph, igraph_vector_int_t *eids,
                    const igraph_vector_int_t *pairs,
                    const igraph_vector_int_t *path,
                    igraph_bool_t directed, igraph_bool_t error);

This function operates in two modes. If the pairs argument is not a null pointer, but the path argument is, then it searches for the edge IDs of all pairs of vertices given in pairs. The pairs of vertex IDs are taken consecutively from the vector, i.e. VECTOR(pairs)[0] and VECTOR(pairs)[1] give the first pair, VECTOR(pairs)[2] and VECTOR(pairs)[3] the second pair, etc.

If the pairs argument is a null pointer, and path is not a null pointer, then the path is interpreted as a path given by vertex IDs and the edges along the path are returned.

If neither pairs nor path are null pointers, then both are considered (first pairs and then path), and the results are concatenated.

If the error argument is true, then it is an error to give pairs of vertices that are not connected. Otherwise -1 is reported for not connected vertices.

If there are multiple edges in the graph, then these are ignored; i.e. for a given pair of vertex IDs, always the same edge ID is returned, even if the pair is given multiple time in pairs or in path. See igraph_get_eids_multi() for a similar function that works differently in case of multiple edges.

Arguments: 

graph:

The input graph.

eids:

Pointer to an initialized vector, the result is stored here. It will be resized as needed.

pairs:

Vector giving pairs of vertices, or a null pointer.

path:

Vector giving vertex IDs along a path, or a null pointer.

directed:

Logical scalar, whether to consider edge directions in directed graphs. This is ignored for undirected graphs.

error:

Logical scalar, whether it is an error to supply non-connected vertices. If false, then -1 is returned for non-connected pairs.

Returns: 

Error code.

Time complexity: O(n log(d)), where n is the number of queried edges and d is the average degree of the vertices.

See also: 

igraph_get_eid() for a single edge, igraph_get_eids_multi() for a version that handles multiple edges better (at a cost).

Example 4.4.  File examples/simple/igraph_get_eids.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2008-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard st, Cambridge MA, 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>
#include <stdlib.h>

void print_vector_int(igraph_vector_int_t *v, FILE *f) {
    igraph_integer_t i;
    for (i = 0; i < igraph_vector_int_size(v); i++) {
        fprintf(f, " %" IGRAPH_PRId, VECTOR(*v)[i]);
    }
    fprintf(f, "\n");
}

int check_simple() {

    igraph_t g;
    igraph_integer_t nodes = 100;
    igraph_integer_t edges = 1000;
    igraph_real_t p = 3.0 / nodes;
    igraph_integer_t runs = 10;
    igraph_integer_t r, e, ecount;
    igraph_vector_int_t eids, pairs, path;

    igraph_rng_seed(igraph_rng_default(), 42); /* make tests deterministic */

    igraph_vector_int_init(&pairs, edges * 2);
    igraph_vector_int_init(&path, 0);
    igraph_vector_int_init(&eids, 0);

    for (r = 0; r < runs; r++) {
        igraph_erdos_renyi_game(&g, IGRAPH_ERDOS_RENYI_GNP, nodes, p,
                                /*directed=*/ 0, /*loops=*/ 0);
        ecount = igraph_ecount(&g);
        for (e = 0; e < edges; e++) {
            igraph_integer_t edge = RNG_INTEGER(0, ecount - 1);
            VECTOR(pairs)[2 * e] = IGRAPH_FROM(&g, edge);
            VECTOR(pairs)[2 * e + 1] = IGRAPH_TO(&g, edge);
        }
        igraph_get_eids(&g, &eids, &pairs, /*path=*/ 0, 0, /*error=*/ 1);
        for (e = 0; e < edges; e++) {
            igraph_integer_t edge = VECTOR(eids)[e];
            igraph_integer_t from1 = VECTOR(pairs)[2 * e];
            igraph_integer_t to1 = VECTOR(pairs)[2 * e + 1];
            igraph_integer_t from2 = IGRAPH_FROM(&g, edge);
            igraph_integer_t to2 = IGRAPH_TO(&g, edge);
            igraph_integer_t min1 = from1 < to1 ? from1 : to1;
            igraph_integer_t max1 = from1 < to1 ? to1 : from1;
            igraph_integer_t min2 = from2 < to2 ? from2 : to2;
            igraph_integer_t max2 = from2 < to2 ? to2 : from2;
            if (min1 != min2 || max1 != max2) {
                return 11;
            }
        }

        igraph_diameter(&g, /*res=*/ 0, /*from=*/ 0, /*to=*/ 0, &path, NULL,
                        IGRAPH_UNDIRECTED, /*unconn=*/ 1);
        igraph_get_eids(&g, &eids, /*pairs=*/ 0, &path, 0, /*error=*/ 1);
        for (e = 0; e < igraph_vector_int_size(&path) - 1; e++) {
            igraph_integer_t edge = VECTOR(eids)[e];
            igraph_integer_t from1 = VECTOR(path)[e];
            igraph_integer_t to1 = VECTOR(path)[e + 1];
            igraph_integer_t from2 = IGRAPH_FROM(&g, edge);
            igraph_integer_t to2 = IGRAPH_TO(&g, edge);
            igraph_integer_t min1 = from1 < to1 ? from1 : to1;
            igraph_integer_t max1 = from1 < to1 ? to1 : from1;
            igraph_integer_t min2 = from2 < to2 ? from2 : to2;
            igraph_integer_t max2 = from2 < to2 ? to2 : from2;
            if (min1 != min2 || max1 != max2) {
                return 12;
            }
        }

        igraph_destroy(&g);
    }

    igraph_vector_int_destroy(&path);
    igraph_vector_int_destroy(&pairs);
    igraph_vector_int_destroy(&eids);

    return 0;
}

int check_multi() {

    igraph_t g;
    igraph_vector_int_t vec;
    igraph_vector_int_t eids;
    igraph_vector_int_t eids2;
    igraph_error_t ret;
    igraph_integer_t i;

    igraph_integer_t q1[] = { 0, 1, 0, 1 };
    igraph_integer_t q2[] = { 0, 1, 0, 1, 0, 1 };
    igraph_integer_t q3[] = { 1, 0, 3, 4, 1, 0, 0, 1, 3, 4, 0, 1 };

    igraph_vector_int_init(&eids, 0);

    /*********************************/
    igraph_small(&g, /*n=*/ 10, /*directed=*/ 1,
                 0, 1, 0, 1, 1, 0, 1, 2, 3, 4, 3, 4, 3, 4, 3, 5, 3, 7,
                 9, 8,
                 -1);

    igraph_vector_int_view(&vec, q1, sizeof(q1) / sizeof(q1[0]));
    igraph_get_eids_multi(&g, &eids, &vec, 0, /*directed=*/ 1, /*error=*/ 1);
    igraph_vector_int_sort(&eids);
    print_vector_int(&eids, stdout);

    igraph_vector_int_view(&vec, q2, sizeof(q2) / sizeof(q2[0]));
    igraph_get_eids_multi(&g, &eids, &vec, 0, /*directed=*/ 0, /*error=*/ 1);
    igraph_vector_int_sort(&eids);
    print_vector_int(&eids, stdout);

    igraph_vector_int_view(&vec, q2, sizeof(q2) / sizeof(q2[0]));
    igraph_set_error_handler(igraph_error_handler_ignore);
    ret = igraph_get_eids_multi(&g, &eids, &vec, 0, /*directed=*/ 1, /*error=*/1);
    if (ret != IGRAPH_EINVAL) {
        return 1;
    }
    igraph_set_error_handler(igraph_error_handler_abort);

    igraph_destroy(&g);
    /*********************************/

    /*********************************/
    igraph_small(&g, /*n=*/10, /*directed=*/0,
                 0, 1, 1, 0, 0, 1, 3, 4, 3, 4, 5, 4, 9, 8,
                 -1);

    igraph_vector_int_view(&vec, q1, sizeof(q1) / sizeof(q1[0]));
    igraph_get_eids_multi(&g, &eids, &vec, 0, /*directed=*/1, /*error=*/ 1);
    igraph_vector_int_sort(&eids);
    print_vector_int(&eids, stdout);

    igraph_vector_int_view(&vec, q3, sizeof(q3) / sizeof(q3[0]));
    igraph_set_error_handler(igraph_error_handler_ignore);
    ret = igraph_get_eids_multi(&g, &eids, &vec, 0, /*directed=*/0, /*error=*/ 1);
    if (ret != IGRAPH_EINVAL) {
        return 2;
    }
    igraph_set_error_handler(igraph_error_handler_abort);

    igraph_destroy(&g);

    /*********************************/

    igraph_vector_int_destroy(&eids);

    /*********************************/
    /* Speed tests */

#define NODES 10000
    igraph_barabasi_game(&g, /*n=*/ NODES, /*power=*/ 1.0, /*m=*/ 3,
                         /*outseq=*/ 0, /*outpref=*/ 0, /*A=*/ 1,
                         /*directed=*/ 1, IGRAPH_BARABASI_BAG,
                         /*start_from=*/ 0);
    igraph_simplify(&g, /*multiple=*/ 1, /*loops=*/ 0, /*edge_comb=*/ 0);

    igraph_vector_int_init(&eids2, NODES / 2);
    igraph_random_sample(&eids2, 0, igraph_ecount(&g) - 1, NODES / 2);
    igraph_vector_int_init(&vec, NODES);
    for (i = 0; i < NODES / 2; i++) {
        VECTOR(vec)[2 * i]   = IGRAPH_FROM(&g, VECTOR(eids2)[i]);
        VECTOR(vec)[2 * i + 1] = IGRAPH_TO(&g, VECTOR(eids2)[i]);
    }
    igraph_vector_int_init(&eids, 0);
    igraph_get_eids_multi(&g, &eids, &vec, 0, /*directed=*/ 1, /*error=*/ 1);
    for (i = 0; i < NODES / 2; i++) {
        if (VECTOR(eids)[i] != VECTOR(eids2)[i]) {
            return 3;
        }
    }

    /**/

    for (i = 0; i < NODES / 2; i++) {
        VECTOR(vec)[2 * i]   = IGRAPH_TO(&g, VECTOR(eids)[i]);
        VECTOR(vec)[2 * i + 1] = IGRAPH_FROM(&g, VECTOR(eids)[i]);
    }
    igraph_get_eids_multi(&g, &eids, &vec, 0, /*directed=*/ 0, /*error=*/ 1);
    for (i = 0; i < NODES / 2; i++) {
        if (VECTOR(eids)[i] != VECTOR(eids2)[i]) {
            return 4;
        }
    }

    igraph_vector_int_destroy(&eids);
    igraph_vector_int_destroy(&eids2);
    igraph_vector_int_destroy(&vec);
    igraph_destroy(&g);

    /*********************************/

    return 0;
}

int main() {
    int ret;

    if ( (ret = check_simple()) != 0) {
        return ret;
    }
    if ( (ret = check_multi()) != 0)  {
        return ret;
    }

    return 0;
}


2.2.10. igraph_get_eids_multi — Query edge IDs based on their adjacent vertices, handle multiple edges.

igraph_error_t igraph_get_eids_multi(const igraph_t *graph, igraph_vector_int_t *eids,
                          const igraph_vector_int_t *pairs,
                          const igraph_vector_int_t *path,
                          igraph_bool_t directed, igraph_bool_t error);

This function operates in two modes. If the pairs argument is not a null pointer, but the path argument is, then it searches for the edge IDs of all pairs of vertices given in pairs. The pairs of vertex IDs are taken consecutively from the vector, i.e. VECTOR(pairs)[0] and VECTOR(pairs)[1] give the first pair, VECTOR(pairs)[2] and VECTOR(pairs)[3] the second pair, etc.

If the pairs argument is a null pointer, and path is not a null pointer, then the path is interpreted as a path given by vertex IDs and the edges along the path are returned.

If the error argument is true, then it is an error to give pairs of vertices that are not connected. Otherwise -1 is returned for not connected vertex pairs.

An error is triggered if both pairs and path are non-null pointers.

This function handles multiple edges properly, i.e. if the same pair is given multiple times and they are indeed connected by multiple edges, then each time a different edge ID is reported.

Arguments: 

graph:

The input graph.

eids:

Pointer to an initialized vector, the result is stored here. It will be resized as needed.

pairs:

Vector giving pairs of vertices, or a null pointer.

path:

Vector giving vertex IDs along a path, or a null pointer.

directed:

Logical scalar, whether to consider edge directions in directed graphs. This is ignored for undirected graphs.

error:

Logical scalar, whether to report an error if non-connected vertices are specified. If false, then -1 is returned for non-connected vertex pairs.

Returns: 

Error code.

Time complexity: O(|E|+n log(d)), where |E| is the number of edges in the graph, n is the number of queried edges and d is the average degree of the vertices.

See also: 

igraph_get_eid() for a single edge, igraph_get_eids() for a faster version that does not handle multiple edges.

2.2.11. igraph_neighbors — Adjacent vertices to a vertex.

igraph_error_t igraph_neighbors(const igraph_t *graph, igraph_vector_int_t *neis, igraph_integer_t pnode,
        igraph_neimode_t mode);

Arguments: 

graph:

The graph to work on.

neis:

This vector will contain the result. The vector should be initialized beforehand and will be resized. Starting from igraph version 0.4 this vector is always sorted, the vertex IDs are in increasing order. If one neighbor is connected with multiple edges, the neighbor will be returned multiple times.

pnode:

The id of the node for which the adjacent vertices are to be searched.

mode:

Defines the way adjacent vertices are searched in directed graphs. It can have the following values: IGRAPH_OUT, vertices reachable by an edge from the specified vertex are searched; IGRAPH_IN, vertices from which the specified vertex is reachable are searched; IGRAPH_ALL, both kinds of vertices are searched. This parameter is ignored for undirected graphs.

Returns: 

Error code: IGRAPH_EINVVID: invalid vertex ID. IGRAPH_EINVMODE: invalid mode argument. IGRAPH_ENOMEM: not enough memory.

Time complexity: O(d), d is the number of adjacent vertices to the queried vertex.

Example 4.5.  File examples/simple/igraph_neighbors.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard st, Cambridge MA, 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

void print_vector(igraph_vector_int_t *v, FILE *f) {
    igraph_integer_t i;
    for (i = 0; i < igraph_vector_int_size(v); i++) {
        fprintf(f, " %" IGRAPH_PRId "", VECTOR(*v)[i]);
    }
    fprintf(f, "\n");
}

int main() {

    igraph_t g;
    igraph_vector_int_t v;
    igraph_error_t ret;

    igraph_vector_int_init(&v, 8);
    VECTOR(v)[0] = 0;
    VECTOR(v)[1] = 1;
    VECTOR(v)[2] = 1;
    VECTOR(v)[3] = 2;
    VECTOR(v)[4] = 2;
    VECTOR(v)[5] = 3;
    VECTOR(v)[6] = 2;
    VECTOR(v)[7] = 2;
    igraph_create(&g, &v, 0, 1);

    igraph_neighbors(&g, &v, 2, IGRAPH_OUT);
    igraph_vector_int_sort(&v);
    print_vector(&v, stdout);

    igraph_neighbors(&g, &v, 2, IGRAPH_IN);
    igraph_vector_int_sort(&v);
    print_vector(&v, stdout);

    igraph_neighbors(&g, &v, 2, IGRAPH_ALL);
    igraph_vector_int_sort(&v);
    print_vector(&v, stdout);

    /* Errors */
    igraph_set_error_handler(igraph_error_handler_ignore);
    ret = igraph_neighbors(&g, &v, 2, (igraph_neimode_t)0); /* conv for c++ */
    if (ret != IGRAPH_EINVMODE) {
        return 1;
    }

    ret = igraph_neighbors(&g, &v, 4, IGRAPH_ALL);
    if (ret != IGRAPH_EINVVID) {
        return 2;
    }

    igraph_vector_int_destroy(&v);
    igraph_destroy(&g);
    return 0;
}


2.2.12. igraph_incident — Gives the incident edges of a vertex.

igraph_error_t igraph_incident(const igraph_t *graph, igraph_vector_int_t *eids, igraph_integer_t pnode,
        igraph_neimode_t mode);

Arguments: 

graph:

The graph object.

eids:

An initialized vector. It will be resized to hold the result.

pnode:

A vertex ID.

mode:

Specifies what kind of edges to include for directed graphs. IGRAPH_OUT means only outgoing edges, IGRAPH_IN only incoming edges, IGRAPH_ALL both. This parameter is ignored for undirected graphs.

Returns: 

Error code. IGRAPH_EINVVID: invalid pnode argument, IGRAPH_EINVMODE: invalid mode argument.

Added in version 0.2.

Time complexity: O(d), the number of incident edges to pnode.

2.2.13. igraph_is_directed — Is this a directed graph?

igraph_bool_t igraph_is_directed(const igraph_t *graph);

Arguments: 

graph:

The graph.

Returns: 

Logical value, TRUE if the graph is directed, FALSE otherwise.

Time complexity: O(1)

Example 4.6.  File examples/simple/igraph_is_directed.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard st, Cambridge MA, 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

int main() {

    igraph_t g;

    igraph_empty(&g, 0, 0);
    if (igraph_is_directed(&g)) {
        return 1;
    }
    igraph_destroy(&g);

    igraph_empty(&g, 0, 1);
    if (!igraph_is_directed(&g)) {
        return 2;
    }
    igraph_destroy(&g);

    return 0;
}


2.2.14. igraph_is_same_graph — Are two graphs identical as labelled graphs?

igraph_error_t igraph_is_same_graph(const igraph_t *graph1, const igraph_t *graph2, igraph_bool_t *res);

Two graphs are considered to be the same if they have the same vertex and edge sets. Graphs which are the same may have multiple different representations in igraph, hence the need for this function.

This function verifies that the two graphs have the same directedness, the same number of vertices, and that they contain precisely the same edges (regardless of their ordering) when written in terms of vertex indices. Graph attributes are not taken into account.

This concept is different from isomorphism. For example, the graphs 0-1, 2-1 and 1-2, 0-1 are considered the same because they only differ in the ordering of their edge lists and the ordering of vertices in an undirected edge. However, they are not the same as 0-2, 1-2, even though they are isomorphic to it. Note that this latter graph contains the edge 0-2 while the former two do not — thus their edge sets differ.

Arguments: 

graph1:

The first graph object.

graph2:

The second graph object.

res:

The result will be stored here.

Returns: 

Error code.

Time complexity: O(E), the number of edges in the graphs.

See also: 

igraph_isomorphic() to test if two graphs are isomorphic.

2.2.15. igraph_degree — The degree of some vertices in a graph.

igraph_error_t igraph_degree(const igraph_t *graph, igraph_vector_int_t *res,
                  const igraph_vs_t vids,
                  igraph_neimode_t mode, igraph_bool_t loops);

This function calculates the in-, out- or total degree of the specified vertices.

Arguments: 

graph:

The graph.

res:

Vector, this will contain the result. It should be initialized and will be resized to be the appropriate size.

vids:

Vector, giving the vertex IDs of which the degree will be calculated.

mode:

Defines the type of the degree. Valid modes are: IGRAPH_OUT, out-degree; IGRAPH_IN, in-degree; IGRAPH_ALL, total degree (sum of the in- and out-degree). This parameter is ignored for undirected graphs.

loops:

Boolean, gives whether the self-loops should be counted.

Returns: 

Error code: IGRAPH_EINVVID: invalid vertex ID. IGRAPH_EINVMODE: invalid mode argument.

Time complexity: O(v) if loops is TRUE, and O(v*d) otherwise. v is the number of vertices for which the degree will be calculated, and d is their (average) degree.

See also: 

igraph_strength() for the version that takes into account edge weights.

Example 4.7.  File examples/simple/igraph_degree.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard street, Cambridge, MA 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

void print_vector(igraph_vector_int_t *v, FILE *f) {
    igraph_integer_t i;
    for (i = 0; i < igraph_vector_int_size(v); i++) {
        fprintf(f, " %" IGRAPH_PRId "", VECTOR(*v)[i]);
    }
    fprintf(f, "\n");
}

int main() {

    igraph_t g;
    igraph_vector_int_t v;
    igraph_vector_int_t v2;
    igraph_vector_int_t seq;
    igraph_error_t ret;
    igraph_integer_t i, mdeg, ndeg, nedges;

    /* Create graph */
    igraph_vector_int_init(&v, 8);
    igraph_vector_int_init(&v2, 8);
    VECTOR(v2)[0] = 0;
    VECTOR(v2)[1] = 1;
    VECTOR(v2)[2] = 1;
    VECTOR(v2)[3] = 2;
    VECTOR(v2)[4] = 2;
    VECTOR(v2)[5] = 3;
    VECTOR(v2)[6] = 2;
    VECTOR(v2)[7] = 2;
    igraph_create(&g, &v2, 0, IGRAPH_DIRECTED);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_OUT, IGRAPH_NO_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_OUT, IGRAPH_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_IN, IGRAPH_NO_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_IN, IGRAPH_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_ALL, IGRAPH_NO_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS);
    print_vector(&v, stdout);

    igraph_set_error_handler(igraph_error_handler_ignore);

    /* Consistency check of the handshaking lemma. */
    /* If d is the sum of all vertex degrees, then d = 2|E|. */
    ndeg = 0;
    nedges = igraph_ecount(&g);
    for (i = 0; i < igraph_vector_int_size(&v); i++) {
        ndeg += VECTOR(v)[i];
    }
    if (ndeg != 2 * nedges) {
        return 1;
    }

    igraph_destroy(&g);

    igraph_vector_int_resize(&v2, 8);
    VECTOR(v2)[0] = 0;
    VECTOR(v2)[1] = 1;
    VECTOR(v2)[2] = 1;
    VECTOR(v2)[3] = 2;
    VECTOR(v2)[4] = 2;
    VECTOR(v2)[5] = 3;
    VECTOR(v2)[6] = 2;
    VECTOR(v2)[7] = 2;
    igraph_create(&g, &v2, 0, IGRAPH_UNDIRECTED);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_OUT, IGRAPH_NO_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_OUT, IGRAPH_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_IN, IGRAPH_NO_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_IN, IGRAPH_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_ALL, IGRAPH_NO_LOOPS);
    print_vector(&v, stdout);

    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS);
    print_vector(&v, stdout);

    /* Consistency check of the handshaking lemma. */
    /* If d is the sum of all vertex degrees, then d = 2|E|. */
    ndeg = 0;
    nedges = igraph_ecount(&g);
    for (i = 0; i < igraph_vector_int_size(&v); i++) {
        ndeg += VECTOR(v)[i];
    }
    if (ndeg != 2 * nedges) {
        return 2;
    }

    /* Degree of the same vertex multiple times */

    igraph_vector_int_init(&seq, 3);
    VECTOR(seq)[0] = 2;
    VECTOR(seq)[1] = 0;
    VECTOR(seq)[2] = 2;
    igraph_degree(&g, &v, igraph_vss_vector(&seq), IGRAPH_ALL, IGRAPH_LOOPS);
    print_vector(&v, stdout);

    /* Errors */
    ret = igraph_degree(&g, &v, igraph_vss_vector(&seq), (igraph_neimode_t)0,
                        IGRAPH_LOOPS);
    if (ret != IGRAPH_EINVMODE) {
        return 3;
    }

    VECTOR(seq)[0] = 4;
    ret = igraph_degree(&g, &v, igraph_vss_vector(&seq), IGRAPH_ALL, IGRAPH_LOOPS);
    if (ret != IGRAPH_EINVVID) {
        return 4;
    }

    igraph_destroy(&g);
    igraph_vector_int_destroy(&seq);

    /* Maximum degree */

    igraph_ring(&g, 10, 0 /*undirected*/, 0 /*undirected*/, 0/*uncircular*/);
    igraph_maxdegree(&g, &mdeg, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS);
    if (mdeg != 2) {
        return 5;
    }
    /* Consistency check of the handshaking lemma. */
    /* If d is the sum of all vertex degrees, then d = 2|E|. */
    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS);
    ndeg = 0;
    nedges = igraph_ecount(&g);
    for (i = 0; i < igraph_vector_int_size(&v); i++) {
        ndeg += VECTOR(v)[i];
    }
    if (ndeg != 2 * nedges) {
        return 6;
    }
    igraph_destroy(&g);

    igraph_full(&g, 10, 0 /*undirected*/, 0/*no loops*/);
    igraph_maxdegree(&g, &mdeg, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS);
    if (mdeg != 9) {
        return 7;
    }
    /* Consistency check of the handshaking lemma. */
    /* If d is the sum of all vertex degrees, then d = 2|E|. */
    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS);
    ndeg = 0;
    nedges = igraph_ecount(&g);
    for (i = 0; i < igraph_vector_int_size(&v); i++) {
        ndeg += VECTOR(v)[i];
    }
    if (ndeg != 2 * nedges) {
        return 8;
    }
    igraph_destroy(&g);

    igraph_star(&g, 10, IGRAPH_STAR_OUT, 0);
    igraph_maxdegree(&g, &mdeg, igraph_vss_all(), IGRAPH_OUT, IGRAPH_LOOPS);
    if (mdeg != 9) {
        return 9;
    }
    igraph_maxdegree(&g, &mdeg, igraph_vss_all(), IGRAPH_IN, IGRAPH_LOOPS);
    if (mdeg != 1) {
        return 10;
    }
    igraph_maxdegree(&g, &mdeg, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS);
    if (mdeg != 9) {
        return 11;
    }
    /* Consistency check of the handshaking lemma. */
    /* If d is the sum of all vertex degrees, then d = 2|E|. */
    igraph_degree(&g, &v, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS);
    ndeg = 0;
    nedges = igraph_ecount(&g);
    for (i = 0; i < igraph_vector_int_size(&v); i++) {
        ndeg += VECTOR(v)[i];
    }
    if (ndeg != 2 * nedges) {
        return 12;
    }
    igraph_destroy(&g);

    igraph_vector_int_destroy(&v);
    igraph_vector_int_destroy(&v2);

    return 0;
}


2.3. Adding and deleting vertices and edges

2.3.1. igraph_add_edge — Adds a single edge to a graph.

igraph_error_t igraph_add_edge(igraph_t *graph, igraph_integer_t from, igraph_integer_t to);

For directed graphs the edge points from from to to.

Note that if you want to add many edges to a big graph, then it is inefficient to add them one by one, it is better to collect them into a vector and add all of them via a single igraph_add_edges() call.

Arguments: 

igraph:

The graph.

from:

The id of the first vertex of the edge.

to:

The id of the second vertex of the edge.

Returns: 

Error code.

See also: 

igraph_add_edges() to add many edges, igraph_delete_edges() to remove edges and igraph_add_vertices() to add vertices.

Time complexity: O(|V|+|E|), the number of edges plus the number of vertices.

2.3.2. igraph_add_edges — Adds edges to a graph object.

igraph_error_t igraph_add_edges(igraph_t *graph, const igraph_vector_int_t *edges,
                     void *attr);

The edges are given in a vector, the first two elements define the first edge (the order is from, to for directed graphs). The vector should contain even number of integer numbers between zero and the number of vertices in the graph minus one (inclusive). If you also want to add new vertices, call igraph_add_vertices() first.

Arguments: 

graph:

The graph to which the edges will be added.

edges:

The edges themselves.

attr:

The attributes of the new edges, only used by high level interfaces currently, you can supply 0 here.

Returns: 

Error code: IGRAPH_EINVEVECTOR: invalid (odd) edges vector length, IGRAPH_EINVVID: invalid vertex ID in edges vector.

This function invalidates all iterators.

Time complexity: O(|V|+|E|) where |V| is the number of vertices and |E| is the number of edges in the new, extended graph.

Example 4.8.  File examples/simple/igraph_add_edges.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard street, Cambridge, MA 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

int main() {

    igraph_t g;
    igraph_vector_int_t v;
    int ret;

    /* Create graph */
    igraph_vector_int_init(&v, 8);
    VECTOR(v)[0] = 0;
    VECTOR(v)[1] = 1;
    VECTOR(v)[2] = 1;
    VECTOR(v)[3] = 2;
    VECTOR(v)[4] = 2;
    VECTOR(v)[5] = 3;
    VECTOR(v)[6] = 2;
    VECTOR(v)[7] = 2;
    igraph_create(&g, &v, 0, 1);

    /* Add edges */
    igraph_vector_int_resize(&v, 4);
    VECTOR(v)[0] = 2;
    VECTOR(v)[1] = 1;
    VECTOR(v)[2] = 3;
    VECTOR(v)[3] = 3;
    igraph_add_edges(&g, &v, 0);

    /* Check result */
    igraph_get_edgelist(&g, &v, 0);
    igraph_vector_int_sort(&v);
    igraph_vector_int_print(&v);

    /* Error, vector length */
    igraph_set_error_handler(igraph_error_handler_ignore);
    igraph_vector_int_resize(&v, 3);
    VECTOR(v)[0] = 0;
    VECTOR(v)[1] = 1;
    VECTOR(v)[2] = 2;
    ret = igraph_add_edges(&g, &v, 0);
    if (ret != IGRAPH_EINVEVECTOR) {
        return 1;
    }

    /* Check result */
    igraph_get_edgelist(&g, &v, 0);
    igraph_vector_int_sort(&v);
    igraph_vector_int_print(&v);

    /* Error, vector IDs */
    igraph_vector_int_resize(&v, 4);
    VECTOR(v)[0] = 0;
    VECTOR(v)[1] = 1;
    VECTOR(v)[2] = 2;
    VECTOR(v)[3] = 4;
    ret = igraph_add_edges(&g, &v, 0);
    if (ret != IGRAPH_EINVVID) {
        return 2;
    }

    /* Check result */
    igraph_get_edgelist(&g, &v, 0);
    igraph_vector_int_sort(&v);
    igraph_vector_int_print(&v);

    igraph_vector_int_destroy(&v);
    igraph_destroy(&g);

    return 0;
}


2.3.3. igraph_add_vertices — Adds vertices to a graph.

igraph_error_t igraph_add_vertices(igraph_t *graph, igraph_integer_t nv, void *attr);

This function invalidates all iterators.

Arguments: 

graph:

The graph object to extend.

nv:

Non-negative integer giving the number of vertices to add.

attr:

The attributes of the new vertices, only used by high level interfaces, you can supply 0 here.

Returns: 

Error code: IGRAPH_EINVAL: invalid number of new vertices.

Time complexity: O(|V|) where |V| is the number of vertices in the new, extended graph.

Example 4.9.  File examples/simple/igraph_add_vertices.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard street, Cambridge, MA 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

int main() {

    igraph_t g1;
    igraph_vector_int_t v1;
    int ret;

    /* Create a graph */
    igraph_vector_int_init(&v1, 8);
    VECTOR(v1)[0] = 0;
    VECTOR(v1)[1] = 1;
    VECTOR(v1)[2] = 1;
    VECTOR(v1)[3] = 2;
    VECTOR(v1)[4] = 2;
    VECTOR(v1)[5] = 3;
    VECTOR(v1)[6] = 2;
    VECTOR(v1)[7] = 2;
    igraph_create(&g1, &v1, 0, 0);
    igraph_vector_int_destroy(&v1);

    /* Add more vertices */
    igraph_add_vertices(&g1, 10, 0);
    if (igraph_vcount(&g1) != 14) {
        return 1;
    }

    /* Add more vertices */
    igraph_add_vertices(&g1, 0, 0);
    if (igraph_vcount(&g1) != 14) {
        return 2;
    }

    /* Error */
    igraph_set_error_handler(igraph_error_handler_ignore);
    ret = igraph_add_vertices(&g1, -1, 0);
    if (ret != IGRAPH_EINVAL) {
        return 3;
    }

    igraph_destroy(&g1);

    return 0;
}


2.3.4. igraph_delete_edges — Removes edges from a graph.

igraph_error_t igraph_delete_edges(igraph_t *graph, igraph_es_t edges);

The edges to remove are given as an edge selector.

This function cannot remove vertices, they will be kept, even if they lose all their edges.

This function invalidates all iterators.

Arguments: 

graph:

The graph to work on.

edges:

The edges to remove.

Returns: 

Error code.

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

Example 4.10.  File examples/simple/igraph_delete_edges.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard street, Cambridge, MA 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

int main() {

    igraph_t g;
    igraph_vector_int_t v;
    int ret;
    igraph_es_t es;

    igraph_vector_int_init(&v, 8);
    VECTOR(v)[0] = 0;
    VECTOR(v)[1] = 1;
    VECTOR(v)[2] = 1;
    VECTOR(v)[3] = 2;
    VECTOR(v)[4] = 2;
    VECTOR(v)[5] = 3;
    VECTOR(v)[6] = 2;
    VECTOR(v)[7] = 2;
    igraph_create(&g, &v, 0, 0);

    igraph_es_pairs_small(&es, IGRAPH_DIRECTED, 3, 2, -1);
    igraph_delete_edges(&g, es);
    if (igraph_ecount(&g) != 3) {
        return 1;
    }

    /* error test, no such edge to delete */
    igraph_set_error_handler(igraph_error_handler_ignore);
    ret = igraph_delete_edges(&g, es);
    if (ret != IGRAPH_EINVAL) {
        printf("Error code: %i\n", ret);
        return 2;
    }
    if (igraph_ecount(&g) != 3) {
        return 3;
    }

    /* error test, invalid vertex ID */
    igraph_es_destroy(&es);
    igraph_es_pairs_small(&es, IGRAPH_DIRECTED, 10, 2, -1);
    ret = igraph_delete_edges(&g, es);
    if (ret != IGRAPH_EINVVID) {
        return 4;
    }
    if (igraph_ecount(&g) != 3) {
        return 5;
    }

    /* error test, invalid (odd) length */
    igraph_es_destroy(&es);
    igraph_es_pairs_small(&es, IGRAPH_DIRECTED, 0, 1, 2, -1);
    ret = igraph_delete_edges(&g, es);
    if (ret != IGRAPH_EINVAL) {
        return 6;
    }
    if (igraph_ecount(&g) != 3) {
        return 7;
    }

    igraph_es_destroy(&es);
    igraph_vector_int_destroy(&v);
    igraph_destroy(&g);

    return 0;
}


2.3.5. igraph_delete_vertices — Removes vertices (with all their edges) from the graph.

igraph_error_t igraph_delete_vertices(igraph_t *graph, const igraph_vs_t vertices);

This function changes the IDs of the vertices (except in some very special cases, but these should not be relied on anyway).

This function invalidates all iterators.

Arguments: 

graph:

The graph to work on.

vertices:

The IDs of the vertices to remove in a vector. The vector may contain the same id more than once.

Returns: 

Error code: IGRAPH_EINVVID: invalid vertex ID.

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

Example 4.11.  File examples/simple/igraph_delete_vertices.c

/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard street, Cambridge, MA 02139 USA

   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 2 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, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include <igraph.h>

int main() {

    igraph_t g;
    igraph_vector_int_t v;
    int ret;

    /* without edges */
    igraph_empty(&g, 5, IGRAPH_DIRECTED);
    igraph_add_vertices(&g, 2, 0);
    igraph_add_vertices(&g, 3, 0);
    igraph_add_vertices(&g, 1, 0);
    igraph_add_vertices(&g, 4, 0);
    if (igraph_vcount(&g) != 15)  {
        return 1;
    }
    igraph_delete_vertices(&g, igraph_vss_1(2));
    if (igraph_vcount(&g) != 14)  {
        return 2;
    }
    igraph_destroy(&g);

    igraph_vector_int_init(&v, 8);
    VECTOR(v)[0] = 0;
    VECTOR(v)[1] = 1;
    VECTOR(v)[2] = 1;
    VECTOR(v)[3] = 2;
    VECTOR(v)[4] = 2;
    VECTOR(v)[5] = 3;
    VECTOR(v)[6] = 2;
    VECTOR(v)[7] = 2;
    igraph_create(&g, &v, 0, 0);
    igraph_vector_int_destroy(&v);

    /* resize vector */
    igraph_delete_vertices(&g, igraph_vss_1(2));
    if (igraph_vcount(&g) != 3) {
        return 3;
    }
    if (igraph_ecount(&g) != 1) {
        return 4;
    }

    /* error test */
    igraph_set_error_handler(igraph_error_handler_ignore);
    ret = igraph_delete_vertices(&g, igraph_vss_1(3));
    if (ret != IGRAPH_EINVVID) {
        return 5;
    }

    igraph_destroy(&g);

    return 0;
}