int dfs_d(const igraph_t *graph, igraph_integer_t root,
igraph_neimode_t mode, igraph_bool_t unreachable,
igraph_vector_t *order,
igraph_vector_t *order_out, igraph_vector_t *father,
igraph_vector_t *dist, igraph_dfshandler_t *in_callback,
igraph_dfshandler_t *out_callback,
void *extra) {
long int no_of_nodes=igraph_vcount(graph);
igraph_lazy_adjlist_t adjlist;
igraph_stack_t stack;
igraph_vector_char_t added;
igraph_vector_long_t nptr;
long int actroot;
long int act_rank=0;
long int rank_out=0;
long int act_dist=0;
if (root < 0 || root >= no_of_nodes) {
IGRAPH_ERROR("Invalid root vertex for DFS", IGRAPH_EINVAL);
}
if (mode != IGRAPH_OUT && mode != IGRAPH_IN &&
mode != IGRAPH_ALL) {
IGRAPH_ERROR("Invalid mode argument", IGRAPH_EINVMODE);
}
if (!igraph_is_directed(graph)) { mode=IGRAPH_ALL; }
IGRAPH_CHECK(igraph_vector_char_init(&added, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_char_destroy, &added);
IGRAPH_CHECK(igraph_stack_init(&stack, 100));
IGRAPH_FINALLY(igraph_stack_destroy, &stack);
IGRAPH_CHECK(igraph_lazy_adjlist_init(graph, &adjlist, mode, /*simplify=*/ 0));
IGRAPH_FINALLY(igraph_lazy_adjlist_destroy, &adjlist);
IGRAPH_CHECK(igraph_vector_long_init(&nptr, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &nptr);
# define FREE_ALL() do { \
igraph_vector_long_destroy(&nptr); \
igraph_lazy_adjlist_destroy(&adjlist); \
igraph_stack_destroy(&stack); \
igraph_vector_char_destroy(&added); \
IGRAPH_FINALLY_CLEAN(4); } while (0)
/* Resize result vectors and fill them with IGRAPH_NAN */
# define VINIT(v) if (v) { \
igraph_vector_resize(v, no_of_nodes); \
igraph_vector_fill(v, IGRAPH_NAN); }
VINIT(order);
VINIT(order_out);
VINIT(father);
VINIT(dist);
# undef VINIT
IGRAPH_CHECK(igraph_stack_push(&stack, root));
VECTOR(added)[(long int)root] = 1;
if (father) { VECTOR(*father)[(long int)root] = -1; }
if (order) { VECTOR(*order)[act_rank++] = root; }
if (dist) { VECTOR(*dist)[(long int)root] = 0; }
if (in_callback) {
igraph_bool_t terminate=in_callback(graph, root, 0, extra);
if (terminate) { FREE_ALL(); return 0; }
}
for (actroot=0; actroot<no_of_nodes; actroot++) {
/* 'root' first, then all other vertices */
if (igraph_stack_empty(&stack)) {
if (!unreachable) { break; }
if (VECTOR(added)[actroot]) { continue; }
IGRAPH_CHECK(igraph_stack_push(&stack, actroot));
VECTOR(added)[actroot] = 1;
if (father) { VECTOR(*father)[actroot] = -1; }
if (order) { VECTOR(*order)[act_rank++] = actroot; }
if (dist) { VECTOR(*dist)[actroot] = 0; }
if (in_callback) {
igraph_bool_t terminate=in_callback(graph, (igraph_integer_t) actroot,
0, extra);
if (terminate) { FREE_ALL(); return 0; }
}
}
while (!igraph_stack_empty(&stack)) {
long int actvect=(long int) igraph_stack_top(&stack);
igraph_vector_t *neis=igraph_lazy_adjlist_get(&adjlist,
(igraph_integer_t) actvect);
long int n=igraph_vector_size(neis);
long int *ptr=igraph_vector_long_e_ptr(&nptr, actvect);
igraph_vector_shuffle(neis);
igraph_vector_print(neis);
/* Search for a neighbor that was not yet visited */
igraph_bool_t any=0;
long int nei;
while (!any && (*ptr) <n) {
nei=(long int) VECTOR(*neis)[(*ptr)];
any=!VECTOR(added)[nei];
(*ptr) ++;
}
if (any) {
/* There is such a neighbor, add it */
IGRAPH_CHECK(igraph_stack_push(&stack, nei));
VECTOR(added)[nei] = 1;
if (father) { VECTOR(*father)[ nei ] = actvect; }
if (order) { VECTOR(*order)[act_rank++] = nei; }
act_dist++;
if (dist) { VECTOR(*dist)[nei] = act_dist; }
if (in_callback) {
igraph_bool_t terminate=in_callback(graph, (igraph_integer_t) nei,
(igraph_integer_t) act_dist,
extra);
if (terminate) { FREE_ALL(); return 0; }
}
} else {
/* There is no such neighbor, finished with the subtree */
igraph_stack_pop(&stack);
if (order_out) { VECTOR(*order_out)[rank_out++] = actvect; }
act_dist--;
if (out_callback) {
igraph_bool_t terminate=out_callback(graph, (igraph_integer_t)
actvect, (igraph_integer_t)
act_dist, extra);
if (terminate) { FREE_ALL(); return 0; }
}
}
}
}
FREE_ALL();
# undef FREE_ALL
return 0;
}
int igraph_biconnected_components(const igraph_t *graph,
igraph_integer_t *no,
igraph_vector_ptr_t *tree_edges,
igraph_vector_ptr_t *component_edges,
igraph_vector_ptr_t *components,
igraph_vector_t *articulation_points) {
long int no_of_nodes=igraph_vcount(graph);
igraph_vector_long_t nextptr;
igraph_vector_long_t num, low;
igraph_vector_bool_t found;
igraph_vector_int_t *adjedges;
igraph_stack_t path;
igraph_vector_t edgestack;
igraph_inclist_t inclist;
long int i, counter, rootdfs=0;
igraph_vector_long_t vertex_added;
long int comps=0;
igraph_vector_ptr_t *mycomponents=components, vcomponents;
IGRAPH_CHECK(igraph_vector_long_init(&nextptr, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &nextptr);
IGRAPH_CHECK(igraph_vector_long_init(&num, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &num);
IGRAPH_CHECK(igraph_vector_long_init(&low, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &low);
IGRAPH_CHECK(igraph_vector_bool_init(&found, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_bool_destroy, &found);
IGRAPH_CHECK(igraph_stack_init(&path, 100));
IGRAPH_FINALLY(igraph_stack_destroy, &path);
IGRAPH_VECTOR_INIT_FINALLY(&edgestack, 0);
IGRAPH_CHECK(igraph_vector_reserve(&edgestack, 100));
IGRAPH_CHECK(igraph_inclist_init(graph, &inclist, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_inclist_destroy, &inclist);
IGRAPH_CHECK(igraph_vector_long_init(&vertex_added, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &vertex_added);
if (no) {
*no=0;
}
if (tree_edges) {
igraph_vector_ptr_clear(tree_edges);
}
if (components) {
igraph_vector_ptr_clear(components);
}
if (component_edges) {
igraph_vector_ptr_clear(component_edges);
}
if (articulation_points) {
igraph_vector_clear(articulation_points);
}
if (component_edges && !components) {
mycomponents=&vcomponents;
IGRAPH_CHECK(igraph_vector_ptr_init(mycomponents, 0));
IGRAPH_FINALLY(igraph_i_free_vectorlist, mycomponents);
}
for (i=0; i<no_of_nodes; i++) {
if (VECTOR(low)[i] != 0) { continue; } /* already visited */
IGRAPH_ALLOW_INTERRUPTION();
IGRAPH_CHECK(igraph_stack_push(&path, i));
counter=1;
rootdfs=0;
VECTOR(low)[i]=VECTOR(num)[i]=counter++;
while (!igraph_stack_empty(&path)) {
long int n;
long int act=(long int) igraph_stack_top(&path);
long int actnext=VECTOR(nextptr)[act];
adjedges=igraph_inclist_get(&inclist, act);
n=igraph_vector_int_size(adjedges);
if (actnext < n) {
/* Step down (maybe) */
long int edge=(long int) VECTOR(*adjedges)[actnext];
long int nei=IGRAPH_OTHER(graph, edge, act);
if (VECTOR(low)[nei] == 0) {
if (act==i) { rootdfs++; }
IGRAPH_CHECK(igraph_vector_push_back(&edgestack, edge));
IGRAPH_CHECK(igraph_stack_push(&path, nei));
VECTOR(low)[nei] = VECTOR(num)[nei]=counter++;
} else {
/* Update low value if needed */
if (VECTOR(num)[nei] < VECTOR(low)[act]) {
VECTOR(low)[act]=VECTOR(num)[nei];
}
}
VECTOR(nextptr)[act] += 1;
} else {
/* Step up */
igraph_stack_pop(&path);
if (!igraph_stack_empty(&path)) {
long int prev=(long int) igraph_stack_top(&path);
/* Update LOW value if needed */
if (VECTOR(low)[act] < VECTOR(low)[prev]) {
VECTOR(low)[prev] = VECTOR(low)[act];
}
/* Check for articulation point */
if (VECTOR(low)[act] >= VECTOR(num)[prev]) {
if (articulation_points && !VECTOR(found)[prev]
&& prev != i /* the root */) {
IGRAPH_CHECK(igraph_vector_push_back(articulation_points, prev));
VECTOR(found)[prev] = 1;
}
if (no) { *no += 1; }
/*------------------------------------*/
/* Record the biconnected component just found */
if (tree_edges || mycomponents) {
igraph_vector_t *v = 0, *v2 = 0;
comps++;
if (tree_edges) {
v=igraph_Calloc(1, igraph_vector_t);
if (!v) { IGRAPH_ERROR("Out of memory", IGRAPH_ENOMEM); }
IGRAPH_CHECK(igraph_vector_init(v, 0));
IGRAPH_FINALLY(igraph_vector_destroy, v);
}
if (mycomponents) {
v2=igraph_Calloc(1, igraph_vector_t);
if (!v2) { IGRAPH_ERROR("Out of memory", IGRAPH_ENOMEM); }
IGRAPH_CHECK(igraph_vector_init(v2, 0));
IGRAPH_FINALLY(igraph_vector_destroy, v2);
}
while (!igraph_vector_empty(&edgestack)) {
long int e=(long int) igraph_vector_pop_back(&edgestack);
long int from=IGRAPH_FROM(graph,e);
long int to=IGRAPH_TO(graph,e);
if (tree_edges) {
IGRAPH_CHECK(igraph_vector_push_back(v, e));
}
if (mycomponents) {
if (VECTOR(vertex_added)[from] != comps) {
VECTOR(vertex_added)[from] = comps;
IGRAPH_CHECK(igraph_vector_push_back(v2, from));
}
if (VECTOR(vertex_added)[to] != comps) {
VECTOR(vertex_added)[to] = comps;
IGRAPH_CHECK(igraph_vector_push_back(v2, to));
}
}
if (from==prev || to==prev) {
break;
}
}
if (mycomponents) {
IGRAPH_CHECK(igraph_vector_ptr_push_back(mycomponents, v2));
IGRAPH_FINALLY_CLEAN(1);
}
if (tree_edges) {
IGRAPH_CHECK(igraph_vector_ptr_push_back(tree_edges, v));
IGRAPH_FINALLY_CLEAN(1);
}
if (component_edges) {
igraph_vector_t *nodes=VECTOR(*mycomponents)[comps-1];
igraph_vector_t *vv=igraph_Calloc(1, igraph_vector_t);
long int ii, no_vert=igraph_vector_size(nodes);
if (!vv) { IGRAPH_ERROR("Out of memory", IGRAPH_ENOMEM); }
IGRAPH_CHECK(igraph_vector_init(vv, 0));
IGRAPH_FINALLY(igraph_vector_destroy, vv);
for (ii=0; ii<no_vert; ii++) {
long int vert=(long int) VECTOR(*nodes)[ii];
igraph_vector_int_t *edges=igraph_inclist_get(&inclist,
vert);
long int j, nn=igraph_vector_int_size(edges);
for (j=0; j<nn; j++) {
long int e=(long int) VECTOR(*edges)[j];
long int nei=IGRAPH_OTHER(graph, e, vert);
if (VECTOR(vertex_added)[nei] == comps && nei<vert) {
IGRAPH_CHECK(igraph_vector_push_back(vv, e));
}
}
}
IGRAPH_CHECK(igraph_vector_ptr_push_back(component_edges, vv));
IGRAPH_FINALLY_CLEAN(1);
}
} /* record component if requested */
/*------------------------------------*/
}
} /* !igraph_stack_empty(&path) */
}
} /* !igraph_stack_empty(&path) */
if (articulation_points && rootdfs >= 2) {
IGRAPH_CHECK(igraph_vector_push_back(articulation_points, i));
}
} /* i < no_of_nodes */
if (mycomponents != components) {
igraph_i_free_vectorlist(mycomponents);
IGRAPH_FINALLY_CLEAN(1);
}
igraph_vector_long_destroy(&vertex_added);
igraph_inclist_destroy(&inclist);
igraph_vector_destroy(&edgestack);
igraph_stack_destroy(&path);
igraph_vector_bool_destroy(&found);
igraph_vector_long_destroy(&low);
igraph_vector_long_destroy(&num);
igraph_vector_long_destroy(&nextptr);
IGRAPH_FINALLY_CLEAN(8);
return 0;
}
int igraph_biconnected_components(const igraph_t *graph,
igraph_integer_t *no,
igraph_vector_ptr_t *components,
igraph_vector_t *articulation_points) {
long int no_of_nodes=igraph_vcount(graph);
igraph_vector_long_t nextptr;
igraph_vector_long_t num, low;
igraph_vector_bool_t found;
igraph_vector_t *adjedges;
igraph_stack_t path;
igraph_vector_t edgestack;
igraph_adjedgelist_t adjedgelist;
long int i, counter, rootdfs=0;
IGRAPH_CHECK(igraph_vector_long_init(&nextptr, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &nextptr);
IGRAPH_CHECK(igraph_vector_long_init(&num, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &num);
IGRAPH_CHECK(igraph_vector_long_init(&low, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &low);
IGRAPH_CHECK(igraph_vector_bool_init(&found, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_bool_destroy, &found);
IGRAPH_CHECK(igraph_stack_init(&path, 100));
IGRAPH_FINALLY(igraph_stack_destroy, &path);
IGRAPH_VECTOR_INIT_FINALLY(&edgestack, 0);
IGRAPH_CHECK(igraph_vector_reserve(&edgestack, 100));
IGRAPH_CHECK(igraph_adjedgelist_init(graph, &adjedgelist, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjedgelist_destroy, &adjedgelist);
if (no) {
*no=0;
}
if (components) {
igraph_vector_ptr_clear(components);
}
if (articulation_points) {
igraph_vector_clear(articulation_points);
}
for (i=0; i<no_of_nodes; i++) {
if (VECTOR(low)[i] != 0) {
continue; /* already visited */
}
IGRAPH_ALLOW_INTERRUPTION();
IGRAPH_CHECK(igraph_stack_push(&path, i));
counter=1;
rootdfs=0;
VECTOR(low)[i]=VECTOR(num)[i]=counter++;
while (!igraph_stack_empty(&path)) {
long int n;
long int act=igraph_stack_top(&path);
long int actnext=VECTOR(nextptr)[act];
adjedges=igraph_adjedgelist_get(&adjedgelist, act);
n=igraph_vector_size(adjedges);
if (actnext < n) {
/* Step down (maybe) */
long int edge=VECTOR(*adjedges)[actnext];
long int nei=IGRAPH_OTHER(graph, edge, act);
if (VECTOR(low)[nei] == 0) {
if (act==i) {
rootdfs++;
}
IGRAPH_CHECK(igraph_vector_push_back(&edgestack, edge));
IGRAPH_CHECK(igraph_stack_push(&path, nei));
VECTOR(low)[nei] = VECTOR(num)[nei]=counter++;
} else {
/* Update low value if needed */
if (VECTOR(num)[nei] < VECTOR(low)[act]) {
VECTOR(low)[act]=VECTOR(num)[nei];
}
}
VECTOR(nextptr)[act] += 1;
} else {
/* Step up */
igraph_stack_pop(&path);
if (!igraph_stack_empty(&path)) {
long int prev=igraph_stack_top(&path);
/* Update LOW value if needed */
if (VECTOR(low)[act] < VECTOR(low)[prev]) {
VECTOR(low)[prev] = VECTOR(low)[act];
}
/* Check for articulation point */
if (VECTOR(low)[act] >= VECTOR(num)[prev]) {
if (articulation_points && !VECTOR(found)[prev]
&& prev != i /* the root */) {
IGRAPH_CHECK(igraph_vector_push_back(articulation_points, prev));
VECTOR(found)[prev] = 1;
}
if (no) {
*no += 1;
}
if (components) {
igraph_vector_t *v=igraph_Calloc(1, igraph_vector_t);
IGRAPH_CHECK(igraph_vector_init(v, 0));
while (!igraph_vector_empty(&edgestack)) {
long int e=igraph_vector_pop_back(&edgestack);
IGRAPH_CHECK(igraph_vector_push_back(v, e));
if (IGRAPH_FROM(graph,e)==prev || IGRAPH_TO(graph,e)==prev) {
break;
}
}
IGRAPH_CHECK(igraph_vector_ptr_push_back(components, v));
}
}
} /* !igraph_stack_empty(&path) */
}
} /* !igraph_stack_empty(&path) */
if (articulation_points && rootdfs >= 2) {
IGRAPH_CHECK(igraph_vector_push_back(articulation_points, i));
}
} /* i < no_of_nodes */
igraph_adjedgelist_destroy(&adjedgelist);
igraph_vector_destroy(&edgestack);
igraph_stack_destroy(&path);
igraph_vector_bool_destroy(&found);
igraph_vector_long_destroy(&low);
igraph_vector_long_destroy(&num);
igraph_vector_long_destroy(&nextptr);
IGRAPH_FINALLY_CLEAN(7);
return 0;
}
int main() {
igraph_stack_t st;
int i;
/* igraph_stack_init, igraph_stack_destroy */
igraph_stack_init(&st, 0);
igraph_stack_destroy(&st);
igraph_stack_init(&st, 10);
igraph_stack_destroy(&st);
/* igraph_stack_reserve */
igraph_stack_init(&st, 0);
igraph_stack_reserve(&st, 10);
igraph_stack_reserve(&st, 5);
/* igraph_stack_empty */
if (!igraph_stack_empty(&st)) {
return 1;
}
igraph_stack_push(&st, 1);
if (igraph_stack_empty(&st)) {
return 2;
}
/* igraph_stack_size */
if (igraph_stack_size(&st) != 1) {
return 3;
}
for (i=0; i<10; i++) {
igraph_stack_push(&st, i);
}
if (igraph_stack_size(&st) != 11) {
return 4;
}
/* igraph_stack_clear */
igraph_stack_clear(&st);
if (!igraph_stack_empty(&st)) {
return 5;
}
igraph_stack_push(&st, 100);
if (igraph_stack_pop(&st) != 100) {
return 6;
}
igraph_stack_clear(&st);
igraph_stack_clear(&st);
/* igraph_stack_push, igraph_stack_pop */
for (i=0; i<100; i++) {
igraph_stack_push(&st, 100-i);
}
for (i=0; i<100; i++) {
if (igraph_stack_pop(&st) != i+1) {
return 7;
}
}
if (!igraph_stack_empty(&st)) {
return 8;
}
igraph_stack_destroy(&st);
if (IGRAPH_FINALLY_STACK_SIZE() != 0) return 9;
return 0;
}
/**
* \ingroup structural
* \function igraph_betweenness_estimate
* \brief Estimated betweenness centrality of some vertices.
*
* </para><para>
* The betweenness centrality of a vertex is the number of geodesics
* going through it. If there are more than one geodesic between two
* vertices, the value of these geodesics are weighted by one over the
* number of geodesics. When estimating betweenness centrality, igraph
* takes into consideration only those paths that are shorter than or
* equal to a prescribed length. Note that the estimated centrality
* will always be less than the real one.
*
* \param graph The graph object.
* \param res The result of the computation, a vector containing the
* estimated betweenness scores for the specified vertices.
* \param vids The vertices of which the betweenness centrality scores
* will be estimated.
* \param directed Logical, if true directed paths will be considered
* for directed graphs. It is ignored for undirected graphs.
* \param cutoff The maximal length of paths that will be considered.
* If zero or negative, the exact betweenness will be calculated
* (no upper limit on path lengths).
* \return Error code:
* \c IGRAPH_ENOMEM, not enough memory for
* temporary data.
* \c IGRAPH_EINVVID, invalid vertex id passed in
* \p vids.
*
* Time complexity: O(|V||E|),
* |V| and
* |E| are the number of vertices and
* edges in the graph.
* Note that the time complexity is independent of the number of
* vertices for which the score is calculated.
*
* \sa Other centrality types: \ref igraph_degree(), \ref igraph_closeness().
* See \ref igraph_edge_betweenness() for calculating the betweenness score
* of the edges in a graph.
*/
int igraph_betweenness_estimate(const igraph_t *graph, igraph_vector_t *res,
const igraph_vs_t vids, igraph_bool_t directed,
igraph_integer_t cutoff) {
long int no_of_nodes=igraph_vcount(graph);
igraph_dqueue_t q=IGRAPH_DQUEUE_NULL;
long int *distance;
long int *nrgeo;
double *tmpscore;
igraph_stack_t stack=IGRAPH_STACK_NULL;
long int source;
long int j, k;
igraph_integer_t modein, modeout;
igraph_vit_t vit;
igraph_vector_t *neis;
igraph_adjlist_t adjlist_out, adjlist_in;
igraph_adjlist_t *adjlist_out_p, *adjlist_in_p;
IGRAPH_CHECK(igraph_vit_create(graph, vids, &vit));
IGRAPH_FINALLY(igraph_vit_destroy, &vit);
directed=directed && igraph_is_directed(graph);
if (directed) {
modeout=IGRAPH_OUT;
modein=IGRAPH_IN;
IGRAPH_CHECK(igraph_adjlist_init(graph, &adjlist_out, IGRAPH_OUT));
IGRAPH_FINALLY(igraph_adjlist_destroy, &adjlist_out);
IGRAPH_CHECK(igraph_adjlist_init(graph, &adjlist_in, IGRAPH_IN));
IGRAPH_FINALLY(igraph_adjlist_destroy, &adjlist_in);
adjlist_out_p=&adjlist_out;
adjlist_in_p=&adjlist_in;
} else {
modeout=modein=IGRAPH_ALL;
IGRAPH_CHECK(igraph_adjlist_init(graph, &adjlist_out, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjlist_destroy, &adjlist_out);
adjlist_out_p=adjlist_in_p=&adjlist_out;
}
distance=igraph_Calloc(no_of_nodes, long int);
if (distance==0) {
IGRAPH_ERROR("betweenness failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, distance);
nrgeo=igraph_Calloc(no_of_nodes, long int);
if (nrgeo==0) {
IGRAPH_ERROR("betweenness failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, nrgeo);
tmpscore=igraph_Calloc(no_of_nodes, double);
if (tmpscore==0) {
IGRAPH_ERROR("betweenness failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, tmpscore);
IGRAPH_DQUEUE_INIT_FINALLY(&q, 100);
igraph_stack_init(&stack, no_of_nodes);
IGRAPH_FINALLY(igraph_stack_destroy, &stack);
IGRAPH_CHECK(igraph_vector_resize(res, IGRAPH_VIT_SIZE(vit)));
igraph_vector_null(res);
/* here we go */
for (source=0; source<no_of_nodes; source++) {
IGRAPH_PROGRESS("Betweenness centrality: ", 100.0*source/no_of_nodes, 0);
IGRAPH_ALLOW_INTERRUPTION();
memset(distance, 0, no_of_nodes*sizeof(long int));
memset(nrgeo, 0, no_of_nodes*sizeof(long int));
memset(tmpscore, 0, no_of_nodes*sizeof(double));
igraph_stack_clear(&stack); /* it should be empty anyway... */
IGRAPH_CHECK(igraph_dqueue_push(&q, source));
nrgeo[source]=1;
distance[source]=0;
while (!igraph_dqueue_empty(&q)) {
long int actnode=igraph_dqueue_pop(&q);
if (cutoff > 0 && distance[actnode] >= cutoff) continue;
neis = igraph_adjlist_get(adjlist_out_p, actnode);
for (j=0; j<igraph_vector_size(neis); j++) {
long int neighbor=VECTOR(*neis)[j];
if (nrgeo[neighbor] != 0) {
/* we've already seen this node, another shortest path? */
if (distance[neighbor]==distance[actnode]+1) {
nrgeo[neighbor]+=nrgeo[actnode];
}
} else {
/* we haven't seen this node yet */
nrgeo[neighbor]+=nrgeo[actnode];
distance[neighbor]=distance[actnode]+1;
IGRAPH_CHECK(igraph_dqueue_push(&q, neighbor));
IGRAPH_CHECK(igraph_stack_push(&stack, neighbor));
}
}
} /* while !igraph_dqueue_empty */
/* Ok, we've the distance of each node and also the number of
shortest paths to them. Now we do an inverse search, starting
with the farthest nodes. */
while (!igraph_stack_empty(&stack)) {
long int actnode=igraph_stack_pop(&stack);
if (distance[actnode]<=1) { continue; } /* skip source node */
/* set the temporary score of the friends */
neis = igraph_adjlist_get(adjlist_in_p, actnode);
for (j=0; j<igraph_vector_size(neis); j++) {
long int neighbor=VECTOR(*neis)[j];
if (distance[neighbor]==distance[actnode]-1 && nrgeo[neighbor] != 0) {
tmpscore[neighbor] +=
(tmpscore[actnode]+1)*nrgeo[neighbor]/nrgeo[actnode];
}
}
}
/* Ok, we've the scores for this source */
for (k=0, IGRAPH_VIT_RESET(vit); !IGRAPH_VIT_END(vit);
IGRAPH_VIT_NEXT(vit), k++) {
long int node=IGRAPH_VIT_GET(vit);
VECTOR(*res)[k] += tmpscore[node];
tmpscore[node] = 0.0; /* in case a node is in vids multiple times */
}
} /* for source < no_of_nodes */
/* divide by 2 for undirected graph */
if (!directed) {
for (j=0; j<igraph_vector_size(res); j++) {
VECTOR(*res)[j] /= 2.0;
}
}
/* clean */
igraph_Free(distance);
igraph_Free(nrgeo);
igraph_Free(tmpscore);
igraph_dqueue_destroy(&q);
igraph_stack_destroy(&stack);
igraph_vit_destroy(&vit);
IGRAPH_FINALLY_CLEAN(6);
if (directed) {
igraph_adjlist_destroy(&adjlist_out);
igraph_adjlist_destroy(&adjlist_in);
IGRAPH_FINALLY_CLEAN(2);
} else {
igraph_adjlist_destroy(&adjlist_out);
IGRAPH_FINALLY_CLEAN(1);
}
return 0;
}
/**
* \ingroup structural
* \function igraph_edge_betweenness_estimate
* \brief Estimated betweenness centrality of the edges.
*
* </para><para>
* The betweenness centrality of an edge is the number of geodesics
* going through it. If there are more than one geodesics between two
* vertices, the value of these geodesics are weighted by one over the
* number of geodesics. When estimating betweenness centrality, igraph
* takes into consideration only those paths that are shorter than or
* equal to a prescribed length. Note that the estimated centrality
* will always be less than the real one.
* \param graph The graph object.
* \param result The result of the computation, vector containing the
* betweenness scores for the edges.
* \param directed Logical, if true directed paths will be considered
* for directed graphs. It is ignored for undirected graphs.
* \param cutoff The maximal length of paths that will be considered.
* If zero or negative, the exact betweenness will be calculated
* (no upper limit on path lengths).
* \return Error code:
* \c IGRAPH_ENOMEM, not enough memory for
* temporary data.
*
* Time complexity: O(|V||E|),
* |V| and
* |E| are the number of vertices and
* edges in the graph.
*
* \sa Other centrality types: \ref igraph_degree(), \ref igraph_closeness().
* See \ref igraph_betweenness() for calculating the betweenness score
* of the vertices in a graph.
*/
int igraph_edge_betweenness_estimate(const igraph_t *graph, igraph_vector_t *result,
igraph_bool_t directed, igraph_integer_t cutoff) {
long int no_of_nodes=igraph_vcount(graph);
long int no_of_edges=igraph_ecount(graph);
igraph_dqueue_t q=IGRAPH_DQUEUE_NULL;
long int *distance;
long int *nrgeo;
double *tmpscore;
igraph_stack_t stack=IGRAPH_STACK_NULL;
long int source;
long int j;
igraph_adjedgelist_t elist_out, elist_in;
igraph_adjedgelist_t *elist_out_p, *elist_in_p;
igraph_vector_t *neip;
long int neino;
long int i;
igraph_integer_t modein, modeout;
directed=directed && igraph_is_directed(graph);
if (directed) {
modeout=IGRAPH_OUT;
modein=IGRAPH_IN;
IGRAPH_CHECK(igraph_adjedgelist_init(graph, &elist_out, IGRAPH_OUT));
IGRAPH_FINALLY(igraph_adjedgelist_destroy, &elist_out);
IGRAPH_CHECK(igraph_adjedgelist_init(graph, &elist_in, IGRAPH_IN));
IGRAPH_FINALLY(igraph_adjedgelist_destroy, &elist_in);
elist_out_p=&elist_out;
elist_in_p=&elist_in;
} else {
modeout=modein=IGRAPH_ALL;
IGRAPH_CHECK(igraph_adjedgelist_init(graph,&elist_out, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjedgelist_destroy, &elist_out);
elist_out_p=elist_in_p=&elist_out;
}
distance=igraph_Calloc(no_of_nodes, long int);
if (distance==0) {
IGRAPH_ERROR("edge betweenness failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, distance);
nrgeo=igraph_Calloc(no_of_nodes, long int);
if (nrgeo==0) {
IGRAPH_ERROR("edge betweenness failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, nrgeo);
tmpscore=igraph_Calloc(no_of_nodes, double);
if (tmpscore==0) {
IGRAPH_ERROR("edge betweenness failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, tmpscore);
IGRAPH_DQUEUE_INIT_FINALLY(&q, 100);
IGRAPH_CHECK(igraph_stack_init(&stack, no_of_nodes));
IGRAPH_FINALLY(igraph_stack_destroy, &stack);
IGRAPH_CHECK(igraph_vector_resize(result, no_of_edges));
igraph_vector_null(result);
/* here we go */
for (source=0; source<no_of_nodes; source++) {
IGRAPH_PROGRESS("Edge betweenness centrality: ", 100.0*source/no_of_nodes, 0);
IGRAPH_ALLOW_INTERRUPTION();
memset(distance, 0, no_of_nodes*sizeof(long int));
memset(nrgeo, 0, no_of_nodes*sizeof(long int));
memset(tmpscore, 0, no_of_nodes*sizeof(double));
igraph_stack_clear(&stack); /* it should be empty anyway... */
IGRAPH_CHECK(igraph_dqueue_push(&q, source));
nrgeo[source]=1;
distance[source]=0;
while (!igraph_dqueue_empty(&q)) {
long int actnode=igraph_dqueue_pop(&q);
if (cutoff > 0 && distance[actnode] >= cutoff ) continue;
neip=igraph_adjedgelist_get(elist_out_p, actnode);
neino=igraph_vector_size(neip);
for (i=0; i<neino; i++) {
igraph_integer_t edge=VECTOR(*neip)[i], from, to;
long int neighbor;
igraph_edge(graph, edge, &from, &to);
neighbor = actnode!=from ? from : to;
if (nrgeo[neighbor] != 0) {
/* we've already seen this node, another shortest path? */
if (distance[neighbor]==distance[actnode]+1) {
nrgeo[neighbor]+=nrgeo[actnode];
}
} else {
/* we haven't seen this node yet */
nrgeo[neighbor]+=nrgeo[actnode];
distance[neighbor]=distance[actnode]+1;
IGRAPH_CHECK(igraph_dqueue_push(&q, neighbor));
IGRAPH_CHECK(igraph_stack_push(&stack, neighbor));
}
}
} /* while !igraph_dqueue_empty */
/* Ok, we've the distance of each node and also the number of
shortest paths to them. Now we do an inverse search, starting
with the farthest nodes. */
while (!igraph_stack_empty(&stack)) {
long int actnode=igraph_stack_pop(&stack);
if (distance[actnode]<1) { continue; } /* skip source node */
/* set the temporary score of the friends */
neip=igraph_adjedgelist_get(elist_in_p, actnode);
neino=igraph_vector_size(neip);
for (i=0; i<neino; i++) {
igraph_integer_t from, to;
long int neighbor;
long int edgeno=VECTOR(*neip)[i];
igraph_edge(graph, edgeno, &from, &to);
neighbor= actnode != from ? from : to;
if (distance[neighbor]==distance[actnode]-1 &&
nrgeo[neighbor] != 0) {
tmpscore[neighbor] +=
(tmpscore[actnode]+1)*nrgeo[neighbor]/nrgeo[actnode];
VECTOR(*result)[edgeno] +=
(tmpscore[actnode]+1)*nrgeo[neighbor]/nrgeo[actnode];
}
}
}
/* Ok, we've the scores for this source */
} /* for source <= no_of_nodes */
IGRAPH_PROGRESS("Edge betweenness centrality: ", 100.0, 0);
/* clean and return */
igraph_Free(distance);
igraph_Free(nrgeo);
igraph_Free(tmpscore);
igraph_dqueue_destroy(&q);
igraph_stack_destroy(&stack);
IGRAPH_FINALLY_CLEAN(5);
if (directed) {
igraph_adjedgelist_destroy(&elist_out);
igraph_adjedgelist_destroy(&elist_in);
IGRAPH_FINALLY_CLEAN(2);
} else {
igraph_adjedgelist_destroy(&elist_out);
IGRAPH_FINALLY_CLEAN(1);
}
/* divide by 2 for undirected graph */
if (!directed || !igraph_is_directed(graph)) {
for (j=0; j<igraph_vector_size(result); j++) {
VECTOR(*result)[j] /= 2.0;
}
}
return 0;
}
