/src/igraph/src/community/fast_modularity.c

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/*
   IGraph library.
   Copyright (C) 2007-2012  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_community.h"

#include "igraph_memory.h"
#include "igraph_iterators.h"
#include "igraph_interface.h"
#include "igraph_progress.h"
#include "igraph_structural.h"
#include "igraph_vector_ptr.h"

#include "core/interruption.h"

/* #define IGRAPH_FASTCOMM_DEBUG */

#ifdef IGRAPH_FASTCOMM_DEBUG
    #define debug(...) fprintf(stderr, __VA_ARGS__)
#else
    #define debug(...)
#endif

/*
 * Implementation of the community structure algorithm originally published
 * by Clauset et al in:
 *
 * A. Clauset, M.E.J. Newman and C. Moore, "Finding community structure in
 * very large networks.". Phys. Rev. E 70, 066111 (2004).
 *
 * The data structures being used are slightly different and they are described
 * most closely in:
 *
 * K. Wakita, T. Tsurumi, "Finding community structure in mega-scale social
 * networks.". arXiv:cs/0702048v1.
 *
 * We maintain a vector of communities, each of which containing a list of
 * pointers to their neighboring communities along with the increase in the
 * modularity score that could be achieved by joining the two communities.
 * Each community has a pointer to one of its neighbors - the one which would
 * result in the highest increase in modularity after a join. The local
 * (community-level) maximums are also stored in an indexed max-heap. The
 * max-heap itself stores its elements in an array which satisfies the heap
 * property, but to allow us to access any of the elements in the array based
 * on the community index (and not based on the array index - which depends on
 * the element's actual position in the heap), we also maintain an index
 * vector in the heap: the ith element of the index vector contains the
 * position of community i in the array of the max-heap. When we perform
 * sifting operations on the heap to restore the heap property, we also maintain
 * the index vector.
 */

/* Structure storing a pair of communities along with their dQ values */
typedef struct s_igraph_i_fastgreedy_commpair {
    igraph_integer_t first;  /* first member of the community pair */
    igraph_integer_t second; /* second member of the community pair */
    igraph_real_t *dq;    /* pointer to a member of the dq vector storing the */
    /* increase in modularity achieved when joining */
    struct s_igraph_i_fastgreedy_commpair *opposite;
} igraph_i_fastgreedy_commpair;

/* Structure storing a community */
typedef struct {
    igraph_integer_t id;      /* Identifier of the community (for merges matrix) */
    igraph_integer_t size;    /* Size of the community */
    igraph_vector_ptr_t neis; /* references to neighboring communities */
    igraph_i_fastgreedy_commpair *maxdq; /* community pair with maximal dq */
} igraph_i_fastgreedy_community;

/* Global community list structure */
typedef struct {
    igraph_integer_t no_of_communities, n; /* number of communities, number of vertices */
    igraph_i_fastgreedy_community *e;     /* list of communities */
    igraph_i_fastgreedy_community **heap; /* heap of communities */
    igraph_integer_t *heapindex; /* heap index to speed up lookup by community idx */
} igraph_i_fastgreedy_community_list;

/* Scans the community neighborhood list for the new maximal dq value.
 * Returns true if the maximum is different from the previous one,
 * false otherwise. */
static igraph_bool_t igraph_i_fastgreedy_community_rescan_max(igraph_i_fastgreedy_community *comm) {
    igraph_integer_t i, n;
    igraph_i_fastgreedy_commpair *p, *best;
    igraph_real_t bestdq, currdq;

    n = igraph_vector_ptr_size(&comm->neis);
    if (n == 0) {
        comm->maxdq = NULL;
        return true;
    }

    best = (igraph_i_fastgreedy_commpair*)VECTOR(comm->neis)[0];
    bestdq = *best->dq;
    for (i = 1; i < n; i++) {
        p = (igraph_i_fastgreedy_commpair*)VECTOR(comm->neis)[i];
        currdq = *p->dq;
        if (currdq > bestdq) {
            best = p;
            bestdq = currdq;
        }
    }

    if (best != comm->maxdq) {
        comm->maxdq = best;
        return true;
    } else {
        return false;
    }
}

/* Destroys the global community list object */
static void igraph_i_fastgreedy_community_list_destroy(
        igraph_i_fastgreedy_community_list *list) {
    igraph_integer_t i;
    for (i = 0; i < list->n; i++) {
        igraph_vector_ptr_destroy(&list->e[i].neis);
    }
    IGRAPH_FREE(list->e);
    if (list->heapindex != NULL) {
        IGRAPH_FREE(list->heapindex);
    }
    if (list->heap != NULL) {
        IGRAPH_FREE(list->heap);
    }
}

/* Community list heap maintenance: sift down */
static void igraph_i_fastgreedy_community_list_sift_down(
        igraph_i_fastgreedy_community_list *list, igraph_integer_t idx) {
    igraph_integer_t root, child, c1, c2;
    igraph_i_fastgreedy_community *dummy;
    igraph_integer_t dummy2;
    igraph_i_fastgreedy_community** heap = list->heap;
    igraph_integer_t *heapindex = list->heapindex;

    root = idx;
    while (root * 2 + 1 < list->no_of_communities) {
        child = root * 2 + 1;
        if (child + 1 < list->no_of_communities &&
            *heap[child]->maxdq->dq < *heap[child + 1]->maxdq->dq) {
            child++;
        }
        if (*heap[root]->maxdq->dq < *heap[child]->maxdq->dq) {
            c1 = heap[root]->maxdq->first;
            c2 = heap[child]->maxdq->first;

            dummy = heap[root];
            heap[root] = heap[child];
            heap[child] = dummy;

            dummy2 = heapindex[c1];
            heapindex[c1] = heapindex[c2];
            heapindex[c2] = dummy2;

            root = child;
        } else {
            break;
        }
    }
}

/* Community list heap maintenance: sift up */
static void igraph_i_fastgreedy_community_list_sift_up(
        igraph_i_fastgreedy_community_list *list, igraph_integer_t idx) {
    igraph_integer_t root, parent, c1, c2;
    igraph_i_fastgreedy_community *dummy;
    igraph_integer_t dummy2;
    igraph_i_fastgreedy_community** heap = list->heap;
    igraph_integer_t *heapindex = list->heapindex;

    root = idx;
    while (root > 0) {
        parent = (root - 1) / 2;
        if (*heap[parent]->maxdq->dq < *heap[root]->maxdq->dq) {
            c1 = heap[root]->maxdq->first;
            c2 = heap[parent]->maxdq->first;

            dummy = heap[parent];
            heap[parent] = heap[root];
            heap[root] = dummy;

            dummy2 = heapindex[c1];
            heapindex[c1] = heapindex[c2];
            heapindex[c2] = dummy2;

            root = parent;
        } else {
            break;
        }
    }
}

/* Builds the community heap for the first time */
static void igraph_i_fastgreedy_community_list_build_heap(
        igraph_i_fastgreedy_community_list *list) {
    igraph_integer_t i;
    for (i = list->no_of_communities / 2 - 1; i >= 0; i--) {
        igraph_i_fastgreedy_community_list_sift_down(list, i);
    }
}

/* Finds the element belonging to a given community in the heap and return its
 * index in the heap array */
#define igraph_i_fastgreedy_community_list_find_in_heap(list, idx) (list)->heapindex[idx]

/* Dumps the heap - for debugging purposes */
/*
static void igraph_i_fastgreedy_community_list_dump_heap(
        igraph_i_fastgreedy_community_list *list) {
    igraph_integer_t i;
    debug("Heap:\n");
    for (i = 0; i < list->no_of_communities; i++) {
        debug("(%ld, %p, %p)", i, list->heap[i],
              list->heap[i]->maxdq);
        if (list->heap[i]->maxdq) {
            debug(" (%" IGRAPH_PRId ", %" IGRAPH_PRId ", %.7f)", list->heap[i]->maxdq->first,
                  list->heap[i]->maxdq->second, *list->heap[i]->maxdq->dq);
        }
        debug("\n");
    }
    debug("Heap index:\n");
    for (i = 0; i < list->no_of_communities; i++) {
        debug("%" IGRAPH_PRId " ", list->heapindex[i]);
    }
    debug("\nEND\n");
}
*/

/* Checks if the community heap satisfies the heap property.
 * Only useful for debugging. */
/*
static void igraph_i_fastgreedy_community_list_check_heap(
        igraph_i_fastgreedy_community_list *list) {
    igraph_integer_t i;
    for (i = 0; i < list->no_of_communities / 2; i++) {
        if ((2 * i + 1 < list->no_of_communities && *list->heap[i]->maxdq->dq < *list->heap[2 * i + 1]->maxdq->dq) ||
            (2 * i + 2 < list->no_of_communities && *list->heap[i]->maxdq->dq < *list->heap[2 * i + 2]->maxdq->dq)) {
            IGRAPH_WARNING("Heap property violated");
            debug("Position: %" IGRAPH_PRId ", %" IGRAPH_PRId " and %" IGRAPH_PRId "\n", i, 2 * i + 1, 2 * i + 2);
            igraph_i_fastgreedy_community_list_dump_heap(list);
        }
    }
}
*/

/* Removes a given element from the heap */
static void igraph_i_fastgreedy_community_list_remove(
        igraph_i_fastgreedy_community_list *list, igraph_integer_t idx) {
    igraph_real_t old;
    igraph_integer_t commidx;

    /* First adjust the index */
    commidx = list->heap[list->no_of_communities - 1]->maxdq->first;
    list->heapindex[commidx] = idx;
    commidx = list->heap[idx]->maxdq->first;
    list->heapindex[commidx] = -1;

    /* Now remove the element */
    old = *list->heap[idx]->maxdq->dq;
    list->heap[idx] = list->heap[list->no_of_communities - 1];
    list->no_of_communities--;

    /* Recover heap property */
    if (old > *list->heap[idx]->maxdq->dq) {
        igraph_i_fastgreedy_community_list_sift_down(list, idx);
    } else {
        igraph_i_fastgreedy_community_list_sift_up(list, idx);
    }
}

/* Removes a given element from the heap when there are no more neighbors
 * for it (comm->maxdq is NULL) */
static void igraph_i_fastgreedy_community_list_remove2(
        igraph_i_fastgreedy_community_list *list, igraph_integer_t idx, igraph_integer_t comm) {
    igraph_integer_t i;

    if (idx == list->no_of_communities - 1) {
        /* We removed the rightmost element on the bottom level, no problem,
         * there's nothing to be done */
        list->heapindex[comm] = -1;
        list->no_of_communities--;
        return;
    }

    /* First adjust the index */
    i = list->heap[list->no_of_communities - 1]->maxdq->first;
    list->heapindex[i] = idx;
    list->heapindex[comm] = -1;

    /* Now remove the element */
    list->heap[idx] = list->heap[list->no_of_communities - 1];
    list->no_of_communities--;

    /* Recover heap property */
    for (i = list->no_of_communities / 2 - 1; i >= 0; i--) {
        igraph_i_fastgreedy_community_list_sift_down(list, i);
    }
}

/* Removes the pair belonging to community k from the neighborhood list
 * of community c (that is, clist[c]) and recalculates maxdq */
static void igraph_i_fastgreedy_community_remove_nei(
        igraph_i_fastgreedy_community_list *list, igraph_integer_t c, igraph_integer_t k) {
    igraph_integer_t i, n;
    igraph_bool_t rescan = false;
    igraph_i_fastgreedy_commpair *p;
    igraph_i_fastgreedy_community *comm;
    igraph_real_t olddq;

    comm = &list->e[c];
    n = igraph_vector_ptr_size(&comm->neis);
    for (i = 0; i < n; i++) {
        p = (igraph_i_fastgreedy_commpair*)VECTOR(comm->neis)[i];
        if (p->second == k) {
            /* Check current maxdq */
            if (comm->maxdq == p) {
                rescan = true;
            }
            break;
        }
    }
    if (i < n) {
        olddq = *comm->maxdq->dq;
        igraph_vector_ptr_remove(&comm->neis, i);
        if (rescan) {
            igraph_i_fastgreedy_community_rescan_max(comm);
            i = igraph_i_fastgreedy_community_list_find_in_heap(list, c);
            if (comm->maxdq) {
                if (*comm->maxdq->dq > olddq) {
                    igraph_i_fastgreedy_community_list_sift_up(list, i);
                } else {
                    igraph_i_fastgreedy_community_list_sift_down(list, i);
                }
            } else {
                /* no more neighbors for this community. we should remove this
                 * community from the heap and restore the heap property */
                debug("REMOVING (NO MORE NEIS): %" IGRAPH_PRId "\n", i);
                igraph_i_fastgreedy_community_list_remove2(list, i, c);
            }
        }
    }
}

/* Auxiliary function to sort a community pair list with respect to the
 * `second` field */
static int igraph_i_fastgreedy_commpair_cmp(const void *p1, const void *p2) {
    igraph_i_fastgreedy_commpair *cp1, *cp2;
    igraph_integer_t diff;
    cp1 = *(igraph_i_fastgreedy_commpair**)p1;
    cp2 = *(igraph_i_fastgreedy_commpair**)p2;
    diff = cp1->second - cp2->second;
    return (diff < 0) ? -1 : (diff > 0) ? 1 : 0;
}

/* Sorts the neighbor list of the community with the given index, optionally
 * optimizing the process if we know that the list is nearly sorted and only
 * a given pair is in the wrong place. */
static void igraph_i_fastgreedy_community_sort_neighbors_of(
        igraph_i_fastgreedy_community_list *list, igraph_integer_t index,
        igraph_i_fastgreedy_commpair *changed_pair) {
    igraph_vector_ptr_t *vec;
    igraph_integer_t i, n;
    igraph_bool_t can_skip_sort = false;
    igraph_i_fastgreedy_commpair *other_pair;

    vec = &list->e[index].neis;
    if (changed_pair != NULL) {
        /* Optimized sorting */

        /* First we look for changed_pair in vec */
        n = igraph_vector_ptr_size(vec);
        for (i = 0; i < n; i++) {
            if (VECTOR(*vec)[i] == changed_pair) {
                break;
            }
        }

        /* Did we find it? We should have -- otherwise it's a bug */
        IGRAPH_ASSERT(i < n);

        /* Okay, the pair that changed is at index i. We need to figure out where
         * its new place should be. We can simply try moving the item all the way
         * to the left as long as the comparison function tells so (since the
         * rest of the vector is sorted), and then move all the way to the right
         * as long as the comparison function tells so, and we will be okay. */

        /* Shifting to the left */
        while (i > 0) {
            other_pair = VECTOR(*vec)[i - 1];
            if (other_pair->second > changed_pair->second) {
                VECTOR(*vec)[i] = other_pair;
                i--;
            } else {
                break;
            }
        }
        VECTOR(*vec)[i] = changed_pair;

        /* Shifting to the right */
        while (i < n - 1) {
            other_pair = VECTOR(*vec)[i + 1];
            if (other_pair->second < changed_pair->second) {
                VECTOR(*vec)[i] = other_pair;
                i++;
            } else {
                break;
            }
        }
        VECTOR(*vec)[i] = changed_pair;

        /* Mark that we don't need a full sort */
        can_skip_sort = true;
    }

    if (!can_skip_sort) {
        /* Fallback to full sorting */
        igraph_vector_ptr_sort(vec, igraph_i_fastgreedy_commpair_cmp);
    }
}

/* Updates the dq value of community pair p in the community with index p->first
 * of the community list clist to newdq and restores the heap property
 * in community c if necessary. Returns 1 if the maximum in the row had
 * to be updated, zero otherwise */
static igraph_bool_t igraph_i_fastgreedy_community_update_dq(
        igraph_i_fastgreedy_community_list *list,
        igraph_i_fastgreedy_commpair *p, igraph_real_t newdq) {

    igraph_integer_t i, j, to, from;
    igraph_real_t olddq;
    igraph_i_fastgreedy_community *comm_to, *comm_from;
    to = p->first; from = p->second;
    comm_to = &list->e[to];
    comm_from = &list->e[from];
    if (comm_to->maxdq == p && newdq >= *p->dq) {
        /* If we are adjusting the current maximum and it is increased, we don't
         * have to re-scan for the new maximum */
        *p->dq = newdq;
        /* The maximum was increased, so perform a sift-up in the heap */
        i = igraph_i_fastgreedy_community_list_find_in_heap(list, to);
        igraph_i_fastgreedy_community_list_sift_up(list, i);
        /* Let's check the opposite side. If the pair was not the maximal in
         * the opposite side (the other community list)... */
        if (comm_from->maxdq != p->opposite) {
            if (*comm_from->maxdq->dq < newdq) {
                /* ...and it will become the maximal, we need to adjust and sift up */
                comm_from->maxdq = p->opposite;
                j = igraph_i_fastgreedy_community_list_find_in_heap(list, from);
                igraph_i_fastgreedy_community_list_sift_up(list, j);
            } else {
                /* The pair was not the maximal in the opposite side and it will
                 * NOT become the maximal, there's nothing to do there */
            }
        } else {
            /* The pair was maximal in the opposite side, so we need to sift it up
             * with the new value */
            j = igraph_i_fastgreedy_community_list_find_in_heap(list, from);
            igraph_i_fastgreedy_community_list_sift_up(list, j);
        }
        return true;
    } else if (comm_to->maxdq != p && (newdq <= *comm_to->maxdq->dq)) {
        /* If we are modifying an item which is not the current maximum, and the
         * new value is less than the current maximum, we don't
         * have to re-scan for the new maximum */
        olddq = *p->dq;
        *p->dq = newdq;
        /* However, if the item was the maximum on the opposite side, we'd better
         * re-scan it */
        if (comm_from->maxdq == p->opposite) {
            if (olddq > newdq) {
                /* Decreased the maximum on the other side, we have to re-scan for the
                 * new maximum */
                igraph_i_fastgreedy_community_rescan_max(comm_from);
                j = igraph_i_fastgreedy_community_list_find_in_heap(list, from);
                igraph_i_fastgreedy_community_list_sift_down(list, j);
            } else {
                /* Increased the maximum on the other side, we don't have to re-scan
                 * but we might have to sift up */
                j = igraph_i_fastgreedy_community_list_find_in_heap(list, from);
                igraph_i_fastgreedy_community_list_sift_up(list, j);
            }
        }
        return false;
    } else {
        /* We got here in two cases:
         (1) the pair we are modifying right now is the maximum in the given
             community and we are decreasing it
         (2) the pair we are modifying right now is NOT the maximum in the
             given community, but we increase it so much that it will become
             the new maximum
         */
        *p->dq = newdq;
        if (comm_to->maxdq != p) {
            /* case (2) */
            comm_to->maxdq = p;
            /* The maximum was increased, so perform a sift-up in the heap */
            i = igraph_i_fastgreedy_community_list_find_in_heap(list, to);
            igraph_i_fastgreedy_community_list_sift_up(list, i);
            /* Opposite side. Chances are that the new value became the maximum
             * in the opposite side, but check it first */
            if (comm_from->maxdq != p->opposite) {
                if (*comm_from->maxdq->dq < newdq) {
                    /* Yes, it will become the new maximum */
                    comm_from->maxdq = p->opposite;
                    j = igraph_i_fastgreedy_community_list_find_in_heap(list, from);
                    igraph_i_fastgreedy_community_list_sift_up(list, j);
                } else {
                    /* No, nothing to do there */
                }
            } else {
                /* Already increased the maximum on the opposite side, so sift it up */
                j = igraph_i_fastgreedy_community_list_find_in_heap(list, from);
                igraph_i_fastgreedy_community_list_sift_up(list, j);
            }
        } else {
            /* case (1) */
            /* This is the worst, we have to re-scan the whole community to find
             * the new maximum and update the global maximum as well if necessary */
            igraph_i_fastgreedy_community_rescan_max(comm_to);
            /* The maximum was decreased, so perform a sift-down in the heap */
            i = igraph_i_fastgreedy_community_list_find_in_heap(list, to);
            igraph_i_fastgreedy_community_list_sift_down(list, i);
            if (comm_from->maxdq != p->opposite) {
                /* The one that we decreased on the opposite side is not the
                 * maximal one. Nothing to do. */
            } else {
                /* We decreased the maximal on the opposite side as well. Re-scan
                 * and sift down */
                igraph_i_fastgreedy_community_rescan_max(comm_from);
                j = igraph_i_fastgreedy_community_list_find_in_heap(list, from);
                igraph_i_fastgreedy_community_list_sift_down(list, j);
            }
        }
    }
    return true;
}

/**
 * \function igraph_community_fastgreedy
 * \brief Finding community structure by greedy optimization of modularity.
 *
 * This function implements the fast greedy modularity optimization
 * algorithm for finding community structure, see
 * A Clauset, MEJ Newman, C Moore: Finding community structure in very
 * large networks, http://www.arxiv.org/abs/cond-mat/0408187 for the
 * details.
 *
 * </para><para>
 * Some improvements proposed in K Wakita, T Tsurumi: Finding community
 * structure in mega-scale social networks,
 * http://www.arxiv.org/abs/cs.CY/0702048v1 have also been implemented.
 *
 * \param graph The input graph. It must be a graph without multiple edges.
 *    This is checked and an error message is given for graphs with multiple
 *    edges.
 * \param weights Potentially a numeric vector containing edge
 *    weights. Supply a null pointer here for unweighted graphs. The
 *    weights are expected to be non-negative.
 * \param merges Pointer to an initialized matrix or \c NULL, the result of the
 *    computation is stored here. The matrix has two columns and each
 *    merge corresponds to one merge, the IDs of the two merged
 *    components are stored. The component IDs are numbered from zero and
 *    the first \c n components are the individual vertices, \c n is
 *    the number of vertices in the graph. Component \c n is created
 *    in the first merge, component <code>n+1</code> in the second merge, etc.
 *    The matrix will be resized as needed. If this argument is \c NULL
 *    then it is ignored completely.
 * \param modularity Pointer to an initialized vector or \c NULL pointer,
 *    in the former case the modularity scores along the stages of the
 *    computation are recorded here. The vector will be resized as
 *    needed.
 * \param membership Pointer to a vector. If not a null pointer, then
 *    the membership vector corresponding to the best split (in terms
 *    of modularity) is stored here.
 * \return Error code.
 *
 * \sa \ref igraph_community_walktrap(), \ref
 * igraph_community_edge_betweenness() for other community detection
 * algorithms, \ref igraph_community_to_membership() to convert the
 * dendrogram to a membership vector.
 *
 * Time complexity: O(|E||V|log|V|) in the worst case,
 * O(|E|+|V|log^2|V|) typically, |V| is the number of vertices, |E| is
 * the number of edges.
 *
 * \example examples/simple/igraph_community_fastgreedy.c
 */
igraph_error_t igraph_community_fastgreedy(const igraph_t *graph,
                                const igraph_vector_t *weights,
                                igraph_matrix_int_t *merges,
                                igraph_vector_t *modularity,
                                igraph_vector_int_t *membership) {
    igraph_integer_t no_of_edges, no_of_nodes, no_of_joins, total_joins;
    igraph_integer_t i, j, k, n, m, from, to, dummy, best_no_of_joins;
    igraph_eit_t edgeit;
    igraph_i_fastgreedy_commpair *pairs, *p1, *p2;
    igraph_i_fastgreedy_community_list communities;
    igraph_vector_t a;
    igraph_vector_int_t degrees;
    igraph_real_t q, *dq, bestq, weight_sum, loop_weight_sum;
    igraph_bool_t has_multiple;
    igraph_matrix_int_t merges_local;

    /*igraph_integer_t join_order[] = { 16,5, 5,6, 6,0, 4,0, 10,0, 26,29, 29,33, 23,33, 27,33, 25,24, 24,31, 12,3, 21,1, 30,8, 8,32, 9,2, 17,1, 11,0, 7,3, 3,2, 13,2, 1,2, 28,31, 31,33, 22,32, 18,32, 20,32, 32,33, 15,33, 14,33, 0,19, 19,2, -1,-1 };*/
    /*igraph_integer_t join_order[] = { 43,42, 42,41, 44,41, 41,36, 35,36, 37,36, 36,29, 38,29, 34,29, 39,29, 33,29, 40,29, 32,29, 14,29, 30,29, 31,29, 6,18, 18,4, 23,4, 21,4, 19,4, 27,4, 20,4, 22,4, 26,4, 25,4, 24,4, 17,4, 0,13, 13,2, 1,2, 11,2, 8,2, 5,2, 3,2, 10,2, 9,2, 7,2, 2,28, 28,15, 12,15, 29,16, 4,15, -1,-1 };*/

    no_of_nodes = igraph_vcount(graph);
    no_of_edges = igraph_ecount(graph);

    if (igraph_is_directed(graph)) {
        IGRAPH_ERROR("Fast greedy community detection works on undirected graphs only.", IGRAPH_UNIMPLEMENTED);
    }

    total_joins = no_of_nodes > 0 ? no_of_nodes - 1 : 0;

    if (weights) {
        if (igraph_vector_size(weights) != no_of_edges) {
            IGRAPH_ERROR("Length of weight vector must agree with number of edges.", IGRAPH_EINVAL);
        }
        if (no_of_edges > 0) {
            igraph_real_t minweight = igraph_vector_min(weights);
            if (minweight < 0) {
                IGRAPH_ERROR("Weights must not be negative.", IGRAPH_EINVAL);
            }
            if (isnan(minweight)) {
                IGRAPH_ERROR("Weights must not be NaN.", IGRAPH_EINVAL);
            }
        }
        weight_sum = igraph_vector_sum(weights);
    } else {
        weight_sum = no_of_edges;
    }

    IGRAPH_CHECK(igraph_has_multiple(graph, &has_multiple));
    if (has_multiple) {
        IGRAPH_ERROR("Fast greedy community detection works only on graphs without multi-edges.", IGRAPH_EINVAL);
    }

    if (membership != NULL && merges == NULL) {
        /* We need the merge matrix because the user wants the membership
         * vector, so we allocate one on our own */
        IGRAPH_CHECK(igraph_matrix_int_init(&merges_local, total_joins, 2));
        IGRAPH_FINALLY(igraph_matrix_int_destroy, &merges_local);
        merges = &merges_local;
    }

    if (merges != NULL) {
        IGRAPH_CHECK(igraph_matrix_int_resize(merges, total_joins, 2));
        igraph_matrix_int_null(merges);
    }

    if (modularity != NULL) {
        IGRAPH_CHECK(igraph_vector_resize(modularity, total_joins + 1));
    }

    /* Create degree vector */
    IGRAPH_VECTOR_INIT_FINALLY(&a, no_of_nodes);
    if (weights) {
        debug("Calculating weighted degrees\n");
        for (i = 0; i < no_of_edges; i++) {
            VECTOR(a)[IGRAPH_FROM(graph, i)] += VECTOR(*weights)[i];
            VECTOR(a)[IGRAPH_TO(graph, i)] += VECTOR(*weights)[i];
        }
    } else {
        debug("Calculating degrees\n");
        IGRAPH_VECTOR_INT_INIT_FINALLY(&degrees, no_of_nodes);
        IGRAPH_CHECK(igraph_degree(graph, &degrees, igraph_vss_all(), IGRAPH_ALL, IGRAPH_LOOPS));
        for (i = 0; i < no_of_nodes; i++) {
            VECTOR(a)[i] = VECTOR(degrees)[i];
        }
        igraph_vector_int_destroy(&degrees);
        IGRAPH_FINALLY_CLEAN(1);
    }

    /* Create list of communities */
    debug("Creating community list\n");
    communities.n = no_of_nodes;
    communities.no_of_communities = no_of_nodes;
    communities.e = IGRAPH_CALLOC(no_of_nodes, igraph_i_fastgreedy_community);
    IGRAPH_CHECK_OOM(communities.e, "Insufficient memory for fast greedy community detection.");
    IGRAPH_FINALLY(igraph_free, communities.e);

    communities.heap = IGRAPH_CALLOC(no_of_nodes, igraph_i_fastgreedy_community*);
    IGRAPH_CHECK_OOM(communities.heap, "Insufficient memory for fast greedy community detection.");
    IGRAPH_FINALLY(igraph_free, communities.heap);

    communities.heapindex = IGRAPH_CALLOC(no_of_nodes, igraph_integer_t);
    IGRAPH_CHECK_OOM(communities.heapindex, "Insufficient memory for fast greedy community detection.");

    IGRAPH_FINALLY_CLEAN(2);
    IGRAPH_FINALLY(igraph_i_fastgreedy_community_list_destroy, &communities);

    for (i = 0; i < no_of_nodes; i++) {
        IGRAPH_CHECK(igraph_vector_ptr_init(&communities.e[i].neis, 0));
        communities.e[i].id = i;
        communities.e[i].size = 1;
    }

    /* Create list of community pairs from edges */
    debug("Allocating dq vector\n");
    dq = IGRAPH_CALLOC(no_of_edges, igraph_real_t);
    IGRAPH_CHECK_OOM(dq, "Insufficient memory for fast greedy community detection.");
    IGRAPH_FINALLY(igraph_free, dq);

    debug("Creating community pair list\n");
    IGRAPH_CHECK(igraph_eit_create(graph, igraph_ess_all(IGRAPH_EDGEORDER_ID), &edgeit));
    IGRAPH_FINALLY(igraph_eit_destroy, &edgeit);
    pairs = IGRAPH_CALLOC(2 * no_of_edges, igraph_i_fastgreedy_commpair);
    IGRAPH_CHECK_OOM(pairs, "Insufficient memory for fast greedy community detection.");
    IGRAPH_FINALLY(igraph_free, pairs);

    loop_weight_sum = 0;
    for (i = 0, j = 0; !IGRAPH_EIT_END(edgeit); i += 2, j++, IGRAPH_EIT_NEXT(edgeit)) {
        igraph_integer_t eidx = IGRAPH_EIT_GET(edgeit);

        /* Create the pairs themselves */
        from = IGRAPH_FROM(graph, eidx); to = IGRAPH_TO(graph, eidx);
        if (from == to) {
            loop_weight_sum += weights ? 2 * VECTOR(*weights)[eidx] : 2;
            continue;
        }

        if (from > to) {
            dummy = from; from = to; to = dummy;
        }
        if (weights) {
            dq[j] = 2 * (VECTOR(*weights)[eidx] / (weight_sum * 2.0) - VECTOR(a)[from] * VECTOR(a)[to] / (4.0 * weight_sum * weight_sum));
        } else {
            dq[j] = 2 * (1.0 / (no_of_edges * 2.0) - VECTOR(a)[from] * VECTOR(a)[to] / (4.0 * no_of_edges * no_of_edges));
        }
        pairs[i].first = from;
        pairs[i].second = to;
        pairs[i].dq = &dq[j];
        pairs[i].opposite = &pairs[i + 1];
        pairs[i + 1].first = to;
        pairs[i + 1].second = from;
        pairs[i + 1].dq = pairs[i].dq;
        pairs[i + 1].opposite = &pairs[i];
        /* Link the pair to the communities */
        IGRAPH_CHECK(igraph_vector_ptr_push_back(&communities.e[from].neis, &pairs[i]));
        IGRAPH_CHECK(igraph_vector_ptr_push_back(&communities.e[to].neis, &pairs[i + 1]));
        /* Update maximums */
        if (communities.e[from].maxdq == NULL || *communities.e[from].maxdq->dq < *pairs[i].dq) {
            communities.e[from].maxdq = &pairs[i];
        }
        if (communities.e[to].maxdq == NULL || *communities.e[to].maxdq->dq < *pairs[i + 1].dq) {
            communities.e[to].maxdq = &pairs[i + 1];
        }
    }
    igraph_eit_destroy(&edgeit);
    IGRAPH_FINALLY_CLEAN(1);

    /* Sorting community neighbor lists by community IDs */
    debug("Sorting community neighbor lists\n");
    for (i = 0, j = 0; i < no_of_nodes; i++) {
        igraph_i_fastgreedy_community_sort_neighbors_of(&communities, i, NULL);
        /* Isolated vertices and vertices with loop edges only won't be stored in
         * the heap (to avoid maxdq == NULL) */
        if (communities.e[i].maxdq != NULL) {
            communities.heap[j] = &communities.e[i];
            communities.heapindex[i] = j;
            j++;
        } else {
            communities.heapindex[i] = -1;
        }
    }
    communities.no_of_communities = j;

    /* Calculate proper vector a (see paper) and initial modularity */
    q = 2.0 * (weights ? weight_sum : no_of_edges);
    if (q == 0) {
        /* All the weights are zero */
    } else {
        igraph_vector_scale(&a, 1.0 / q);
        q = loop_weight_sum / q;
        for (i = 0; i < no_of_nodes; i++) {
            q -= VECTOR(a)[i] * VECTOR(a)[i];
        }
    }

    /* Initialize "best modularity" value and best merge counter */
    bestq = q;
    best_no_of_joins = 0;

    /* Initializing community heap */
    debug("Initializing community heap\n");
    igraph_i_fastgreedy_community_list_build_heap(&communities);

    debug("Initial modularity: %.4f\n", q);

    /* Let's rock ;) */
    no_of_joins = 0;
    while (no_of_joins < total_joins) {
        IGRAPH_ALLOW_INTERRUPTION();
        IGRAPH_PROGRESS("Fast greedy community detection", no_of_joins * 100.0 / total_joins, 0);

        /* Store the modularity */
        if (modularity) {
            VECTOR(*modularity)[no_of_joins] = q;
        }

        /* Update best modularity if needed */
        if (q >= bestq) {
            bestq = q;
            best_no_of_joins = no_of_joins;
        }

        /* Some debug info if needed */
        /* igraph_i_fastgreedy_community_list_check_heap(&communities); */
#ifdef IGRAPH_FASTCOMM_DEBUG
        debug("===========================================\n");
        for (i = 0; i < communities.n; i++) {
            if (communities.e[i].maxdq == 0) {
                debug("Community #%ld: PASSIVE\n", i);
                continue;
            }
            debug("Community #%ld\n ", i);
            for (j = 0; j < igraph_vector_ptr_size(&communities.e[i].neis); j++) {
                p1 = (igraph_i_fastgreedy_commpair*)VECTOR(communities.e[i].neis)[j];
                debug(" (%ld,%ld,%.4f)", p1->first, p1->second, *p1->dq);
            }
            p1 = communities.e[i].maxdq;
            debug("\n  Maxdq: (%ld,%ld,%.4f)\n", p1->first, p1->second, *p1->dq);
        }
        debug("Global maxdq is: (%ld,%ld,%.4f)\n", communities.heap[0]->maxdq->first,
              communities.heap[0]->maxdq->second, *communities.heap[0]->maxdq->dq);
        for (i = 0; i < communities.no_of_communities; i++) {
            debug("(%ld,%ld,%.4f) ", communities.heap[i]->maxdq->first, communities.heap[i]->maxdq->second, *communities.heap[0]->maxdq->dq);
        }
        debug("\n");
#endif
        if (communities.heap[0] == NULL) {
            break;    /* no more communities */
        }
        if (communities.heap[0]->maxdq == NULL) {
            break;    /* there are only isolated comms */
        }
        to = communities.heap[0]->maxdq->second;
        from = communities.heap[0]->maxdq->first;

        debug("Q[%ld] = %.7f\tdQ = %.7f\t |H| = %ld\n",
              no_of_joins, q, *communities.heap[0]->maxdq->dq, no_of_nodes - no_of_joins - 1);

        /* IGRAPH_FASTCOMM_DEBUG */
        /* from=join_order[no_of_joins*2]; to=join_order[no_of_joins*2+1];
        if (to == -1) break;
        for (i=0; i<igraph_vector_ptr_size(&communities.e[to].neis); i++) {
          p1=(igraph_i_fastgreedy_commpair*)VECTOR(communities.e[to].neis)[i];
          if (p1->second == from) communities.maxdq = p1;
        } */

        n = igraph_vector_ptr_size(&communities.e[to].neis);
        m = igraph_vector_ptr_size(&communities.e[from].neis);
        /*if (n>m) {
          dummy=n; n=m; m=dummy;
          dummy=to; to=from; from=dummy;
        }*/
        debug("  joining: %ld <- %ld\n", to, from);
        q += *communities.heap[0]->maxdq->dq;

        /* Merge the second community into the first */
        i = j = 0;
        while (i < n && j < m) {
            p1 = (igraph_i_fastgreedy_commpair*)VECTOR(communities.e[to].neis)[i];
            p2 = (igraph_i_fastgreedy_commpair*)VECTOR(communities.e[from].neis)[j];
            debug("Pairs: %" IGRAPH_PRId "-%" IGRAPH_PRId " and %" IGRAPH_PRId "-%" IGRAPH_PRId "\n", p1->first, p1->second,
                  p2->first, p2->second);
            if (p1->second < p2->second) {
                /* Considering p1 from now on */
                debug("    Considering: %" IGRAPH_PRId "-%" IGRAPH_PRId "\n", p1->first, p1->second);
                if (p1->second == from) {
                    debug("    WILL REMOVE: %" IGRAPH_PRId "-%" IGRAPH_PRId "\n", to, from);
                } else {
                    /* chain, case 1 */
                    debug("    CHAIN(1): %ld-%ld %ld, now=%.7f, adding=%.7f, newdq(%ld,%ld)=%.7f\n",
                          to, p1->second, from, *p1->dq, -2 * VECTOR(a)[from]*VECTOR(a)[p1->second], p1->first, p1->second, *p1->dq - 2 * VECTOR(a)[from]*VECTOR(a)[p1->second]);
                    igraph_i_fastgreedy_community_update_dq(&communities, p1, *p1->dq - 2 * VECTOR(a)[from]*VECTOR(a)[p1->second]);
                }
                i++;
            } else if (p1->second == p2->second) {
                /* p1->first, p1->second and p2->first form a triangle */
                debug("    Considering: %" IGRAPH_PRId "-%" IGRAPH_PRId " and %" IGRAPH_PRId "-%" IGRAPH_PRId "\n", p1->first, p1->second,
                      p2->first, p2->second);
                /* Update dq value */
                debug("    TRIANGLE: %ld-%ld-%ld, now=%.7f, adding=%.7f, newdq(%ld,%ld)=%.7f\n",
                      to, p1->second, from, *p1->dq, *p2->dq, p1->first, p1->second, *p1->dq + *p2->dq);
                igraph_i_fastgreedy_community_update_dq(&communities, p1, *p1->dq + *p2->dq);
                igraph_i_fastgreedy_community_remove_nei(&communities, p1->second, from);
                i++;
                j++;
            } else {
                debug("    Considering: %" IGRAPH_PRId "-%" IGRAPH_PRId "\n", p2->first, p2->second);
                if (p2->second == to) {
                    debug("    WILL REMOVE: %" IGRAPH_PRId "-%" IGRAPH_PRId "\n", p2->second, p2->first);
                } else {
                    /* chain, case 2 */
                    debug("    CHAIN(2): %ld %ld-%ld, newdq(%ld,%ld)=%.7f\n",
                          to, p2->second, from, to, p2->second, *p2->dq - 2 * VECTOR(a)[to]*VECTOR(a)[p2->second]);
                    p2->opposite->second = to;
                    /* p2->opposite->second changed, so it means that
                     * communities.e[p2->second].neis (which contains p2->opposite) is
                     * not sorted anymore. We have to find the index of p2->opposite in
                     * this vector and move it to the correct place. Moving should be an
                     * O(n) operation; re-sorting would be O(n*logn) or even worse,
                     * depending on the pivoting strategy used by qsort() since the
                     * vector is nearly sorted */
                    igraph_i_fastgreedy_community_sort_neighbors_of(
                        &communities, p2->second, p2->opposite);
                    /* link from.neis[j] to the current place in to.neis if
                     * from.neis[j] != to */
                    p2->first = to;
                    IGRAPH_CHECK(igraph_vector_ptr_insert(&communities.e[to].neis, i, p2));
                    n++; i++;
                    if (*p2->dq > *communities.e[to].maxdq->dq) {
                        communities.e[to].maxdq = p2;
                        k = igraph_i_fastgreedy_community_list_find_in_heap(&communities, to);
                        igraph_i_fastgreedy_community_list_sift_up(&communities, k);
                    }
                    igraph_i_fastgreedy_community_update_dq(&communities, p2, *p2->dq - 2 * VECTOR(a)[to]*VECTOR(a)[p2->second]);
                }
                j++;
            }
        }

        p1 = NULL;
        while (i < n) {
            p1 = (igraph_i_fastgreedy_commpair*)VECTOR(communities.e[to].neis)[i];
            if (p1->second == from) {
                debug("    WILL REMOVE: %" IGRAPH_PRId "-%" IGRAPH_PRId "\n", p1->first, from);
            } else {
                /* chain, case 1 */
                debug("    CHAIN(1): %ld-%ld %ld, now=%.7f, adding=%.7f, newdq(%ld,%ld)=%.7f\n",
                      to, p1->second, from, *p1->dq, -2 * VECTOR(a)[from]*VECTOR(a)[p1->second], p1->first, p1->second, *p1->dq - 2 * VECTOR(a)[from]*VECTOR(a)[p1->second]);
                igraph_i_fastgreedy_community_update_dq(&communities, p1, *p1->dq - 2 * VECTOR(a)[from]*VECTOR(a)[p1->second]);
            }
            i++;
        }
        while (j < m) {
            p2 = (igraph_i_fastgreedy_commpair*)VECTOR(communities.e[from].neis)[j];
            if (to == p2->second) {
                j++;
                continue;
            }
            /* chain, case 2 */
            debug("    CHAIN(2): %ld %ld-%ld, newdq(%ld,%ld)=%.7f\n",
                  to, p2->second, from, p1 ? p1->first : -1, p2->second, *p2->dq - 2 * VECTOR(a)[to]*VECTOR(a)[p2->second]);
            p2->opposite->second = to;
            /* need to re-sort community nei list `p2->second` */
            igraph_i_fastgreedy_community_sort_neighbors_of(&communities, p2->second, p2->opposite);
            /* link from.neis[j] to the current place in to.neis if
             * from.neis[j] != to */
            p2->first = to;
            IGRAPH_CHECK(igraph_vector_ptr_push_back(&communities.e[to].neis, p2));
            if (*p2->dq > *communities.e[to].maxdq->dq) {
                communities.e[to].maxdq = p2;
                k = igraph_i_fastgreedy_community_list_find_in_heap(&communities, to);
                igraph_i_fastgreedy_community_list_sift_up(&communities, k);
            }
            igraph_i_fastgreedy_community_update_dq(&communities, p2, *p2->dq - 2 * VECTOR(a)[to]*VECTOR(a)[p2->second]);
            j++;
        }

        /* Now, remove community `from` from the neighbors of community `to` */
        if (communities.no_of_communities > 2) {
            debug("    REMOVING: %" IGRAPH_PRId "-%" IGRAPH_PRId "\n", to, from);
            igraph_i_fastgreedy_community_remove_nei(&communities, to, from);
            i = igraph_i_fastgreedy_community_list_find_in_heap(&communities, from);
            igraph_i_fastgreedy_community_list_remove(&communities, i);
        }
        communities.e[from].maxdq = NULL;

        /* Update community sizes */
        communities.e[to].size += communities.e[from].size;
        communities.e[from].size = 0;

        /* record what has been merged */
        /* igraph_vector_ptr_clear is not enough here as it won't free
         * the memory consumed by communities.e[from].neis. Thanks
         * to Tom Gregorovic for pointing that out. */
        igraph_vector_ptr_destroy(&communities.e[from].neis);
        if (merges) {
            MATRIX(*merges, no_of_joins, 0) = communities.e[to].id;
            MATRIX(*merges, no_of_joins, 1) = communities.e[from].id;
            communities.e[to].id = no_of_nodes + no_of_joins;
        }

        /* Update vector a */
        VECTOR(a)[to] += VECTOR(a)[from];
        VECTOR(a)[from] = 0.0;

        no_of_joins++;
    }
    /* TODO: continue merging when some isolated communities remained. Always
     * joining the communities with the least number of nodes results in the
     * smallest decrease in modularity every step. Now we're simply deleting
     * the excess rows from the merge matrix */
    if (merges != NULL) {
        if (no_of_joins < total_joins) {
            igraph_integer_t *ivec;
            igraph_integer_t merges_nrow = igraph_matrix_int_nrow(merges);

            ivec = IGRAPH_CALLOC(merges_nrow, igraph_integer_t);
            IGRAPH_CHECK_OOM(ivec, "Insufficient memory for fast greedy community detection.");
            IGRAPH_FINALLY(igraph_free, ivec);

            for (i = 0; i < no_of_joins; i++) {
                ivec[i] = i + 1;
            }

            igraph_matrix_int_permdelete_rows(merges, ivec, total_joins - no_of_joins);

            IGRAPH_FREE(ivec);
            IGRAPH_FINALLY_CLEAN(1);
        }
    }
    IGRAPH_PROGRESS("Fast greedy community detection", 100.0, 0);

    if (modularity) {
        VECTOR(*modularity)[no_of_joins] = q;
        IGRAPH_CHECK(igraph_vector_resize(modularity, no_of_joins + 1));
    }

    /* Internally, the algorithm does not create NaN values.
     * If the graph has no edges, the final modularity will be zero.
     * We change this to NaN for consistency. */
    if (modularity && no_of_edges == 0) {
        IGRAPH_ASSERT(no_of_joins == 0);
        VECTOR(*modularity)[0] = IGRAPH_NAN;
    }

    debug("Freeing memory\n");
    IGRAPH_FREE(pairs);
    IGRAPH_FREE(dq);
    igraph_i_fastgreedy_community_list_destroy(&communities);
    igraph_vector_destroy(&a);
    IGRAPH_FINALLY_CLEAN(4);

    if (membership) {
        IGRAPH_CHECK(igraph_community_to_membership(merges,
                     no_of_nodes,
                     /*steps=*/ best_no_of_joins,
                     membership,
                     /*csize=*/ NULL));
    }

    if (merges == &merges_local) {
        igraph_matrix_int_destroy(&merges_local);
        IGRAPH_FINALLY_CLEAN(1);
    }

    return IGRAPH_SUCCESS;
}

#ifdef IGRAPH_FASTCOMM_DEBUG
    #undef IGRAPH_FASTCOMM_DEBUG
#endif

Coverage Report

Created: 2025-07-18 07:05