First commit on github -- NetBunch 1.0

1 files changed, 495 insertions, 0 deletions

diff --git a/src/gn/gn.c b/src/gn/gn.c
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+/**
+ *  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 3 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, see
+ *  <http://www.gnu.org/licenses/>.
+ *
+ *  (c) Vincenzo Nicosia 2009-2017 -- <v.nicosia@qmul.ac.uk>
+ * 
+ *  This file is part of NetBunch, a package for complex network
+ *  analysis and modelling. For more information please visit:
+ *
+ *             http://www.complex-networks.net/
+ *
+ *  If you use this software, please add a reference to 
+ *
+ *               V. Latora, V. Nicosia, G. Russo             
+ *   "Complex Networks: Principles, Methods and Applications"
+ *              Cambridge University Press (2017) 
+ *                ISBN: 9781107103184
+ *
+ ***********************************************************************
+ *
+ *  This program implements the Girvan-Newman algorithm for community
+ *  detection, based on the removal of edges with largest betweenness.
+ *
+ *
+ *  References: 
+ *
+ * [1] M. Girvan and M. E. J. Newman. "Community structure in social
+ *     and biological networks". P. Natl. Acad. Sci. USA 99 (2002),
+ *     7821--7826.  
+ *
+ */
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <time.h>
+#include <math.h>
+
+#include "utils.h"
+
+void usage(char *argv[]){
+
+  printf("********************************************************************\n"
+         "**                                                                **\n"
+         "**                         -*-   gn   -*-                         **\n"
+         "**                                                                **\n"
+         "**   Find the communities of the input graph 'graph_in' using     **\n"
+         "**   the Girvan-Newman algorithm (successive removal of edges     **\n"
+         "**   with high betweeneess).                                      **\n"
+         "**                                                                **\n"
+         "**   The input file 'graph_in' is an edge-list:                   **\n"
+         "**                                                                **\n"
+         "**                            I_1 J_1                             **\n"
+         "**                            I_2 J_2                             **\n"
+         "**                            I_3 J_3                             **\n"
+         "**                            ... ...                             **\n"
+         "**                            I_K J_K                             **\n"
+         "**                                                                **\n"
+         "**    If 'graph_in' is equal to '-' (dash), read the file from    **\n" 
+         "**    the standard input (STDIN).                                 **\n"
+         "**                                                                **\n"
+         "**    The program prints on STDOUT the partition corresponding    **\n"
+         "**    to the largest value of modularity, in the format:          **\n"
+         "**                                                                **\n"
+         "**        node_1 comm_1                                           **\n"
+         "**        node_2 comm_2                                           **\n"
+         "**        node_3 comm_3                                           **\n"
+         "**       .....                                                    **\n"
+         "**                                                                **\n"
+         "**    where 'comm_1' is the community to which 'node_1' belongs.  **\n"
+         "**                                                                **\n"
+         "**    The program prints on STDERR the number of communities and  **\n"
+         "**    the value of modularity obtained after the removal of each  **\n"
+         "**    edge, in the format:                                        **\n"
+         "**                                                                **\n"
+         "**                                                                **\n"
+         "**        ## nc: NUM_COMM Q_max: Q_MAX                            **\n"
+         "**        nc_1 Q_1                                                **\n"
+         "**        nc_2 Q_2                                                **\n"
+         "**        nc_3 Q_3                                                **\n"
+         "**        ...                                                     **\n"
+         "**                                                                **\n"
+         "**    where 'nc_1', 'nc_2', 'nc_3', etc. is the number of         **\n"
+         "**    communities (connected components) remaining after the      **\n"
+         "**    1st, 2nd, 3rd, etc. edge has been removed, and 'Q_1',       **\n"
+         "**    'Q_2', 'Q_3', etc. are the value of the modularity          **\n"
+         "**    function of the corresponding node partition. The first     **\n"
+         "**    output line reports the number of communities NUM_COMM      **\n"
+         "**    and corresponding value of modularity Q_MAX of the best     **\n"
+         "**    partition found.                                            **\n"
+         "**                                                                **\n"
+         "********************************************************************\n"
+         " This is Free Software - You can use and distribute it under \n"
+         " the terms of the GNU General Public License, version 3 or later\n\n"
+         " Please visit http://www.complex-networks.net for more information\n\n"
+         " (c) Vincenzo Nicosia 2009-2017 (v.nicosia@qmul.ac.uk)\n"
+         "********************************************************************\n\n"
+         );
+  printf("Usage: %s <graph_in>\n", argv[0]);
+  exit(1);
+}
+
+
+void add_predecessor(unsigned int **pred, unsigned int k){
+  
+  (*pred)[0] += 1;
+  *pred = realloc(*pred, ((*pred)[0] + 1)  * sizeof(unsigned int));
+  (*pred)[ (*pred)[0] ] = k;
+}
+
+
+
+/*
+ *
+ * Compute node and edge betweenness, based on shortest paths
+ * originating on the "num" nodes specified in "nlist".  "edge_bet"
+ * should be an appropriately allocated (and initialised to zero!!!!)
+ * vector of length equal to J_slap, and will contain the values of
+ * edge betweenness.
+ *
+ */
+double* compute_bet_dependency_active(unsigned int N, unsigned int *J_slap, unsigned int *r_slap, 
+                                      double *edge_bet, char *active){
+  
+  static unsigned int  *marked, **preds, *dist, *nj;
+  static double  *delta, *cB;
+  int i, j, k, w, idx, cur_node;
+  double val;
+  unsigned int d;
+  unsigned int n, nd, ndp;
+  unsigned int edge_pos;
+
+  if (!dist)
+    dist = malloc(N * sizeof(unsigned int));
+  if (!marked)
+    marked = malloc(N * sizeof(unsigned int));
+  if (!preds)
+    preds = malloc(N * sizeof(unsigned int *));
+  if (!nj)
+    nj = malloc(N * sizeof(unsigned int));
+  if (!delta)
+    delta = malloc(N * sizeof(double));
+  if (!cB)
+    cB = malloc(N * sizeof(double));
+  
+  for (i=0; i<N; i++){
+    cB[i] = 0;
+    preds[i] = NULL;
+  }
+
+  for (j=0; j<N; j++){
+    for(i=0; i<N; i++){
+      dist[i] = N;
+      if (preds[i] == NULL){
+        preds[i] = malloc(sizeof(unsigned int));
+      }
+      preds[i][0] = 0; /* The list of predecessors is now empty! */
+      
+      nj[i] = 0;
+      delta[i]= 0;
+    }
+    dist[j] = 0;
+    nj[j] = 1;
+    marked[0] = j;
+    d = 0;
+    n = 0;
+    nd = 1;
+    ndp = 0;
+    while (d<N && nd > 0){
+      for(i = n; i< n+nd; i ++){
+        cur_node = marked[i];
+        for (k=r_slap[cur_node]; k<r_slap[cur_node +1] ; k++){
+          w = J_slap[k];
+          if (!active[k])
+            /* discard inactive links */
+            continue;
+          
+          if ( dist[w] == d+1){
+            add_predecessor((unsigned int **)(preds + w), cur_node);
+            nj[w] += nj[cur_node];
+          }
+          if ( dist[w] == N){
+            dist[w] = d+1;
+            marked[n + nd + ndp] = w;
+            add_predecessor(preds + w, cur_node);
+            ndp +=1;
+            nj[w] += nj[cur_node];
+          }
+        }
+      }
+      n = n + nd;
+      nd = ndp;
+      ndp = 0;
+      d += 1; 
+    }
+    for (k= n-1; k>=1; k--){
+      w = marked[k];
+      for (idx=1; idx <= preds[w][0]; idx ++ ){
+        i = preds[w][idx];
+        val = 1.0 * nj[i] / nj[w] * (1 + delta[w]);
+        delta[i] += val;
+        /* Now we should update the betweenness of the edge (i,w) in
+           the appropriate position of the vector  edge_bet*/
+        find_neigh_in_Jslap(J_slap, r_slap, N, i, w, &edge_pos);
+        edge_bet[edge_pos] += val;
+        find_neigh_in_Jslap(J_slap, r_slap, N, w, i, &edge_pos);
+        edge_bet[edge_pos] += val;
+      }
+      cB[w] += delta[w];
+    }
+  }
+  //free(marked);
+  return cB;
+}
+
+
+
+/**
+ *
+ * Depth-First search on the node i.... 
+ *
+ */
+int dfs_active(unsigned int i, unsigned int *J_slap, unsigned int *r_slap, 
+               unsigned int N, unsigned int nc, unsigned int *ic, unsigned int *f, 
+               char reset, char *active){
+  
+  static unsigned int time;
+  unsigned int j, s;
+  
+  if(reset){
+    time = 0;
+  }
+  
+  ic[i] = nc;
+  s = 1;
+  time += 1;
+  
+  for(j=r_slap[i]; j<r_slap[i+1]; j++){
+    if (ic[J_slap[j]] == 0 && active[j]){
+      s += dfs_active(J_slap[j], J_slap, r_slap, N, nc, ic, f, 0, active);
+    }
+  }
+  time += 1;
+  f[i] = time;
+  return s;
+}
+
+/**
+ * 
+ * Find all the components of the given graph
+ *
+ */
+
+int components(unsigned int *J_slap, unsigned int *r_slap, unsigned int N, 
+               unsigned int *ic, unsigned int *f, unsigned int *sizes, 
+               char *active){
+
+  unsigned int nc, s;
+  unsigned int i;
+  
+  
+  for(i=0; i<N; i++){
+    ic[i] = 0;
+    f[i] = 0;
+  }
+  nc = 0;
+  for(i=0; i<N; i++){
+    while( i<N && ic[i] != 0)
+      i += 1;
+    if (i == N)
+      break;
+    nc += 1;
+    s = dfs_active(i, J_slap, r_slap, N, nc, ic, f, 1, active);
+    sizes[nc] = s;
+  }
+  return nc;
+}
+
+
+/**
+ * find the position of the element in v with maximal value. If there
+ * are more than one element with the same value, return the position
+ * of the last one found. In order to introduce randomness, the search
+ * starts from a position sampled uniformly at random
+ *
+ */
+unsigned int find_pos_max_rand(double *v, unsigned int K, char *active){
+  
+  unsigned int i;
+  double max;
+  unsigned int base, pos_max;
+  
+  base = rand() % K;
+  while(! active[base] )
+    base = (base + 1) % K;
+  max = v[base];
+  pos_max = base;
+  
+  for(i=base; i<base + K; i++){
+    if (v[i % K] >= max && active[i % K]){
+      max = v[i % K];
+      pos_max = i % K;
+    }
+  }
+  return pos_max;
+}
+
+
+unsigned int find_pos_max(double *v, unsigned int K, char *active){
+  
+  unsigned int i;
+  double max;
+  unsigned int base, pos_max;
+  
+  base = 0;
+  while(! active[base] )
+    base = (base + 1) % K;
+  max = v[base];
+  pos_max = base;
+  
+  for(i=base; i<base + K; i++){
+    if (v[i % K] >= max && active[i % K]){
+      max = v[i % K];
+      pos_max = i % K;
+    }
+  }
+  return pos_max;
+}
+
+
+/* This function compute the modularity function of the partition
+   'part'...*/
+double compute_modularity(unsigned int *J_slap, unsigned int *r_slap, unsigned int N, 
+                          unsigned int *part, unsigned int nc){
+  static double *e, *a;
+  
+  unsigned int i, j, n, K;
+  unsigned int ci, cj;
+  double Q;
+
+  if(!e)
+    e = malloc((N+1) * sizeof(double));
+  if(!a)
+    a = malloc((N+1) * sizeof(double));
+
+  memset(e, 0, (N+1) * sizeof(double));
+  memset(a, 0, (N+1) * sizeof(double));
+
+  K = r_slap[N];
+  
+  for (i=0; i<N; i++){
+    ci = part[i];
+    a[ci] += (r_slap[i+1] - r_slap[i]); 
+    for(j=r_slap[i]; j< r_slap[i+1]; j++){
+      cj = part[J_slap[j]];
+      if (ci == cj){
+        e[ci] += 1;
+      }
+    }
+  }
+  
+  Q = 0.0;
+  for (n=1; n<=nc; n++){
+    Q += 1.0 * e[n]/(1.0 * K ) - pow(1.0 * a[n]/K, 2);
+  }
+  return Q;
+}
+
+
+unsigned int* girvan_newman(unsigned int *J_slap, unsigned int *r_slap, unsigned int N){
+  
+  unsigned int K, nc, pos;
+  double *edge_bet = NULL;
+  char *active = NULL;
+  double Q, Q_max;
+
+  unsigned int *ic, *f, *sizes;
+  unsigned int *best_part;
+  
+  int i, j, nc_max;
+  
+  K = r_slap[N];
+
+  ic = malloc((N) * sizeof(unsigned int));
+  f = malloc(N * sizeof(unsigned int));
+  sizes = malloc((N+1) * sizeof(unsigned int));
+  best_part = malloc(N * sizeof(unsigned int));
+  
+
+  /* We initialise the vector "active" which idicates active edges */
+  
+  active = malloc(K * sizeof(char));
+  for (i=0; i<K; i++){
+    active[i] = 1;
+  }
+
+  edge_bet = malloc(K * sizeof(double));
+  nc_max = 0;
+  Q_max = -1000;
+  
+  for(j=0; j<K; j++){
+    memset(edge_bet, 0, K * sizeof(double));
+    /* compute edge betweenness */
+    compute_bet_dependency_active(N, J_slap, r_slap, edge_bet, active);
+    /* find edge with maximal betweenness... */
+    pos = find_pos_max_rand(edge_bet, K, active);
+    /* and knock it down */
+    active[pos] = 0;
+    /* compute connected components */
+    nc = components(J_slap, r_slap, N, ic, f, sizes, active);
+    /* compute the modularity of the partition induced by components */
+    Q = compute_modularity(J_slap, r_slap, N, ic, nc);
+    fprintf(stderr, "%d %g\n", nc, Q);
+    /* if Q is maximal, save the current partition */
+    if (j > 0){
+      if (Q > Q_max){
+        Q_max = Q;
+        nc_max = nc;
+        memcpy (best_part, ic, N * sizeof(unsigned int));
+      }
+    }
+    else{
+      Q_max = Q;
+      memcpy(best_part, ic, N*sizeof(unsigned int));
+    }
+  }
+  /* Return the best partition */
+  fprintf(stdout, "### nc: %d Q_max: %g\n", nc_max, Q_max);
+  free(f);
+  free(ic);
+  free(sizes);
+  free(edge_bet);
+  free(active);
+  return best_part;
+}
+
+
+
+void dump_partition(unsigned int *p, unsigned int N){
+  
+  unsigned int i;
+  for(i=0; i<N; i++){
+    fprintf(stdout, "%d %d\n", i, p[i]);
+  }
+}
+
+
+int main(int argc, char *argv[]){
+  
+
+  unsigned int *J_slap=NULL, *r_slap=NULL;
+  unsigned int K, N;
+  FILE *filein;
+  unsigned int *part;
+  
+  
+  if(argc < 2){
+    usage(argv);
+    exit(1);
+  }
+  
+  
+  srand(time(NULL));
+  
+  if (!strcmp(argv[1], "-")){
+    /* take the input from STDIN */
+    filein = stdin;
+  }
+  else {
+    filein = openfile_or_exit(argv[1], "r", 2);
+  }
+  
+  read_slap(filein, &K, &N, &J_slap, &r_slap);
+  sort_neighbours(J_slap, r_slap, N);
+  fclose(filein);
+  
+  part = girvan_newman(J_slap, r_slap, N);
+  dump_partition(part, N);
+  free(J_slap);
+  free(r_slap);
+  free(part);
+
+}