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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
*
***********************************************************************
*
* Take a graph and a partition, and compute the modularity function
* associated to that partition.
*
* References:
*
* [1] M. E. J. Newman and M. Girvan. "Finding and evaluating
* community structure in networks". Phys. Rev. E 69, (2004),
* 026113.
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "utils.h"
void usage(char *argv[]){
printf("********************************************************************\n"
"** **\n"
"** -*- modularity -*- **\n"
"** **\n"
"** Compute the modularity function associated to a partition **\n"
"** of the nodes of the graph provided as input. **\n"
"** **\n"
"** If 'graph_in' is equal to '-' (dash), read the edge list **\n"
"** from standard input (STDIN). The parameter 'partition' MUST **\n"
"** be a file in the format: **\n"
"** **\n"
"** node_0 community_0 **\n"
"** node_1 community_1 **\n"
"** node_2 community_2 **\n"
"** ..... **\n"
"** **\n"
"** where 'node_0', 'node_1', etc. are node labels, and **\n"
"** 'community_0', 'community_1', etc. is the label of the **\n"
"** community to which a node belongs. Notice that a node can **\n"
"** belong to exactly one community. This format is compatible **\n"
"** with the output of the programs which compute community **\n"
"** partitions, such as `gn`, `cnm`, `label_prop`, etc. **\n"
"** **\n"
"** The program prints on STDOUT the modularity of the partition, **\n"
"** and prints on STDERR a single line in the format: **\n"
"** **\n"
"** ## nc: NUM_COMMUNITIES **\n"
"** **\n"
"** where 'NUM_COMMUNITIES' is the number of communities in the **\n"
"** partition given as input. **\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> <partition>\n", argv[0]);
}
/* This is the function that computes the value of the modularity function */
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, deg_i;
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];
deg_i = (r_slap[i+1] - r_slap[i]);
if (deg_i == 0)
continue;
a[ci] += deg_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;
fprintf(stderr, "### nc: %d\n", nc);
for (n=0; n<=nc; n++){
Q += 1.0 * e[n]/(1.0 * K ) - pow(1.0 * a[n]/K, 2);
}
free(a);
free(e);
return Q;
}
/*
* This function remaps the original partition labels into a
* consecutive set of integers, starting at 0 (zero)
*/
int normalise_labels(unsigned int *labels, unsigned int N,
unsigned int *label_count){
unsigned int *label_map;
int i, j, num = 0;
label_map = malloc(N * sizeof(unsigned int));
label_map[0] = labels[0];
labels[0] = 0;
label_count[0] = 1;
num = 1;
for(i=1; i<N; i ++){
for(j=0; j<num; j++){
if (labels[i] == label_map[j])
break;
}
if (j == num){
label_map[j] = labels[i];
label_count[j] = 0;
num +=1;
}
labels[i] = j;
label_count[j] += 1;
}
free(label_map);
return num;
}
int main(int argc, char *argv[]){
unsigned int N, K, nc;
unsigned int *J_slap=NULL, *r_slap=NULL, *part = NULL;
unsigned int *label_count;
FILE *f_net, *f_part;
double Q;
if (argc < 3){
usage(argv);
exit(1);
}
if(!strcmp(argv[1], "-")){
f_net = stdin;
}
else{
f_net = openfile_or_exit(argv[1], "r", 2);
}
f_part = openfile_or_exit(argv[2], "r", 3);
read_slap(f_net, &K, &N, &J_slap, &r_slap);
part = malloc(N * sizeof(unsigned int));
memset(part, 0, N * sizeof(unsigned int));
label_count = malloc(N * sizeof(unsigned int));
nc = read_partition(f_part, N, part);
fclose(f_net);
fclose(f_part);
nc = normalise_labels(part, N, label_count);
Q = compute_modularity(J_slap, r_slap, N, part, nc);
printf("%g\n", Q);
free(J_slap);
free(r_slap);
free(part);
free(label_count);
}
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