diff options
Diffstat (limited to 'src/hidden')
| -rw-r--r-- | src/hidden/Makefile.am | 7 | ||||
| -rw-r--r-- | src/hidden/Makefile.in | 585 | ||||
| -rw-r--r-- | src/hidden/hv_net.c | 337 |
3 files changed, 929 insertions, 0 deletions
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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 in an implementation of the hidden-variable model by Bogunya' + * and Pastor-Satorras. The program creates a random graph whose + * joint degree distribution is identical to that of a network given + * as input. + * + * References: + * + * [1] M. Boguna and R. Pastor-Satorras. "Class of correlated random + * networks with hidden variables". Phys. Rev. E 68 (2003), 036112. + * + */ + +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include <time.h> +#include <math.h> + +#include "utils.h" +#include "cum_distr.h" + + +void usage(char *argv[]){ + printf("********************************************************************\n" + "** **\n" + "** -*- hv_net -*- **\n" + "** **\n" + "** Create a random graph whose joint degree distribution is **\n" + "** identical to that of a network provided as input. **\n" + "** **\n" + "** If 'graph_in' is equal to '-' (dash), read the edge list **\n" + "** from STDIN. **\n" + "** **\n" + "** The program prints on STDOUT the edge-list of the sampled **\n" + "** graph. **\n" + "** **\n" + "** If 'SHOW' is specified as second parameter, the program **\n" + "** prints on STDERR the values of the hidden variable **\n" + "** associated to each node and of the actual degree they have **\n" + "** in the newly-created random graph, in the format: **\n" + "** **\n" + "** h_1 k_1 **\n" + "** h_2 k_2 **\n" + "** ... **\n" + "** h_N k_N **\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" + " (c) Vincenzo Nicosia 2009-2017 (v.nicosia@qmul.ac.uk)\n\n" + "********************************************************************\n\n" + ); + printf("Usage: %s <graph_in> [SHOW]\n", argv[0]); +} + + + +typedef struct{ + unsigned int N; + unsigned int K; + unsigned int *J_slap; + unsigned int *r_slap; + unsigned int k_min; + unsigned int k_max; + double *pk; /* degree distribution -- this is equal to rho!!!! */ + double **pkk; /* joint degree distribution */ + double **f; /* the linking function */ + unsigned int *h; /* The array containing hidden variables for the N nodes */ + unsigned int *new_degs; /* the new degrees of the sampled graph */ +} params_t; + + +/** + * + * sample the hidden degrees of the nodes using the cumulative + * distribution P(k) + * + */ +void sample_node_variables(params_t *p, cum_distr_t *P){ + + unsigned int i; + unsigned int k; + + + for(i=0; i<p->N; i++){ + k = cum_distr_sample(P); + p->h[i] = k; + } +} + +/** + * + * Compute the function f(h,h') for each pair of degrees + * + */ +void compute_fhh(params_t *p){ + + unsigned int k1, k2; + double avg_k; + + avg_k = 1.0 * p->K / p->N; + + for(k1 = p->k_min; k1 <= p->k_max; k1++){ + for(k2 = k1; k2 <= p->k_max; k2++){ + p->f[k1][k2] = p->f[k2][k1] = avg_k * p->pkk[k1][k2] / (p->N * p->pk[k1] * p->pk[k2]); + } + } +} + + + +/** + * + * Sample the edges of the graph + * + */ +void sample_edges(params_t *p){ + + unsigned int i, j, ki, kj; + double val; + + for(i=0; i<p->N; i++){ + ki = p->h[i]; + for (j=i+1; j<p->N; j++){ + kj = p->h[j]; + val = 1.0 * rand() / RAND_MAX; + /* we create the edge (i,j) with proability f[ki][kj]*/ + if (val < p->f[ki][kj]){ + printf("%d %d\n", i, j); + p->new_degs[i] += 1; + p->new_degs[j] += 1; + } + } + } +} + + +void init_hv_params(params_t *p){ + + unsigned int i; + + p->h = malloc(p->N * sizeof(unsigned int)); + p->f = malloc((p->k_max + 1) * sizeof(double*)); + p->new_degs = malloc(p->N * sizeof(unsigned int)); + + for(i=0; i<=p->k_max; i++){ + p->f[i] = malloc((p->k_max + 1) * sizeof(double)); + } + for (i=0; i<p->N; i++){ + p->new_degs[i] = 0; + } +} + + + +void compute_distributions(params_t *g){ + + unsigned int i,j, neigh, k1, k2; + double sumk, sumkk; + + g->k_min = g->N; + g->k_max = 0; + + g->pk = NULL; + + /* Compute (and allocate on the fly) the degree distribution */ + + for(i=0; i< g->N; i ++){ + k1 = g->r_slap [i+1] - g->r_slap[i]; + if (k1 > g->k_max){ + g->pk = realloc(g->pk, (k1 + 1) * sizeof(double)); + for(j=g->k_max+1; j<=k1; j++){ + g->pk[j] = 0; + } + g->k_max = k1; + } + else if(k1 < g->k_min){ + g->k_min = k1; + } + g->pk[k1] += 1; + } + + /* Allocate and initialise the joint degree distribution */ + g->pkk = malloc((g->k_max + 1 ) * sizeof(double*)); + for(i=0; i<=g->k_max ; i++){ + g->pkk[i] = malloc((g->k_max + 1) * sizeof(double)); + memset(g->pkk[i], 0, (g->k_max + 1) * sizeof(double)); + } + + for(i=0; i<g->N; i++){ + k1 = g->r_slap[i+1] - g->r_slap[i]; + for(j=g->r_slap[i]; j< g->r_slap[i+1]; j++){ + neigh = g->J_slap[j]; + k2 = g->r_slap[neigh+1] - g->r_slap[neigh]; + g->pkk[k1][k2] += 1; + } + } + + /* Now we normalise both pk and pkk...*/ + + sumk = sumkk = 0.0; + + for(i=0; i<=g->k_max; i++){ + g->pk[i] /= g->N; + sumk += g->pk[i]; + g->pkk[i][i] /= (g->K); + sumkk += g->pkk[i][i]; + for(j=i+1; j<=g->k_max; j++){ + g->pkk[i][j] /= (g->K); + g->pkk[j][i] = g->pkk[i][j]; + sumkk += 2* g->pkk[i][j]; + } + } + +} + + +void compute_rho(params_t *g, cum_distr_t *P){ + + unsigned int k; + + for(k=g->k_min; k<= g->k_max; k++){ + + if(g->pk[k] > 0){ + if (cum_distr_add(P, k, g->pk[k]) != 0){ + fprintf(stderr, "Error in the computation of the cumulative degree distribution!!!!" + " Exiting!!!\n"); + exit(3); + } + } + } +} + +void dump_deg_h(params_t *p){ + + unsigned int i; + + for(i=0; i<p->N; i++){ + fprintf(stderr, "%d %d\n", p->h[i], p->new_degs[i]); + } +} + + +int main(int argc, char *argv[]){ + + params_t p; + cum_distr_t *P; + int i; + + FILE *filein; + + + 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); + } + + p.J_slap = p.r_slap = NULL; + + read_slap(filein, &(p.K), &(p.N), &(p.J_slap), &(p.r_slap)); + + fclose(filein); + + compute_distributions(&p); + + init_hv_params(&p); + + P = cum_distr_init(p.k_max + 1); + compute_rho(&p, P); + compute_fhh(&p); + + sample_node_variables(&p, P); + sample_edges(&p); + + /* + * If 'SHOW' is provided, print on STDERR the value of the hidden + * variable of each node + */ + if (argc > 2 && !my_strcasecmp(argv[2], "SHOW")){ + dump_deg_h(&p); + } + + cum_distr_destroy(P); + free(p.J_slap); + free(p.r_slap); + free(p.pk); + free(p.h); + free(p.new_degs); + for(i=0; i<=p.k_max ; i++){ + free(p.pkk[i]); + free(p.f[i]); + } + free(p.pkk); + free(p.f); +} + |