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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 grows a weighted network using the model proposed by
+ * Barrat, Barthelemy, and Vespignani.
+ *
+ * References:
+ *
+ * [1] A. Barrat, M. Barthelemy, and A. Vespignani. "Weighted
+ * Evolving Networks: Coupling Topology and Weight
+ * Dynamics". Phys. Rev. Lett. 92 (2004), 228701.
+ *
+ * [2] A. Barrat, M. Barthelemy, and A. Vespignani. "Modeling the
+ * evolution of weighted networks". Phys. Rev. E 70 (2004),
+ * 066149.
+ *
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+#include <math.h>
+
+#include "cum_distr.h"
+
+void usage(char *argv[]){
+ printf("********************************************************************\n"
+ "** **\n"
+ "** -*- bbv -*- **\n"
+ "** **\n"
+ "** Grow a weighted network of 'N' nodes using the model **\n"
+ "** proposed by Barrat-Barthelemy-Vespignani. **\n"
+ "** **\n"
+ "** The initial network is a clique of 'n0' nodes, and each new **\n"
+ "** node creates 'm' edges. All edges have an initial weight **\n"
+ "** equal to 'w0', and the attachment probability in of the **\n"
+ "** form: **\n"
+ "** **\n"
+ "** P(i->j) ~ s_j **\n"
+ "** **\n"
+ "** where s_j is the strength of node j. The parameter 'delta' **\n"
+ "** tunes the rearrangement of edge weights due to the **\n"
+ "** addition of a new edge. The degree, strength, and weight **\n"
+ "** distributions of the created graphs are power-laws, **\n"
+ "** whose esponents depend on the values of 'w0' and 'delta'. **\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 <N> <m> <n0> <w0> <delta>\n", argv[0]);
+}
+
+
+typedef struct{
+ int id;
+ double w;
+ double delta_w;
+} link_t;
+
+
+typedef struct {
+ int id;
+ int size;
+ int deg;
+ double s;
+ link_t *neighs;
+} node_t;
+
+
+/* create the initial graph as a clique of n0 nodes */
+void init_seed(node_t *G, int n0, double w0, cum_distr_t *d){
+
+ int i, j, n;
+
+ for(i=0; i< n0; i++){
+ G[i].neighs = malloc((n0-1) * sizeof(link_t));
+ G[i].size = n0-1;
+ G[i].deg = n0-1;
+ n= 0;
+ for (j=0; j<n0; j++){
+ if (i != j){
+ G[i].neighs[n].id = j;
+ G[i].neighs[n].w = w0;
+ n += 1;
+ }
+ }
+ G[i].s = (n0-1) * w0;
+ cum_distr_add(d, i, G[i].s);
+ }
+}
+
+/* add j to the neighbourhood of i with a weight w0, and update the
+ strength of i */
+void add_neigh(node_t *G, unsigned int i, unsigned int j, double w0){
+
+ if (G[i].deg == G[i].size){
+ G[i].size += 5;
+ G[i].neighs= realloc(G[i].neighs, G[i].size * sizeof(link_t));
+ }
+ G[i].neighs[G[i].deg].id = j;
+ G[i].neighs[G[i].deg].w = w0;
+ G[i].deg += 1;
+ G[i].s += w0;
+}
+
+/* Add w to the weight of the edge (i,j) */
+void add_weight(node_t *G, int i, int j, double w){
+
+ int k;
+ for(k=0; k<G[i].deg; k++){
+ if(G[i].neighs[k].id == j){
+ G[i].neighs[k].w += w;
+ }
+ }
+}
+
+/* Compute the weight increase for each edge connected to node i */
+void compute_delta_weights(node_t *G, int i, double delta){
+ int j;
+ double s;
+
+ s = G[i].s;
+
+ for(j=0; j< G[i].deg; j++){ /* for each neighbour of i */
+ /* compute the delta_weight */
+ G[i].neighs[j].delta_w = delta * G[i].neighs[j].w / s;
+ }
+}
+
+/* set the new weights on the edges connected to node i */
+void set_delta_weights(node_t *G, int i, cum_distr_t *distr){
+
+ int j, neigh;
+
+ double delta_w;
+
+ for(j=0; j<G[i].deg; j++){
+ neigh = G[i].neighs[j].id;
+ delta_w = G[i].neighs[j].delta_w;
+ /* add delta_w to the weight of (i, neigh) and of (neigh, i) */
+ add_weight(G, i, neigh, delta_w);
+ add_weight(G, neigh, i, delta_w);
+
+ /* update the strength of neigh */
+ G[neigh].s += delta_w;
+ /* add delta_w to the fraction of cum_distr associated to neigh */
+ cum_distr_add(distr, neigh, delta_w);
+ }
+}
+
+/* return 1 if i is in the array v */
+
+int is_neigh(int *v, int N, int i){
+
+ int j;
+
+ for(j=0; j<N; j++){
+ if (v[j] == i)
+ return 1;
+ }
+ return 0;
+}
+
+/*
+ * print the edges of the undirected graph G, with the corresponding
+ * weight. Each edge is printed only once
+ *
+ */
+void dump_net(node_t *G, int N){
+
+ int i, j;
+
+ double tot_w = 0.0;
+
+ for(i=0; i<N; i++){
+ for(j=0; j<G[i].deg; j++){
+ if(G[i].neighs[j].id > i){
+ tot_w += G[i].neighs[j].w;
+ printf("%d %d %g\n", i, G[i].neighs[j].id, G[i].neighs[j].w);
+ }
+ }
+ }
+}
+
+
+/* grow a weighted graph using the BBV model */
+node_t* bbv(unsigned int N, unsigned int n0, unsigned int m, double w0, double delta){
+
+ node_t *G;
+ int t, i, j;
+ cum_distr_t *distr = NULL;
+ int *tmp_neighs;
+
+ distr = cum_distr_init(N * m);
+
+
+ G = malloc(N * sizeof(node_t));
+ tmp_neighs = malloc(m * sizeof(int));
+
+ init_seed(G, n0, w0, distr);
+
+
+ for(t=n0; t<N; t++){
+ /* Initialize the new node */
+ G[t].neighs = malloc(m * sizeof(link_t));
+ G[t].size = m;
+ G[t].deg = 0;
+ /* Sample the m neighbours */
+ for(i=0; i<m; i++){
+ j = cum_distr_sample(distr);
+ while(is_neigh(tmp_neighs, i, j)){
+ j = cum_distr_sample(distr);
+ }
+ tmp_neighs[i] = j;
+ }
+ /* compute the weight increase for the neighbours of the
+ new node t */
+ for(i=0; i<m; i++){/* for each neighbour 'l' of the new node t */
+ /* compute the weight increase for the edges around 'l' */
+ compute_delta_weights(G, tmp_neighs[i], delta);
+ }
+ /* Now we update the weights */
+ for(i=0; i<m; i++){/* for each neighbour 'l' of the new node t */
+ set_delta_weights(G, tmp_neighs[i], distr);
+ add_neigh(G, t, tmp_neighs[i], w0);
+ add_neigh(G, tmp_neighs[i], t, w0);
+ /* We need to add delta to the strength of tmp_neighs[i] {notice
+ that w0 has been already added by the previous call to
+ add_neigh()}*/
+ G[tmp_neighs[i]].s += delta;
+ cum_distr_add(distr, tmp_neighs[i], delta + w0);
+ }
+
+ /* Finally, we update the strength of node t */
+ G[t].s = w0 * m;
+ cum_distr_add(distr, t, G[t].s);
+ }
+ free(tmp_neighs);
+ cum_distr_destroy(distr);
+ return G;
+}
+
+
+
+int main(int argc, char *argv[]){
+
+ int N, n0, m, i;
+ double w0, delta;
+
+ node_t *net;
+
+ if (argc < 6){
+ usage(argv);
+ exit(1);
+ }
+
+ N = atoi(argv[1]);
+ m = atoi(argv[2]);
+ n0 = atoi(argv[3]);
+ w0 = atof(argv[4]);
+ delta = atof(argv[5]);
+
+ srand(time(NULL));
+
+ if (N < 1){
+ fprintf(stderr, "N must be positive\n");
+ exit(1);
+ }
+ if(m > n0){
+ fprintf(stderr, "n0 cannot be smaller than m\n");
+ exit(1);
+
+ }
+ if (n0<1){
+ fprintf(stderr, "n0 must be positive\n");
+ exit(1);
+ }
+
+ if (m < 1){
+ fprintf(stderr, "m must be positive\n");
+ exit(1);
+ }
+
+ if (w0 <= 0.0){
+ fprintf(stderr, "w0 must be positive\n");
+ exit(1);
+ }
+
+ if (delta < 0.0){
+ fprintf(stderr, "delta must be positive\n");
+ exit(1);
+ }
+
+
+ net = bbv(N, n0, m, w0, delta);
+ dump_net(net, N);
+
+ for(i=0; i<N; i++){
+ free(net[i].neighs);
+ }
+
+ free(net);
+}
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