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-rw-r--r--models/growth/nibilab_nonlinear.c493
1 files changed, 493 insertions, 0 deletions
diff --git a/models/growth/nibilab_nonlinear.c b/models/growth/nibilab_nonlinear.c
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+++ b/models/growth/nibilab_nonlinear.c
@@ -0,0 +1,493 @@
+/**
+ *
+ * NiBiLaB model (Nicosia, Bianconi, Latora, Barthelemy) of multiplex
+ * non-linear preferential attachment.
+ *
+ * The probability for a newly arrived node $i$ to create a link to an
+ * existing node $j$ is
+ *
+ * p_{i->j} \propto k\lay{1}^{\alpha}/k\lay{2}^{\beta}
+ *
+ * where alpha and beta are two parameters.
+ *
+ * Nodes arrive at the same time on both layers.
+ *
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <time.h>
+#include <math.h>
+
+
+typedef struct{
+ int size;
+ int N;
+ int *val;
+} int_array_t;
+
+
+typedef struct{
+ int K;
+ int N;
+ int size;
+ int *i;
+ int *j;
+ int *degrees;
+ int *arrived;
+ double *cumul;
+ int_array_t *times;
+ double *eta;
+} ij_net_t;
+
+
+
+typedef struct{
+ double a;
+ double b;
+ double c;
+ double d;
+} coupling_t;
+
+
+typedef struct{
+ int N;
+ double x_min;
+ double *distr;
+ double gamma;
+} distr_t;
+
+
+int init_network(ij_net_t *G, int m0){
+
+ int n;
+
+ for(n=0; n<m0; n++){
+ G->i[n] = n;
+ G->j[n] = n+1 % m0;
+ G->degrees[n] = 2;
+ G->arrived[n] = n;
+ }
+ G->K = m0;
+ G->N = m0;
+ return n;
+}
+
+
+
+void dump_network(ij_net_t *G){
+
+ int i;
+ for(i=0; i< G->K; i ++){
+ printf("%d %d\n",G->i[i], G->j[i]);
+ }
+}
+
+
+void dump_network_to_file(ij_net_t *G, char *fname){
+
+
+ FILE *f;
+ int i;
+
+
+ f = fopen(fname, "w+");
+
+ for(i=0; i< G->K; i ++){
+ fprintf(f, "%d %d\n",G->i[i], G->j[i]);
+ }
+ fclose(f);
+}
+
+
+
+double f1(double v1, double v2, coupling_t *matr){
+ return v1 * matr->a + v2 * matr->b;
+}
+
+double f2(double v1, double v2, coupling_t *matr){
+ return v1 * matr->c + v2 * matr->d;
+}
+
+
+void compute_cumul_nlin(ij_net_t *G1, ij_net_t *G2, double alpha){
+
+ int i;
+ double val;
+
+ /* The bias at layer 1 is k1/k2^2 */
+ if (G1->degrees[G1->arrived[0]] > 0 && G2->degrees[ G1->arrived[0] ])
+ G1->cumul[0] = (G1->degrees[G1->arrived[0]]) * 1.0 / pow(G2->degrees[ G1->arrived[0] ],alpha) ;
+ else
+ G1->cumul[0] = 0.0;
+
+ if (G2->degrees[G2->arrived[0]] > 0 && G1->degrees[ G2->arrived[0] ] > 0)
+ G2->cumul[0] = ( G2->degrees[G2->arrived[0]]) * 1.0/ pow(G1->degrees[ G2->arrived[0] ],alpha);
+ else
+ G2->cumul[0] = 0.0;
+
+ for(i=1; i<G1->N; i ++){
+ if (G1->degrees[G1->arrived[i]] > 0 && G2->degrees[ G1->arrived[i] ] > 0)
+ val = (G1->degrees[G1->arrived[i]]) * 1.0 / pow(G2->degrees[ G1->arrived[i] ],alpha) ;
+ else
+ val = 0;
+ G1->cumul[i] = G1->cumul[i-1] + val;
+ }
+ for(i=1; i<G2->N; i ++){
+ if (G2->degrees[G2->arrived[i]] > 0 && G1->degrees[ G2->arrived[i] ] )
+ val = (G2->degrees[G2->arrived[i]]) * 1.0/ pow(G1->degrees[ G2->arrived[i] ], alpha);
+ else
+ val = 0.0;
+ G2->cumul[i] = G2->cumul[i-1] + val;
+ }
+}
+
+
+void compute_cumul_nlin_2(ij_net_t *G1, ij_net_t *G2, double alpha, double beta){
+
+ int i;
+ double val;
+
+ /* The bias at layer 1 is k1/k2^2 */
+ if (G1->degrees[G1->arrived[0]] > 0 && G2->degrees[ G1->arrived[0] ])
+ G1->cumul[0] = pow(G1->degrees[G1->arrived[0]], alpha) / pow(G2->degrees[ G1->arrived[0] ],beta) ;
+ else
+ G1->cumul[0] = 0.0;
+
+ if (G2->degrees[G2->arrived[0]] > 0 && G1->degrees[ G2->arrived[0] ] > 0)
+ G2->cumul[0] = pow(G2->degrees[G2->arrived[0]], alpha)/pow(G1->degrees[ G2->arrived[0] ], beta);
+ else
+ G2->cumul[0] = 0.0;
+
+ for(i=1; i<G1->N; i ++){
+ if (G1->degrees[G1->arrived[i]] > 0 && G2->degrees[ G1->arrived[i] ] > 0)
+ val = pow(G1->degrees[G1->arrived[i]], alpha)/pow(G2->degrees[ G1->arrived[i] ],beta) ;
+ else
+ val = 0;
+ G1->cumul[i] = G1->cumul[i-1] + val;
+ }
+ for(i=1; i<G2->N; i ++){
+ if (G2->degrees[G2->arrived[i]] > 0 && G1->degrees[ G2->arrived[i] ] )
+ val = pow(G2->degrees[G2->arrived[i]],alpha)/pow(G1->degrees[ G2->arrived[i] ], beta);
+ else
+ val = 0.0;
+ G2->cumul[i] = G2->cumul[i-1] + val;
+ }
+}
+
+
+void dump_cumul(ij_net_t *G){
+
+ int i;
+
+ for (i=0; i<G->N; i ++){
+ printf("%d %2.6f\n", G->times[i], G->cumul[i]);
+ }
+
+}
+
+
+
+int select_neigh_cumul(ij_net_t *G){
+
+ double r;
+ int j;
+
+ r = (rand() * 1.0 / RAND_MAX) * G->cumul[ G->N-1 ];
+ //printf(" r: %f ", r);
+
+ j = 0;
+ /* Change with a binary search ???!?!?!?! */
+ while (r > G->cumul[j]){
+ j ++;
+ }
+ return G->arrived[j];
+}
+
+int already_neighbour(ij_net_t *G, int j, int d, int offset){
+
+ int i;
+
+ for(i=G-> K + offset; i< G->K + offset + j; i ++){
+ if (G->j[i] == d)
+ return 1;
+ }
+ return 0;
+}
+
+
+void sample_edges(ij_net_t *G, int n, int m, int offset){
+
+ int j;
+ int d;
+
+ //printf("----");
+ for(j=0; j<m; j++){
+ G->i[G->K + offset + j] = n;
+ d = select_neigh_cumul(G);
+ while(already_neighbour(G, j, d, offset)){
+ d = select_neigh_cumul(G);
+ }
+ //printf(" link %d--%d\n", n, d);
+ G->j[G->K + offset + j] = d;
+ G->degrees[d] += 1;
+ }
+ //printf("\n");
+}
+
+void create_distr(double *v, double gamma, int x_min, int x_max){
+ int n, i;
+ double sum, new_sum;
+
+ n = x_max-x_min + 1;
+
+ sum = 0;
+ for(i=0; i<n; i++){
+ v[i] = pow((x_min + i), gamma);
+ sum += v[i];
+ }
+ new_sum = 0;
+ /* Now we normalize the array*/
+ for(i=0; i<n; i++){
+ v[i]/= sum;
+ new_sum += v[i];
+ }
+ //printf("New_sum: %lf\n", new_sum);
+ /* Now we compute the cumulative distribution*/
+ for(i=1; i<n; i++){
+ v[i] += v[i-1];
+ }
+}
+
+
+inline int find_degree(double *v, int dim, double xi){
+ int i;
+
+ i=0;
+ while(xi > v[i])
+ i++;
+ return i;
+
+}
+
+
+int sample_power_law(distr_t *d){
+
+ double xi, q, val;
+ int k;
+
+ while(1){
+ xi = rand()* 1.0 / RAND_MAX;
+ k = find_degree(d->distr, d->N, xi);
+ val = rand()*1.0/RAND_MAX;
+ q = d->x_min + xi * d->N;
+ q = q / (floor(q) + 1);
+ q = pow(q, d->gamma);
+ if (val <= q){
+ return k;
+ }
+ }
+}
+
+
+
+
+int grow_multi_net_nlin_2(ij_net_t *G1, ij_net_t *G2, int N, int m,
+ int m0, double alpha, double beta){
+
+ int i, j;
+ int d;
+ int i2;
+
+
+ for(i=m0; i<N; i++){
+ compute_cumul_nlin_2(G1, G2, alpha, beta);
+ //dump_cumul(G1);
+ //dump_cumul(G2);
+ //n = m0 + i; /* This is the id of the new node */
+ G1->arrived[i] = i;
+ sample_edges(G1, G1->arrived[i], m, 0);
+ G1->degrees[G1->arrived[i]] += m;
+
+ G2->arrived[i] = i;
+ sample_edges(G2, G2->arrived[i], m, 0);
+ G2->degrees[G2->arrived[i]] += m;
+ G1->N += 1;
+ G1->K += m;
+ G2->N += 1;
+ G2->K += m ;
+ }
+ return 0;
+}
+
+void init_structure(ij_net_t *G, int N){
+
+ int i;
+
+ G->i = malloc(G->size * sizeof(int));
+ G->j = malloc(G->size * sizeof(int));
+ G->degrees = malloc(N * sizeof(int));
+ G->arrived = malloc(N * sizeof(int));
+ G->cumul = malloc(N * sizeof(double));
+ G->eta = malloc(N * sizeof(double));
+ G->times = malloc(N * sizeof(int_array_t));
+ for (i=0; i<N; i++){
+ G->times[i].size = 5;
+ G->times[i].N = 0;
+ G->times[i].val = malloc(5 * sizeof(int));
+ }
+ memset(G->degrees, 0, N*sizeof(int));
+ G->N = 0;
+
+}
+
+void add_node_to_time(ij_net_t *G, int node, int t){
+
+ if (G->times[t].size == G->times[t].N){
+ G->times[t].size += 5;
+ G->times[t].val = realloc(G->times[t].val, G->times[t].size);
+ }
+ G->times[t].val[G->times[t].N] = node;
+ G->times[t].N += 1;
+}
+
+
+void init_times_delta(ij_net_t *G, int N){
+
+ int i;
+
+ for (i=0; i<N; i ++){
+ add_node_to_time(G,i,i);
+ }
+
+}
+
+
+
+void init_times_delay(ij_net_t *G, distr_t *d, int m0, int N){
+ int i;
+ int t;
+
+ for (i=m0; i<N; i ++){
+ t = sample_power_law(d);/* So t is in the interval [1,N] */
+ printf(" %d", t);
+ if (i+t < N){
+ add_node_to_time(G, i, t+i);
+ }
+ }
+ printf("\n");
+}
+
+
+
+void dump_times(ij_net_t *G, int N){
+
+ int i, j;
+
+ for (i=0; i<N; i++){
+ printf("%d: ", i);
+ for (j=0; j< G->times[i].N; j++){
+ printf(" %d", G->times[i].val[j]);
+ }
+ printf("\n");
+ }
+
+}
+
+
+void init_eta_random(ij_net_t *G, int N){
+
+ int i;
+ double val;
+
+ for (i=0; i<N; i ++){
+ val = rand() * 1.0/RAND_MAX;
+ G->eta[i] = val;
+ }
+}
+
+void init_eta_ass(ij_net_t *G2, ij_net_t *G1, int N){
+ int i;
+
+ for (i=0; i<N; i ++){
+ G2->eta[i] = G1->eta[i];
+ }
+
+}
+
+void init_eta_dis(ij_net_t *G2, ij_net_t *G1, int N){
+ int i;
+
+ for (i=0; i<N; i ++){
+ G2->eta[i] = 1 - G1->eta[i];
+ }
+
+}
+
+
+int main(int argc, char *argv[]){
+
+ ij_net_t G1, G2;
+
+ int N, m, m0, k_max;
+ coupling_t matr;
+ double alpha, beta;
+ distr_t delay_distr;
+
+ char str[256];
+
+ if (argc < 6){
+ printf("Usage: %s <N> <m> <m0> <outfile> <alpha> <beta>\n", argv[0]);
+ exit(1);
+ }
+
+ srand(time(NULL));
+
+ /* Diagonal coupling */
+
+ N = atoi(argv[1]);
+ m = atoi(argv[2]);
+ m0 = atoi(argv[3]);
+ alpha=atof(argv[5]);
+ beta = atof(argv[6]);
+
+ G1.size = (N+m0) * m;
+ G2.size = (N+m0) * m;
+
+ init_structure(&G1, N);
+ init_structure(&G2, N);
+
+
+ G1.K = init_network(&G1, m0);
+ G2.K = init_network(&G2, m0);
+
+ //init_eta_random(&G1, N);
+ //init_eta_random(&G2, N);
+
+
+
+ //init_times_delta(&G1, N);
+ //init_times_delta(&G2, N);
+
+ //dump_times(&G2, N);
+
+ fprintf(stderr, "Init finished!\n");
+
+ grow_multi_net_nlin_2(&G1, &G2, N, m, m0, alpha, beta);
+
+ //printf("### G1\n");
+ sprintf(str, "%s_layer1.txt", argv[4]);
+ dump_network_to_file(&G1, str);
+
+ //printf("### G2\n");
+ sprintf(str, "%s_layer2.txt", argv[4]);
+ dump_network_to_file(&G2, str);
+
+ /* dump_network_to_file(S, S_num, argv[4]); */
+ /* printf("Network dumped!\n"); */
+ /* k_max = degree_distr(S, S_num, &distr); */
+ /* printf("k_max is: %d\n", k_max); */
+ /* dump_distr_to_file(distr, k_max, argv[5]); */
+
+}
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