1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
|
/**
* 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 Dorogovtsev-Samukhin-Mendes preferential
* attachment, where the attachment probability is:
*
* \Pi_{i->j} \propto k_j + a
*
* Here a > -m is a tunable parameter. The resulting network has a
* powerlaw degree distribution with exponent:
*
* \gamma = 3 + a/m
*
* References:
*
* [1] S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin. "Structure
* of Growing Networks with Preferential Linking".
* Phys. Rev. Lett. 85 (2000), 4633-4636.
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include "cum_distr.h"
void usage(char *argv[]){
printf("********************************************************************\n"
"** **\n"
"** -*- dms -*- **\n"
"** **\n"
"** Grow a scale-free network of 'N' nodes using the modified **\n"
"** linear preferential attachment model proposed by **\n"
"** Dorogovtsev-Mendes-Samukhin. **\n"
"** **\n"
"** The initial network is a clique of 'n0' nodes, and each new **\n"
"** node creates 'm' edges. The attachment probability is of **\n"
"** the form: **\n"
"** **\n"
"** P(i->j) ~ k_j + a **\n"
"** **\n"
"** where a > -m is the fourth parameter. The resulting **\n"
"** network will have a power-law degree distribution with **\n"
"** exponent **\n"
"** **\n"
"** gamma = 3 + a/m **\n"
"** **\n"
"** The program prints on STDOUT the edge-list of the final **\n"
"** graph. **\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> <a>\n", argv[0]);
}
int init_network(unsigned int *I, unsigned int *J, int n0,
double a, cum_distr_t *d){
unsigned int n, i, S_num;
S_num = 0;
for(n=0; n<n0; n++){
for(i=n+1; i<n0; i++){
I[S_num] = n;
J[S_num] = i % n0;
S_num += 1;
}
cum_distr_add(d, n, n0+a);
}
return S_num;
}
int already_neighbour(unsigned int *J, int S_num, int j, int dest){
int i;
for(i=S_num; i< S_num + j; i ++){
if (J[i] == dest)
return 1;
}
return 0;
}
int dms(unsigned int *I, unsigned int *J, unsigned int N,
unsigned int m, unsigned int n0, double a){
cum_distr_t *d = NULL;
unsigned int n, j, dest, S_num;
d = cum_distr_init(N * m);
S_num = init_network(I, J, n0, a, d);
n = n0;
while (n<N){
for(j=0; j<m; j++){
I[S_num+j] = n;
dest = cum_distr_sample(d);
while(already_neighbour(J, S_num, j, dest)){
dest = cum_distr_sample(d);
}
J[S_num + j] = dest;
}
cum_distr_add(d, n, m + a);
for (j=0; j<m; j++){
cum_distr_add(d, J[S_num + j], 1);
}
S_num += m;
n += 1;
}
cum_distr_destroy(d);
return S_num;
}
int main(int argc, char *argv[]){
int N, m, n0, K, i;
unsigned int *I, *J;
double a;
if (argc < 5){
usage(argv);
exit(1);
}
N = atoi(argv[1]);
m = atoi(argv[2]);
n0 = atoi(argv[3]);
a = atof(argv[4]);
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 (a < -m){
fprintf(stderr, "a must be larger than -m\n");
exit(1);
}
I = malloc(N * m * sizeof(unsigned int));
J = malloc(N * m * sizeof(unsigned int));
K = dms(I, J, N, m, n0, a);
for(i=0; i<K; i++){
printf("%d %d\n", J[i], I[i]);
}
free(I);
free(J);
}
|
