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
|
/**
* 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 samples a multigraph (i.e., a graph that might
* contain self-loops and/or multiple edges) from the configuration
* model, using the degree sequence provided as input.
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include "utils.h"
#include "iltree.h"
/* Usage*/
void usage(char *argv[]){
printf("********************************************************************\n"
"** **\n"
"** -*- conf_model_deg_nocheck -*- **\n"
"** **\n"
"** Sample a multigraph from the configuration model associated **\n"
"** to the degree sequence provided as input. **\n"
"** **\n"
"** The degree sequence is a file with format: **\n"
"** **\n"
"** k_1 **\n"
"** k_2 **\n"
"** k_3 **\n"
"** .... **\n"
"** k_N **\n"
"** **\n"
"** where 'k_i' is the degree of the i-th node. The program **\n"
"** prints on output the edge-list of the resulting graph. The **\n"
"** final graph might contain self-loops and multiple edges. **\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 2010-2017 (v.nicosia@qmul.ac.uk)\n"
"********************************************************************\n\n"
);
printf("Usage: %s <degs>\n\n" , argv[0]);
}
unsigned int count_stubs(unsigned int *nodes, int N){
int i;
unsigned int cnt;
cnt = 0;
for (i=0; i<N; i ++){
cnt += nodes[i];
}
return cnt;
}
/* sample a multigraph from the configuration model */
void sample_graph_conf_nocheck(unsigned int *nodes, int N){
unsigned int S;
unsigned int i, j;
unsigned int n_stubs;
unsigned int *stubs;
unsigned int L1, L2, I1, I2, tmp;
n_stubs = count_stubs(nodes, N);
if (n_stubs %2){
fprintf(stderr, "The sequence is not even!\n");
exit(3);
}
stubs = malloc(n_stubs * sizeof(unsigned int));
/*
* We first initialize the stubs
*/
S = 0;
for(i=0; i<N; i ++){
for(j=0; j<nodes[i]; j ++){
stubs[S] = i;
S += 1;
}
}
while (S > 0){
/* sample the first stub */
L1 = rand() % S;
I1 = stubs[L1];
S -= 1;
/* sample the second stub */
L2 = rand() % S;
I2 = stubs[L2];
S -= 1;
if (L1 == L2){/* If L1 and L2 are the same element, discard the
sample */
/* reset S to the value it had before */
S += 2;
continue;
}
if (I1 > I2){
tmp = I2;
I2 = I1;
I1 = tmp;
}
printf("%d %d\n", I1, I2);
/* And then we remove the two stubs */
stubs[L1] = stubs[S+1];
stubs[L2] = stubs[S];
}
free(stubs);
}
int main(int argc, char *argv[]){
unsigned int *nodes= NULL;
int N;
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);
}
N = read_deg_seq(filein, &nodes);
fclose(filein);
sample_graph_conf_nocheck(nodes, N);
free(nodes);
}
|
