Датотека:Centrality.svg
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Opis izmene
| Opis |
English: Examples of A) Degree centrality, B) Closeness centrality, C) Betweenness centrality, D) Eigenvector centrality, E) Katz centrality and F) Alpha centrality. |
| Datum | |
| Izvor | Sopstveno delo |
| Autor | Claudio Rocchini |
Licenciranje
Ja, nosilac autorskog prava nad ovim delom, objavljujem isto pod sledećom licencom:
Ova datoteka je dostupna pod licencom Creative Commons Autorstvo-Deliti pod istim uslovima 3.0 Unported.
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- da delite – da umnožavate, raspodeljujete i prenosite delo
- da prerađujete – da preradite delo
- Pod sledećim uslovima:
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Source Code
The source code needs http://www.gnu.org/s/gsl/ .
/**********************************
* (C)2012 Claudio Rocchini *
* www.rockini.name *
* CC-BY 3.0 *
**********************************/
#include <stdio.h>
#include <stdlib.h>
#include <vector>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_eigen.h>
#include "rand.h"
static inline unsigned char f2b( double f ) {
if(f<0) f = 0; if(f>1) f = 1;
int i = int(f*256);
return i<0 ? 0 : i>255 ? 255 : i;
}
void HSV2RGB(double h, double s, double v, unsigned char rgb[3] ) {
if (s == 0) {
rgb[0] = rgb[1] = rgb[2] = f2b(v);
} else {
double v_h = h * 6;
double v_i = floor(v_h);
double v_1 = v * (1 - s);
double v_2 = v * (1 - s * (v_h - v_i));
double v_3 = v * (1 - s * (1 - (v_h - v_i)));
double v_r,v_g,v_b;
if (v_i == 0) {v_r = v; v_g = v_3; v_b = v_1;}
else if (v_i == 1) {v_r = v_2; v_g = v; v_b = v_1;}
else if (v_i == 2) {v_r = v_1; v_g = v; v_b = v_3;}
else if (v_i == 3) {v_r = v_1; v_g = v_2; v_b = v ;}
else if (v_i == 4) {v_r = v_3; v_g = v_1; v_b = v ;}
else {v_r = v; v_g = v_1; v_b = v_2;};
rgb[0] = f2b(v_r);
rgb[1] = f2b(v_g);
rgb[2] = f2b(v_b);
}
}
class point2 {
public:
double x,y;
};
double squared_dist( const point2 & p, const point2 & q ) {
const double dx = p.x - q.x;
const double dy = p.y - q.y;
return dx*dx+dy*dy;
}
class edge {
public:
int a,b;
edge() {}
edge( int na, int nb ): a(na),b(nb) {}
};
void floyd_warshall( int NV, const std::vector<edge> & e,
std::vector<double> & dist, std::vector<int> & conn ) {
dist.resize(NV*NV); conn.resize(NV*NV);
std::fill(dist.begin(),dist.end(),0.0);
std::fill(conn.begin(),conn.end(),-1);
std::vector<edge>::const_iterator ie;
for(ie=e.begin();ie!=e.end();++ie) {
dist[(*ie).a+NV*(*ie).b] = 1;
dist[(*ie).b+NV*(*ie).a] = 1;
}
for(int k=0;k<NV;++k) for(int i=0;i<NV;++i) for(int j=0;j<NV;++j)
if((dist[i+NV*k] * dist[k+NV*j] != 0) && (i != j))
if((dist[i+NV*k] + dist[k+NV*j] < dist[i+NV*j]) || (dist[i+NV*j] == 0)) {
conn[i+NV*j] = k;
dist[i+NV*j] = dist[i+NV*k] + dist[k+NV*j];
}
}
void central_degree( int NV, const std::vector<edge> & e, std::vector<double> & C ) {
std::fill(C.begin(),C.end(),0.0);
std::vector<edge>::const_iterator i;
for(i=e.begin();i!=e.end();++i) {
C[(*i).a] += 1;
C[(*i).b] += 1;
}
}
void central_closeness( int NV, const std::vector<edge> & e, std::vector<double> & C ) {
std::vector<double> dist;
std::vector<int> conn;
floyd_warshall(NV,e,dist,conn);
for(int i=0;i<NV;++i) {
C[i] = 0;
for(int j=0;j<NV;++j) C[i] += dist[i+NV*j];
if(C[i]!=0.0) C[i] = 1.0/C[i];
}
}
void central_betweenness( int NV, const std::vector<edge> & e, std::vector<double> & C ) {
std::vector<double> dist; std::vector<int> conn;
floyd_warshall(NV,e,dist,conn);
std::fill(C.begin(),C.end(),0.0);
for(size_t i=0;i<conn.size();++i)
if(conn[i]>=0 && conn[i]<NV) C[conn[i]] += 1.0;
for(size_t j=0;j<C.size();++j) C[j] = log(1+C[j]); // NOTE: the log!
}
void central_eigenvector( int NV, const std::vector<edge> & e, std::vector<double> & C ) {
int i,j;
gsl_eigen_symmv_workspace * w = gsl_eigen_symmv_alloc(NV);
gsl_matrix * A = gsl_matrix_alloc(NV,NV);
gsl_vector * eval = gsl_vector_alloc(NV);
gsl_matrix * evec = gsl_matrix_alloc(NV,NV);
for(i=0;i<NV;++i) for(j=0;j<NV;++j)
gsl_matrix_set(A,i,j,0.0);
for(std::vector<edge>::const_iterator ei=e.begin();ei!=e.end();++ei) {
gsl_matrix_set(A,(*ei).a,(*ei).b,1.0);
gsl_matrix_set(A,(*ei).b,(*ei).a,1.0);
}
gsl_eigen_symmv(A,eval,evec,w);
int maxj = 0; double maxv = gsl_vector_get(eval,0);
for(j=1;j<NV;++j)
if(maxv<gsl_vector_get(eval,j)) {
maxv = gsl_vector_get(eval,j);
maxj = j;
}
for(i=0;i<NV;++i)
C[i] = log(gsl_matrix_get(evec,i,maxj)); // NOTE: the log!
gsl_matrix_free(evec);
gsl_vector_free(eval);
gsl_matrix_free(A);
gsl_eigen_symmv_free(w);
}
void central_katz( int NV, const std::vector<edge> & e, std::vector<double> & C ) {
const double alpha = 0.5;
std::vector<double> dist; std::vector<int> conn;
floyd_warshall(NV,e,dist,conn);
for(int i=0;i<NV;++i) {
C[i] = 0.0;
for(int j=0;j<NV;++j) if(i!=j)
C[i] += pow(alpha,dist[i+NV*j]);
}
}
void central_alpha( int NV, const std::vector<edge> & e, std::vector<double> & C ) {
const double alpha = 0.1;
int i,j;
gsl_matrix * A = gsl_matrix_alloc(NV,NV);
for(i=0;i<NV;++i) for(j=0;j<NV;++j)
gsl_matrix_set(A,i,j,0.0);
for(std::vector<edge>::const_iterator ei=e.begin();ei!=e.end();++ei) {
gsl_matrix_set(A,(*ei).a,(*ei).b,1.0);
gsl_matrix_set(A,(*ei).b,(*ei).a,1.0);
}
for(i=0;i<NV;++i) for(j=0;j<NV;++j) {
double t = -alpha*gsl_matrix_get(A,i,j);
if(i==j) t += 1.0;
gsl_matrix_set(A,i,j,t);
}
gsl_vector * x = gsl_vector_alloc(NV);
gsl_vector * b = gsl_vector_alloc(NV);
for(i=0;i<NV;++i) gsl_vector_set(b,i,1.0);
gsl_linalg_HH_solve(A,b,x);
for(i=0;i<NV;++i) C[i] = gsl_vector_get(x,i);
gsl_vector_free(b);
gsl_vector_free(x);
gsl_matrix_free(A);
}
void central( int NV, const std::vector<edge> & e, std::vector<double> & C, double & minv, double & maxv, int m ) {
C.resize(NV);
switch(m) {
case 0: central_degree(NV,e,C); break;
case 1: central_closeness(NV,e,C); break;
case 2: central_betweenness(NV,e,C); break;
case 3: central_eigenvector(NV,e,C); break;
case 4: central_katz(NV,e,C); break;
case 5: central_alpha(NV,e,C); break;
}
minv = maxv = C[0];
for(int i=1;i<NV;++i) {
if(minv>C[i]) minv = C[i];
if(maxv<C[i]) maxv = C[i];
}
}
int main() {
const int N = 256;
const int NR = 3;
const int NC = 2;
const double SS = 300;
const double SX=SS*NC, SY=SS*NR;
const double R=5, B=6;
const double MD2=(0.03)*(0.03),D2=(0.1)*(0.1);
int i,j;
point2 pts[N];
for(i=0;i<N;++i)
do {
pts[i].x = DRand();
pts[i].y = DRand();
for(j=0;j<i;++j) if(squared_dist(pts[i],pts[j])<MD2) break;
} while(j<i);
std::vector<edge> edges;
for(i=0;i<N-1;++i) for(j=i+1;j<N;++j)
if(squared_dist(pts[i],pts[j])<D2)
edges.push_back(edge(i,j));
FILE * fo = fopen("central.svg","w");
fprintf(fo,
"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n"
"<svg xmlns:svg=\"http://www.w3.org/2000/svg\" xmlns=\"http://www.w3.org/2000/svg\"\n"
"version=\"1.0\" width=\"%g\" height=\"%g\" id=\"central\">\n"
,SX,SY
);
for(int ir=0;ir<NR;++ir) {
for(int ic=0;ic<NC;++ic) {
std::vector<double> C;
double minv,maxv;
central(N,edges,C,minv,maxv,ic+NC*ir);
fprintf(fo,"<g style=\"stroke:#000000;stroke-width:1;stroke-linejoin:round;fill:none\">\n");
for(i=0;i<int(edges.size());++i)
fprintf(fo,"<line x1=\"%6.2f\" y1=\"%6.2f\" x2=\"%6.2f\" y2=\"%6.2f\"/>\n"
,SX*ic/NC + (SX/NC-B*2)*pts[edges[i].a].x
,SY*ir/NR + (SY/NR-B*2)*pts[edges[i].a].y
,SX*ic/NC + (SX/NC-B*2)*pts[edges[i].b].x
,SY*ir/NR + (SY/NR-B*2)*pts[edges[i].b].y
);
fprintf(fo,"</g>\n");
for(i=0;i<N;++i) {
unsigned char rgb[3];
HSV2RGB( (2*(maxv-C[i]))/(3*(maxv-minv)),0.9,1.0,rgb);
fprintf(fo,"<circle cx=\"%6.2f\" cy=\"%6.2f\" r=\"%6.2f\" style=\"stroke:#000000;"
"stroke-width:0.5;stroke-linejoin:round;fill:#%02X%02X%02X\"/>\n"
,SX*ic/NC + (SX/NC-B*2)*pts[i].x
,SY*ir/NR + (SY/NR-B*2)*pts[i].y
,R
,rgb[0],rgb[1],rgb[2]
);
}
}
}
fprintf(fo,"</svg>\n");
fclose(fo);
return 0;
}
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| Datum/vreme | Minijatura | Dimenzije | Korisnik | Komentar | |
|---|---|---|---|---|---|
| trenutna | 17:01, 15. novembar 2012. | | 600 × 900 (476 kB) | Rocchini | User created page with UploadWizard |
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