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/* -*- mode: C -*- */
/* vim:set ts=2 sw=2 sts=2 et: */
/*
IGraph library.
Copyright (C) 2011-2012 Gabor Csardi <csardi.gabor@gmail.com>
334 Harvard street, Cambridge, MA 02139 USA
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 2 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, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301 USA
*/
#include "infomap_FlowGraph.h"
#define plogp( x ) ( (x) > 0.0 ? (x)*log(x) : 0.0 )
void FlowGraph::init(int n, const igraph_vector_t *v_weights) {
alpha = 0.15;
beta = 1.0 - alpha;
Nnode = n;
node = new Node*[Nnode];
if (v_weights) {
for (int i=0;i<Nnode;i++) {
node[i] = new Node(i, (double)VECTOR(*v_weights)[i]);
}
} else {
for (int i=0;i<Nnode;i++) { node[i] = new Node(i, 1.0); }
}
}
FlowGraph::FlowGraph(int n) {
init(n, NULL);
}
FlowGraph::FlowGraph(int n, const igraph_vector_t *v_weights) {
init(n, v_weights);
}
/* Build the graph from igraph_t object
*/
FlowGraph::FlowGraph(const igraph_t * graph,
const igraph_vector_t *e_weights,
const igraph_vector_t *v_weights) {
int n = (int)igraph_vcount(graph);
init(n, v_weights);
int directed = (int) igraph_is_directed(graph);
double linkWeight = 1.0;
igraph_integer_t from, to;
long int Nlinks = (long int) igraph_ecount(graph);
if (!directed) Nlinks = Nlinks * 2 ;
for (int i=0; i<Nlinks; i++) {
if (!directed) { // not directed
if (i%2==0) {
linkWeight = e_weights ? (double)VECTOR(*e_weights)[i/2] : 1.0;
igraph_edge(graph, i/2 , &from, &to);
} else {
igraph_edge(graph, (i-1)/2, &to, &from);
}
} else { // directed
linkWeight = e_weights ? (double)VECTOR(*e_weights)[i] : 1.0;
igraph_edge(graph, i, &from, &to);
}
// Populate node from igraph_graph
if (linkWeight > 0.0) {
if (from != to) {
node[(int) from]->outLinks.push_back(make_pair((int)to, linkWeight));
node[(int) to]->inLinks.push_back(make_pair((int) from, linkWeight));
}
}
}
}
FlowGraph::FlowGraph(FlowGraph * fgraph) {
int n = fgraph->Nnode;
init(n, NULL);
for (int i=0; i<n; i++) {
cpyNode(node[i], fgraph->node[i]);
}
//XXX: quid de danglings et Ndanglings?
alpha = fgraph->alpha ;
beta = fgraph->beta ;
exit = fgraph->exit;
exitFlow = fgraph->exitFlow;
exit_log_exit = fgraph->exit_log_exit;
size_log_size = fgraph->size_log_size ;
nodeSize_log_nodeSize = fgraph->nodeSize_log_nodeSize;
codeLength = fgraph->codeLength;
}
/** construct a graph by extracting a subgraph from the given graph
*/
FlowGraph::FlowGraph(FlowGraph * fgraph, int sub_Nnode, int * sub_members) {
init(sub_Nnode, NULL);
//XXX: use set of integer to ensure that elements are sorted
set<int> sub_mem;
for (int j=0 ; j<sub_Nnode ; j++) { sub_mem.insert(sub_members[j]); }
set<int>::iterator it_mem = sub_mem.begin();
vector<int> sub_renumber = vector<int>(fgraph->Nnode);
// id --> sub_id
for (int j=0; j<fgraph->Nnode; j++) { sub_renumber[j] = -1; }
for (int j=0; j<sub_Nnode; j++) {
//int orig_nr = sub_members[j];
int orig_nr = (*it_mem);
node[j]->teleportWeight = fgraph->node[orig_nr]->teleportWeight;
node[j]->selfLink = fgraph->node[orig_nr]->selfLink;
// Take care of self-link
int orig_NoutLinks = fgraph->node[orig_nr]->outLinks.size();
int orig_NinLinks = fgraph->node[orig_nr]->inLinks.size();
sub_renumber[orig_nr] = j;
for (int k=0; k<orig_NoutLinks; k++) {
int to = fgraph->node[orig_nr]->outLinks[k].first;
int to_newnr = sub_renumber[to];
double link_weight = fgraph->node[orig_nr]->outLinks[k].second;
if (to < orig_nr) {
// we add links if the destination (to) has already be seen
// (ie. smaller than current id) => orig
if (sub_mem.find(to) != sub_mem.end()) {
// printf("%2d | %4d to %4d\n", j, orig_nr, to);
// printf("from %4d (%4d:%1.5f) to %4d (%4d)\n", j, orig_nr,
// node[j]->selfLink, to_newnr, to);
node[j]->outLinks.push_back(make_pair(to_newnr, link_weight));
node[to_newnr]->inLinks.push_back(make_pair(j, link_weight));
}
}
}
for (int k=0; k<orig_NinLinks; k++) {
int to = fgraph->node[orig_nr]->inLinks[k].first;
int to_newnr = sub_renumber[to];
double link_weight = fgraph->node[orig_nr]->inLinks[k].second;
if (to < orig_nr) {
if (sub_mem.find(to) != sub_mem.end()) {
node[j]->inLinks.push_back(make_pair(to_newnr,link_weight));
node[to_newnr]->outLinks.push_back(make_pair(j,link_weight));
}
}
}
it_mem++;
}
}
FlowGraph::~FlowGraph() {
//printf("delete FlowGraph !\n");
for (int i=0;i<Nnode;i++) {
delete node[i];
}
delete [] node;
}
void delete_FlowGraph(FlowGraph *fgraph) {
delete fgraph;
}
/** Swap the graph with the one given
the graph is "re" calibrate
but NOT the given one.
*/
void FlowGraph::swap(FlowGraph * fgraph) {
Node ** node_tmp = fgraph->node;
int Nnode_tmp = fgraph->Nnode;
fgraph->node = node;
fgraph->Nnode = Nnode;
node = node_tmp;
Nnode = Nnode_tmp;
calibrate();
}
/** Initialisation of the graph, compute the flow inside the graph
* - count danglings nodes
* - normalized edge weights
* - Call eigenvector() to compute steady state distribution
* - call calibrate to compute codelenght
*/
void FlowGraph::initiate() {
// Take care of dangling nodes, normalize outLinks, and calculate
// total teleport weight
Ndanglings = 0;
double totTeleportWeight = 0.0;
for (int i=0;i<Nnode;i++) totTeleportWeight += node[i]->teleportWeight;
for (int i=0;i<Nnode;i++) {
node[i]->teleportWeight /= totTeleportWeight;
// normalize teleportation weight
if (node[i]->outLinks.empty() && (node[i]->selfLink <= 0.0)) {
danglings.push_back(i);
Ndanglings++;
} else { // Normalize the weights
int NoutLinks = node[i]->outLinks.size();
double sum = node[i]->selfLink; // Take care of self-links
for (int j=0;j < NoutLinks; j++) sum += node[i]->outLinks[j].second;
node[i]->selfLink /= sum;
for (int j=0;j < NoutLinks; j++) node[i]->outLinks[j].second /= sum;
}
}
// Calculate steady state matrix
eigenvector();
// Update links to represent flow
for (int i=0; i<Nnode; i++) {
node[i]->selfLink = beta * node[i]->size * node[i]->selfLink;
// (1 - \tau) * \pi_i * P_{ii}
if (!node[i]->outLinks.empty()) {
int NoutLinks = node[i]->outLinks.size();
for (int j=0;j < NoutLinks; j++) {
node[i]->outLinks[j].second = beta * node[i]->size *
node[i]->outLinks[j].second;
// (1 - \tau) * \pi_i * P_{ij}
}
// Update values for corresponding inlink
for (int j=0; j < NoutLinks; j++) {
int NinLinks = node[node[i]->outLinks[j].first]->inLinks.size();
for (int k=0; k < NinLinks; k++) {
if (node[node[i]->outLinks[j].first]->inLinks[k].first == i) {
node[node[i]->outLinks[j].first]->inLinks[k].second =
node[i]->outLinks[j].second;
k = NinLinks;
}
}
}
}
}
// To be able to handle dangling nodes efficiently
for (int i=0;i<Nnode;i++)
if (node[i]->outLinks.empty() && (node[i]->selfLink <= 0.0)) {
node[i]->danglingSize = node[i]->size;
} else {
node[i]->danglingSize = 0.0;
}
nodeSize_log_nodeSize = 0.0 ;
// The exit flow from each node at initiation
for (int i=0;i<Nnode;i++) {
node[i]->exit = node[i]->size // Proba to be on i
- (alpha * node[i]->size + beta * node[i]->danglingSize) *
node[i]->teleportWeight // Proba teleport back to i
- node[i]->selfLink; // Proba stay on i
// node[i]->exit == q_{i\exit}
nodeSize_log_nodeSize += plogp(node[i]->size);
}
calibrate();
}
/* Compute steady state distribution (ie. PageRank) over the network
* (for all i update node[i]->size)
*/
void FlowGraph::eigenvector() {
vector<double> size_tmp = vector<double>(Nnode,1.0/Nnode);
int Niterations = 0;
double danglingSize;
double sqdiff = 1.0;
double sqdiff_old;
double sum;
do {
// Calculate dangling size
danglingSize = 0.0;
for (int i=0;i<Ndanglings;i++) {
danglingSize += size_tmp[danglings[i]];
}
// Flow from teleportation
for (int i=0;i<Nnode;i++)
node[i]->size = (alpha + beta*danglingSize) * node[i]->teleportWeight;
// Flow from network steps
for (int i=0;i<Nnode;i++) {
node[i]->size += beta * node[i]->selfLink * size_tmp[i];
int Nlinks = node[i]->outLinks.size();
for (int j=0; j < Nlinks; j++)
node[node[i]->outLinks[j].first]->size += beta *
node[i]->outLinks[j].second * size_tmp[i];
}
// Normalize
sum = 0.0;
for (int i=0;i<Nnode;i++) {
sum += node[i]->size;
}
sqdiff_old = sqdiff;
sqdiff = 0.0;
for (int i=0;i<Nnode;i++) {
node[i]->size /= sum;
sqdiff += fabs(node[i]->size - size_tmp[i]);
size_tmp[i] = node[i]->size;
}
Niterations++;
if (sqdiff == sqdiff_old) {
alpha += 1.0e-10;
beta = 1.0-alpha;
}
} while ((Niterations < 200) && (sqdiff > 1.0e-15 || Niterations < 50));
danglingSize = 0.0;
for (int i=0;i<Ndanglings;i++) {
danglingSize += size_tmp[danglings[i]];
}
// cout << "done! (the error is " << sqdiff << " after " << Niterations
// << " iterations)" << endl;
}
/* Compute the codeLength of the given network
* note: (in **node, one node == one module)
*/
void FlowGraph::calibrate() {
exit_log_exit = 0.0;
exitFlow = 0.0;
size_log_size = 0.0;
for (int i=0; i<Nnode; i++) { // For each module
// own node/module codebook
size_log_size += plogp(node[i]->exit + node[i]->size);
// use of index codebook
exitFlow += node[i]->exit;
exit_log_exit += plogp(node[i]->exit);
}
exit = plogp(exitFlow);
codeLength = exit - 2.0*exit_log_exit + size_log_size -
nodeSize_log_nodeSize;
}
/* Restore the data from the given FlowGraph object
*/
void FlowGraph::back_to(FlowGraph * fgraph) {
// delete current nodes
for (int i=0 ; i<Nnode ; i++) { delete node[i]; }
delete [] node;
Nnode = fgraph->Nnode;
// copy original ones
node = new Node*[Nnode];
for (int i=0;i<Nnode;i++) {
node[i] = new Node();
cpyNode(node[i], fgraph->node[i]);
}
// restore atributs
alpha = fgraph->alpha ;
beta = fgraph->beta ;
exit = fgraph->exit;
exitFlow = fgraph->exitFlow;
exit_log_exit = fgraph->exit_log_exit;
size_log_size = fgraph->size_log_size ;
nodeSize_log_nodeSize = fgraph->nodeSize_log_nodeSize;
codeLength = fgraph->codeLength;
}
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