double mitk::ConnectomicsSimulatedAnnealingCostFunctionModularity::CalculateModularity( mitk::ConnectomicsNetwork::Pointer network, ToModuleMapType* vertexToModuleMap ) const
{
double modularity( 0.0 );
int numberOfModules = getNumberOfModules( vertexToModuleMap );
if( network->GetNumberOfVertices() != vertexToModuleMap->size() )
{
MBI_ERROR << "Number of vertices and vertex to module map size do not match!";
return modularity;
}
int numberOfLinksInNetwork( 0 );
std::vector< int > numberOfLinksInModule, sumOfDegreesInModule;
numberOfLinksInModule.resize( numberOfModules, 0 );
sumOfDegreesInModule.resize( numberOfModules, 0 );
// get vector of all vertex descriptors in the network
const std::vector< VertexDescriptorType > allNodesVector
= network->GetVectorOfAllVertexDescriptors();
for( int nodeNumber( 0 ); nodeNumber < allNodesVector.size() ; nodeNumber++)
{
int correspondingModule = vertexToModuleMap->find( allNodesVector[ nodeNumber ] )->second;
const std::vector< VertexDescriptorType > adjacentNodexVector
= network->GetVectorOfAdjacentNodes( allNodesVector[ nodeNumber ] );
numberOfLinksInNetwork += adjacentNodexVector.size();
sumOfDegreesInModule[ correspondingModule ] += adjacentNodexVector.size();
for( int adjacentNodeNumber( 0 ); adjacentNodeNumber < adjacentNodexVector.size() ; adjacentNodeNumber++)
{
if( correspondingModule == vertexToModuleMap->find( adjacentNodexVector[ adjacentNodeNumber ] )->second )
{
numberOfLinksInModule[ correspondingModule ]++;
}
}
}
// the numbers for links have to be halved, as each edge was counted twice
numberOfLinksInNetwork = numberOfLinksInNetwork / 2;
// if the network contains no links return 0
if( numberOfLinksInNetwork < 1)
{
return 0;
}
for( int index( 0 ); index < numberOfModules ; index++)
{
numberOfLinksInModule[ index ] = numberOfLinksInModule[ index ] / 2;
}
//Calculate modularity M:
//M = sum_{s=1}^{N_{M}} [ (l_{s} / L) - (d_{s} / ( 2L ))^2 ]
//where N_{M} is the number of modules
//L is the number of links in the network
//l_{s} is the number of links between nodes in the module
//s is the module
//d_{s} is the sum of degrees of the nodes in the module
//( taken from Guimera, R. AND Amaral, L. A. N.
// Cartography of complex networks: modules and universal roles
// Journal of Statistical Mechanics: Theory and Experiment, 2005, 2005, P02001 )
for( int moduleID( 0 ); moduleID < numberOfModules; moduleID++ )
{
modularity += (((double) numberOfLinksInModule[ moduleID ]) / ((double) numberOfLinksInNetwork)) -
(
(((double) sumOfDegreesInModule[ moduleID ]) / ((double) 2 * numberOfLinksInNetwork) ) *
(((double) sumOfDegreesInModule[ moduleID ]) / ((double) 2 * numberOfLinksInNetwork) )
);
}
return modularity;
}
