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##	This function calculates the nodes selection without using seed node
##	last modified: 02-11-2015
##	connectivity: lambda; interconnectivity: gamma; sparsity: eta

##	Formula: c'f - lambda*f'Lf + gama*f'Af - eta*f'f = ( c + lambda*d )'f + ( gama + lambda )f'Af - eta*f'f
library(igraph)
core <- function(net, lambda, gama, eta) 
{
	v_names = V(net)$name
	if( any(c( 's', 't' ) %in% v_names) ) { cat('Error: vertex names should be different from \'s\', \'t\'. They were used for the additional source and sink node\n'); return(-1); }
	##nodes should have the 'weight' attribute
	if( !'weight' %in% vertex_attr_names( net ) ) { cat('Error: Vertices should have a \'weight\' attribute\n'); return(-1); }
	##edges should have the 'weight' attribute
	if( !'weight' %in% edge_attr_names( net ) ) { cat('Error: Edges should have a \'weight\' attribute. Edge weight should be set as 1 for unweighted graph\n'); return(-1); }
	
	v_weight = V(net)$weight
	
	d =  strength( net ) ## L = D - W for weighted graph. Modified 29-05-2015 
		
	##generate the augmented graph
	{
		net = net + 's' + 't'
		net <- add.edges(net, as.vector(rbind('s', v_names)))
		net <- add.edges(net, as.vector(rbind('t', v_names)))

		W = as_adjacency_matrix(net, attr='weight')
		A = (gama + lambda) * W
		cf = v_weight + gama*d - eta ##favours nodes with high degree
		change_points = sort( pmax(v_weight + gama*d, 0),  decreasing=TRUE )
		change_points = unname(change_points[change_points > 0])
		# if( eta > max( change_points ) ) { cat('\n Parameter inappropriate. Eta should be in:', range(change_points), '\n'); return(-1) }
			
		A['s', v_names] =  cf*(cf >= 0) ##keep edges on 's' side
		A['t', v_names] = -cf*(cf < 0) ##keep edges on 't' side 
		A[,'s'] = A['s',]
		A[,'t'] = A['t',]
		st_net = graph_from_adjacency_matrix( A, mode="undirected", weighted=TRUE )
	}
		
	st_cut = graph.maxflow( st_net, source='s', target='t', capacity=E(st_net)$weight )
	selected = sort( setdiff( V(st_net)[st_cut$partition1]$name, 's' ) )
	
	st_cut_info = list( st_net = st_net, st_cut=st_cut, selected=selected, change_points=change_points )
	return( st_cut_info )
}