title: Graph partitioning based on nodes and edges weights
body: <p>I have a graph G=(V,E) that both edges and nodes have  weights. I want to partition this graph to create equal sized partitions. The definition of the size of partition is sum(vi)-sum(ej) where vi is a node inside that partition and ej is an edge between two nodes in that partition. In my problem the graph is very dense (almost complete). Is there any approximation algorithm for that? </p>
  
  <p>This is somehow similar to the problem in <a href="https://stackoverflow.com/questions/11649024/bin-packing-with-overlapping-objects">bin packing with overlapping objects</a> where bins have the same size. Weight of nodes are their size and weight of Edges show how much two object can overlap.</p>