Have a look at METIS and ParMETIS. Both libraries allow weights for edges and partition to minimize edge cuts by considering number of interpartition edges and edges' weight.

thank you sir , 

Is this KaHIP can be applicable for the directed graph or not.. if not suggest me for directed graph.

Thank you sir,

can you suggest me best graph partition algorithm for directed graph 

Sir ,here i attached a directed like that, the Digraph contains 1000 or + nodes and some  weights between the nodes. for that type of graphs have to do the partitioning and need to find sub graphs

large graph is partitioned in to 'n' from that finding the subgraphs among all partitions