As the number of IPs and the communication volume among them have constantly increased, on-chip crossbar network is now the most widely-used on-chip communication backbone of contemporary SoCs. The on-chip crossbar network consists of multiple crossbars and the connections among the IPs and the crossbars. As the complexity of SoCs increases, it has also become more and more complex to determine the topology of the crossbar network. To tackle this problem, this paper proposes an on-chip crossbar network topology method for application-specific systems. The proposed method uses mixed integer linear programming to solve the topology synthesis problem, thus the global optimality is guaranteed. Unlike the previous MILP-based methods which represent the topology with adjacency matrixes of IPs and crossbar switches, the proposed method uses the communication edges among IPs as the basic element of the representation. The experimental results show that the proposed MILP formulation outperforms the previous one by improving the synthesis speed by 77.1 times on average, for 4 realistic benchmarks.