Interconnection network ideally transfers the maximum amount of communication dataset within the least amount of time to fully exploit the parallelism of target applications on parallel computer systems. To this goal, we propose a selective data-compression interconnection network. Data compression virtually increases the effective network bandwidth, while each compute node introduces additional latency overhead to perform (de-)compression operation to end-To-end communication latency. To minimize the effect of the compression latency overhead on the end-To-end communication latency, we selectively apply a compression technique to a packet. The compression operation is taken for long packets and is also taken when network congestion is detected at a network interface. Evaluation results show that simple lossless and lossy compression algorithms have up to 3.0 and 1.8 compression ratios for integer and floating-point communication data in some parallel applications, respectively, while the lossy compression algorithm successfully satisfies the required quality of results. Through a cycle-network simulation, the selective compression method using the above compression algorithms improves by up to 46% the network throughput with the moderate increase of the communication latency of short packets.