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A relation between the -3 dB bandwidths of graded-index plastic optical fibers (GI POFs) and the total power penalty of 50-m GI POF links is investigated in detail. The bandwidth of the GI POF is deliberately varied by controlling the index profile. It is theoretically and experimentally confirmed that sufficiently high bandwidth on the order of gigahertz is necessary for the GI POF, even for several hundreds of megabit per second (Mb/s) data rate, in order to achieve the power penalty free in the bit error rate performance of the link. In the case of silica-based multimode fiber links, it has been reported that the launch condition strongly affects the bit error rate performances; hence, a special launching technology for the silica-based multimode fiber is developed to achieve a 1-Gb/s transmission in the gigabit Ethernet protocol. In this paper, it is also found that the power penalty-free state is realized in the GI POF link, which is independent of the launch condition, when a GI POF with a nearly ideal index profile is used. The GI POF is a promising physical layer for realizing stable, high-speed and low-cost data-com networks.