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For usage models of coverage extension and throughput enhancement, a novel framework, Multi-hop Relay (MR) network, which consists of various kinds of stations such as the base station (MR-BS), the relay station (RS), and the mobile station (MS) is proposed by the study group under the IEEE 802.16 WG. With the help of RSs, data transmissions between MR-BS and MS become more reliable and effective. In the paper, we propose a new measurement, called effective radio resource index (ERRI), to indicate the effectiveness of radio resource of a link used to transmit data. The ERRI of a link is normalized and compared to the metric defined as the bandwidth unit required for transmitting a fixed amount of data using 64-QAM CC 5/6 with repetition 1. Additionally, a cost function of a relay path between MR-BS and MS is also proposed to efficiently facilitate the evaluation of path selection schemes for MR networks. Simulation results show that the relay path selection scheme with ERRI considerations is indeed effective in terms of network throughput.