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This paper evaluates the performance of an opportunistic scheduling scheme for a multiuser two-way relay network, wherein an analog network coding (ANC)-based relay assists the communication between multiple pairs of users. To ensure fairness for each user pair, we consider a scheduler based on maximizing the normalized minimum of the instantaneous signal-to-noise ratios (SNRs) at each user of the pair. Under a high SNR assumption, we derive upper and lower bound expressions for the outage probability and the average sum-rate in a Rayleigh fading environment and establish that a multiuser diversity of order equal to the number of user pairs is harnessed by the scheme. Numerical and simulation results are presented to confirm the performance gain of the proposed scheme.