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This paper considers a fully-connected interference network with a relay inwhich multiple users equipped with a single antenna want to exchange multipleunicast messages with other users in the network by sharing the relay equippedwith multiple antennas. For such a network, the degrees of freedom (DoF) arederived by considering various message exchange scenarios: a multi-userfully-connected Y channel, a two-pair two-way interference channel with therelay, and a two-pair two-way X channel with the relay. Further, consideringdistributed relays employing a single antenna in the two-way interferencechannel and the three-user fully-connected Y channel, achievable sum-DoF arealso derived in the two-way interference channel and the three-userfully-connected Y channel. A major implication of the derived DoF results isthat a relay with multiple antennas or multiple relays employing a singleantenna increases the capacity scaling law of the multi-user interferencenetwork when multiple directional information flows are considered, even if thenetworks are fully-connected and all nodes operate in half-duplex. Theseresults reveal that the relay is useful in the multi-way interference networkwith practical considerations.

Multi-Way Information Exchange Over Completely-Connected Interference Networks with a Multi-Antenna Relay