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The 60 GHz technology has a great potential to provide wireless communication at multi-gigabit rates in future home networks. To maintain the network connectivity with 60 GHz links, which are highly susceptible to propagation and penetration losses, is a major challenge. The quality and the robustness of the 60 GHz links can be improved by employing relay nodes in the network. In this paper, the contribution of relaying to the connectivity and the quality of the 60 GHz radio links is studied by modeling three indoor scenarios. It is analytically and through simulations shown that having a relay node in a 60 GHz network decreases the average freespace path loss 33% in the worst case scenario. The effects of relay device position and the obstacle density on the improvement of the average received signal level are investigated with a verified 3D ray tracing tool. A comparative simulation study on the performance of different relay configurations under various network conditions is conducted. The results yield that even a single relay device positioned at the height of other nodes can improve 50% of the links in considerable levels in a 60 GHz indoor network. It is also shown that additional relay nodes do not contribute to 60 GHz indoor connectivity significantly, if there are two properly positioned relay devices in a network which is moderately populated.