The paper proposes methods for designing communication graph for the decentralized periodic averaging SGD (DPASGD) in the federated learning set up focusing on reducing the per-iteration complexity (cycle time). The reviews were very appreciative of the good system and experimental design aspects of the paper that accounts for various types of delays in realistic scenarios. I would like to thank the authors for their effort. The reviewers were quite engaged and have provided many useful feedback and I hope these will be used to improve the paper. In particular, I would like to comment of few points -- please see full reviews for details - Although the authors motivate the need for focusing on cycle time over convergence rate in the introduction, based on the reviews, I believe it would be useful to include this discussion explicitly as a highlighted paragraph or subsection (see also comments by R2 on digraph constraint) - I would also encourage you to consider the title change suggestion by R2 (or something similar) as I and other reviewers agree that the current title is too generic. - technical terms like edge-capacitated and node-capacitated networks, access delay are used quite prominently but not precisely/formally defined. For a general audience and some in-field reviewers, this was confusing. Please organize these definitions more systematically. Relating to the above, the AC had the following question which was not clarified in the submission and I hope the authors will address in the final version. “My understanding is that in edge-capacitated networks the M/min(C_up/N_i,C_dn/N_j,A(i',j')) is ignored while in node capacitated networks they cannot be. This would mean that the MSR and RING topologies suggested in Sec 3.1 for edge-capacited networks should be optimal when bandwidth is *large* enough. However Fig 3 and the discussion seems to suggest that these algorithms are more effective for smaller bandwidths. The discussion in lines 270-275 also suggests that RING is faster for slower networks. Isnt this contradictory?”