We would like to thank the reviewers for their very valuable comments and suggestion for improvement. Our revised version of manuscript addresses their comments and suggestions, and we provide point by point response below: (we have indicated quotations from the reviewers by prefixing lines with ‘>’) >Reviewer # 1 >The authors engage with existing research in the field and establish the limitations of existing methods of generative model selection, which they seek to address. >They suggest a new sophisticated methodology, which appears to be sound and results in convincing outcomes. We thank the reviewer for his positive comments. > The descriptions are not always clear, in particular how the two processes, (1) learning of network similarity and (2) model selection based on classification exactly interact/inform each other is not entirely clear to me. > The authors are encouraged to proof-read their paper again and correct typos etc. As desired by the reviewer the manuscript was modified to improve the readability. >Reviewer # 2 > The authors use a grab-bag of network features, hoping to capture the topology of networks. My concern is with one of their features; the assortativity coefficient, has been shown to depend upon network size (Nelly Litvak and Remco van der Hofstad, Physical Review E 87, 022801 (2013)). A size-dependent feature is at odds with the authors’ aim to have a “distance metric that is agnostic” to network size. This is especially relevant for at least two of the models used in their set of generative models: the Barabasi-Albert model and the Watts-Strogatz model. We thank the reviewer for the comments and his input on the size-dependence of assortativity feature. A paragraph (subsection 4.4) has been added in the revised manuscript to specifically address this issue. Here is the explanation of changes introduced. We carried out an extensive analysis of this issue and plotted the assortativity feature as a function of network size for all types of networks considered in this study. Further, we examined how critical this particular feature is for the conclusions reached in our proposed method by re-evaluating the whole model in the absence of this feature. In Appendix A: Figures 7 to 12 the revised manuscript shows the boxplots of assortativity in various network size ranges for different network types. We do confirm that for a few network types, particularly the Barabasi-Albert model, assortativity slightly increases with network size. The major implication of this observation is that the proposed approach should not be used for a very large range of network sizes. It is to be noted that the dependencies are rather weak, with a reasonable range of network sizes; hence the proposed model can be used effectively as has been demonstrated in our study. Further, we carried out an additional experiment in which we removed the assortativity feature from our model and the results shows that this feature is not critical to the overall strategy of the proposed network comparison methodology. Thus, if users intend to reuse our model for a very large range of network sizes, they are advised to remove assortativity features and the cost of doing so in terms of model performance is not very high. > In the results section, figure 3 is a convincing, low dimension, demonstration of why the model selection method as presented is effective. The figure clearly shows that the distance measure learned is an effective discriminator between network models. However their evaluation of the model selection approach (Table 1) seems to indicate that their generated model instances (and I am speculating here in the absence of any indication of the range of model parameters used) do not have enough variability. The reviewer finds our results shown in figure 3 convincing which means the generative models are well distinct (not clustered together). Table 1 shows predictability of instances of different generative models is almost 100 percent. The reviewers comment about the variability in Table 1 seems to be not relevant. > While the authors take some care to present their method, the main result, called Case Study, for real networks is simply given as a table with the closest generative model selected for each real network. There is no way for the reader to assess how well the generative model fits the data. The method developed by the authors learns a metric. It would be useful to see the closeness of the fit for each generative models to each real network. This could be achieved by giving a measure of the distance of each real network from each generative model. In this paper, we consider model selection as a classification problem. As discussed in the manuscript, we can also utilize network similarity measures for the model selection problem. As suggested by the reviewer we added Table 3 in our revised manuscript that shows the average Euclidean distance between embedded features of real network and all instances of a particular generative model. Smallest average distance shows a stronger similarity between real network and generative network. We have seen in our study that the model selected through model selection (using classification scheme) and the model selected through network similarity (using Euclidean distance measure) agreed completely refer Tables 2 and 3. > In the current form, I would not accept the paper for publication. Perhaps with significant changes, the paper may be acceptable. The reasons for the decision: The result, in Table 2, for one of the real networks citHepTh, the selected generative model is the Erdos-Renyi random graph model. This result only indicates that none of the other 5 models fit the data well - fitting to a random graph model is like a “base-line” fit. There is no discussion of the results. I am not sure what the 1 2 “Discussion” section is trying to convey. Thanks for the reviewer for pointing out the error in Table 2 where the selected generative model should be FF instead of ER. We have corrected this mistake. As desired by the reviewer section 5 “Discussion” in revised manuscript is modified. > The paper has many typos and grammatical errors. Examples (not exhaustive) are: >page 2, line 13: ‘ ...to perform an effective model selection.....’, remove ‘an’. >page 2, lines15-17: A run-on sentence that is out of place. >page 3, line 4: ‘estimte’ >page 11, line 20: ‘1000 of network instances......’ >page 11, line 22: Missing ‘is’ in the first sentence. >page 11, line 30: ‘ecah iteartion’ >page 12, line 8: Missing space before ‘More’. >page 12, line 37: ‘....the randomly chosen pair of nodes.’ page 12, line 37: ‘....the the....’ >page 13, line 34: ‘....we computes.....’ >page 13, line 34: ‘The question is, Is the euclidean....’ should be: The question: is the Euclidean...... >page 13, line 39: heatmap should not be capitalized. >page 13, line 40: ‘....feture....’ >page 13, line 40: ‘.....diffrent.....’ >page 15, line 34: ‘ Despite most of the existing methods [19, 25, 27], the proposed distance based method.....’ >I am not sure of what the authors mean. >page 15, line 42: ‘perhaps smaller from the size of the target network’ the ‘from’ should be ‘than’ Thanks and sorry for inconvenience. The above concerns are addressed in revised manuscript.