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Continuing the series of articles (... well actually is just the second one) on restricted combinatorial objects constrained by a recursively defined statistic and initiated by [this work](https://papers-gamma.link/paper/38/Dyck%20paths%20with%20a%20first%20return%20decomposition%20constrained%20by%20height) we submitted to review a new paper of subject.

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Great title!

> Great title!
Second it!

I think the paper is also nice. :)

I think this is a great paper. I like how the subject is presented, in particular the state of the art and the motivation are well-written. In my humble opinion, more papers should have an introduction as well-written as this. Although one has to readily accept that having to compare large graphs together is an important task, once this is accepted there is no ambiguity about where the authors want to lead the reader. There is a good overview of the problems with common methods in the literature, clear enough that the reader knows what is going on, yet simple enough not to feel overwhelming. Then, the authors clearly state how they positioned themselves in regard to these problems. The problem statement, in section 3, also follows this pattern of clearly exposing what is what and then using this information to expose what their contribution is. Now, I am not an expert on the subject so I can't make any serious judgment on the scope of the contribution. Some parts about scaling to large graphs seems a bit underwhelming to me, as the authors point out themselves that the Taylor expansion "provides a rather dubious approximation". Still, the theoretical work is well exposed and well developped. Thus, I expect anyone in this field could use this as a great starting point to improve on the experimental results.
Overall, I wish more papers were written with such clarity. The authors took time to clearly state their problem, which enabled me, an outsider to such questions of graph comparison techniques, to easily follow their argument. This was an enjoyable read.

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