First, I would like to thank you for your comment. The points you raised are very important since they are the key of the clustering algorithm.

We have tested our results when cells are defined in different ways (larger cells, changing the *placement*, and others): Cells and clusters are not the same objects. The cells are defined with a grid that is initially placed *on the map*. Once cells are defined, one runs the clustering algorithm to obtain the clusters by recursively joining populated neighboring cells. The algorithm stops when the cluster boundary has no new neighboring populated cells.

About your first objection, larger cells can be understood as a larger level of coarse-graining. This should be seen as a feature of the algorithm and not as a weakness, since it allows for studying population dynamics at different length-scales. In addition, in the paper we study the effect of modifying the level of coarse-graining and found no statistical difference (unless the coarse-graining is extremely large, of the order of the largest cluster).

About your second objection, the *placement* of the cells is irrelevant. If you have 4 populated neighboring cells, the clustering algorithm will make them part of the same cluster, regardless of where the four cells are located.

About your third objection. This is related to the previous objection: Two neighboring populated cells are part of the same cluster, so that New York is always one cluster (New York is never broken up into many smaller cities because all the cells composing it are populated so that the clustering algorithm joins them into the same cluster).

This paper presents an unbiased way to define population clusters through an algorithm that has a feature: one can modify the level of coarse-graining depending on what one is studying.

Thank a lot again for your comment, and please let me know if you have any questions.

]]>There’s the one obvious objection that is mentioned here, namely that the size of the cells is arbitrary, and the larger cell you choose, the larger the city becomes.

There’s another, the *placement* of the cell-boundaries have similar effects. Place the cells so that they meet downtown, and any city magically splits into four smaller cities.

There’s a third; If you uniformly use the same cell-size, then either new-york breaks up into dozens of smaller cities, or really small cities, separated from eachothers by miles of farmland, join into one.

Then again, this paper isn’t even about the clusterin-algorithm, but rather gives some results on city-growth, the clustering is just used to obtain raw data.

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