We wish to thank for the careful reviews on the article. We did take into account most of the remarks of the Reviewers, and in fact added even more along the same lines.
The main changes are:
1. A paragraph has been added to the end of the section mathematical definition of the SOM.
2. A new section Extensions of the SOM has been added pursuing the suggestions by a reviewer.
3. A number of references have been added.
In the following, we list the differences between reviewers' suggestions and the new edited version.
1. The *point density* of the grid nodes has so far only been analyzed in the one-dimensional case in the literature. Since the problem has not been solved completely, we did not want to discuss the special (unrealistic) one-dimensional case (Ritter et al. 1992 and many others) only.
2. There exist numerous but different approaches to the *measure of topology preservation*. It did not seem justified to single out one of them (Villman et al. 1997).
3. The non-Euclidean lattice, or rather, the Minkowski-type neighborhood (Ontrup & Ritter 2006) is a detailed variant of the SOM that is not yet generally accepted, and although it it seems interesting, it might have lead the discussion astray. If we had included it, we should have also included a plethora of other variants.
4. The tree structures of the SOM also constitute a special line of research, not very well established in literature.
We felt that this text was meant for an encyclopaedic article. Since over 7700 full scientific articles, together some 115 000 pages, on the SOM have been published (cf. the two bibliographies given as references), it would not have been possible to expound the field in its entirety. Introduction of too many specific details would only have disguised the main message.