# Talk:Geometric median

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## DyK

Here's a permalink of that page. --Hirak 99 10:16, 2 April 2007 (UTC)

## 1-median of a graph or tree

Do we have a Wikipedia article that explains the median of a graph or tree (i.e., a node that minimises the average distance to all other nodes)? A similar concept is the graph center, which minimises the maximum distance, and facility location problems in graphs are also related. But I couldn't find a page that explicitly mentions the concept of a median of a graph. Median graph is something different. 1-center problem has a lot of relevant links, but they are all red.

Here are some references if someone is interested in writing more about medians of graphs:

One might also cover more general k-medians; see, e.g.:

I think there are at least enough references to show that the concept is notable enough to have some coverage in Wikipedia. But I am not sure if it is best to create a new article or extend an existing article (e.g., this page). — Miym (talk) 16:27, 11 October 2009 (UTC)

I think median graph is less different than you suggest: trees are median graphs, and median graphs are the graphs in which the 1-median of any three vertices is uniquely determined as meeting the obvious lower bound on average distance. Regardless, I think graph-theoretic medians are too separate a topic to be included in this article. —David Eppstein (talk) 16:46, 11 October 2009 (UTC)
Yes, you are right, but I do not think it makes sense to try to explain the concept of the 1-median of a graph in the median graph article, either. (But if we had an article on graph median, then it would certainly be a good idea to explain the connection between median graphs and graph medians, like you said.) — Miym (talk) 17:43, 11 October 2009 (UTC)