by **gorcee** » Fri Mar 16, 2012 4:48 pm UTC

I'm a little uncertain what you mean by length. Do you mean length in terms of graph distance, which is a measure of the number of "steps" it takes to get from one point to another? (ie, from A to B to D would be distance 2). In such a case, the properties you're talking about would require the graph to be totally connected (every node is 1 step away from every other node).

Typically, we don't really care about the location of the nodes in some externally-fixed coordinate system, so, for instance, a Euclidean metric doesn't really mean much. We can get around that by assigning a weight to each connection, and link that weight to the physical separation between nodes w/r.t. some external metric. If this is what you're doing, you could just call the graph uniformly weighted.

These aren't really terms, per se, but rather a combination of phrases that have more or less universal meaning.