Talk:Null graph

Usage of "empty graph"

To me this term is analogous to inflammable. In that famous example, the ambiguous prefix in- can either mean "causing or bringing to" or imply negation. As a result, most writers on style and usage recommend avoiding the word entirely, and using the context-appropriate one of its two (unambiguous) alternatives: flammable and non-flammable. In a similar way, my own advice to authors is to avoid the term "empty graph" entirely and use instead either "null graph" or "edgeless graph," depending on one's intent.

But although edgeless is straightforward, the term null might still be interpreted as meaning edgeless, when in fact it is intended with the stronger meaning of having zero edges and zero vertices. This doesn't happen with flammable/non-flammable, whose meanings are always unique. —Preceding unsigned comment added by 83.132.117.124 (talk) 19:18, 27 January 2010 (UTC)

But, of course, typical Wikipedia pages should be descriptive, rather than prescriptive. And since there is clearly no single, universally agreed convention on this point of terminology, I've tried in the mods I've just made to the null graph article merely to point out and clarify the range of uses actually encountered in the literature and highlight the risk of the ambiguity.—PaulTanenbaum (talk) 14:56, 14 September 2008 (UTC)

Radius and Diameter

Why is the radius of the null graph 0? And why is the diameter 0? According to the definitions in Wikipedia, the radius of the null graph is the minimum of some function, taken over an empty set. The convention in these cases is to put $\infty$ as the result. Similarly, the diameter is defined to be the maximum of some function take over an empty set. By the same convention, this should be $-\infty$. Am I wrong? Peleg (talk) 20:28, 30 November 2016 (UTC)

The diameter can be defined either as a maximum (of distances between pairs of vertices) or a minimum (of numbers d such that all pairs of vertices have paths of length at most d). Similarly, the radius is either a minimum (over vertices, of the longest distance from that vertex to any other) or a maximum (over distances d such that every vertex has another vertex at distance at least d from it). I think it would be better just to leave out these two numbers, unless we get a reliable source that chooses one of these conventions for them. —David Eppstein (talk) 21:30, 30 November 2016 (UTC)