John Cremona <john.crem...@gmail.com> writes: > [...] and then you will not have the silly > situation that (in 5.11) > > sage: G = Graph([]); G > Graph on 0 vertices > sage: G.is_connected() > True > sage: G.connected_components() > [] > as to me it seems contradictory to have a graph claiming to be > connected but having no connected components.
Why? A graph is connected iff every pair of vertices is connected, which is to say that every connected component is the same as every other connected component (i.e. a uniqueness property). The existence of a connected component seems to me to be independent from the uniqueness of a connected component, and so either 0 or 1 connected components should be admitted. Anyway, I'm not trying to argue that the empty graph should be considered connected. Maybe it is more useful to define connectedness by existence *and uniqueness* of connected components, after all. I like the nLab wiki link that darij provided in the ticket description [1]. I'm especially tickled by the example, "False is not true" :) -Keshav [1] http://ncatlab.org/nlab/show/too+simple+to+be+simple -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
