I will argue against False. We've had the convention that
Graph().is_connected() is True for the last n years. This was an
arbitrary (if heedless) choice at the boundary of several definitions.
It doesn't seem to be an undue source of bugs, so the only impact of
changing this arbitrary choice to another arbitrary choice will be to
subtly break backwards-compatibility and add warning noise.
I just consulted NetworkX, and I am convinced that their solution is
the only reasonable change we could make:
if len(G)==0:
raise nx.NetworkXPointlessConcept(
"""Connectivity is undefined for the null graph.""")
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