Is the empty graph always connected ? I've looked through some sources (for example Diestels "Graph theory") and this special case seems to be ommited. What is the general opinion for this case ?
As I could gather from reading Diestel Graph theory, the disconnected graphs and the trivial graph (meaning the one with just one vertex) are 0-connected. But the trivial graph is connected, since there always is a path from that node to itself. So isn't the terminology a bit misleading ? Because one could take "0-connected" to mean "disconnected", but in the case of the trivial graph this doesn't hold anymore, which seems to me to be - at the level of terminology - unaesthetic.