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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 17th 2018

needed to be able to point to connected graph, so I created some minimum

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeJan 17th 2018

I was going to add in the non-empty condition (I think that’s right, isn’t it?), but am getting that cookies editing problem and have to dash now.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 17th 2018

• CommentRowNumber4.
• CommentAuthorRodMcGuire
• CommentTimeJan 17th 2018

Wouldn’t a more direct and more general definition be

A connected graph is an inhabited graph that cannot be decomposed as the disjoint union of two inhabited graphs.

If the graph is undirected then each pair of vertices is connected by a sequence of edges - every homset in its free category is inhabited.

if the graph is directed the decompositional definition is sometimes called weakly connected while the stronger homset definition can be called strongly connected or path connected.

These definitions only talk of graphs as structures. The article can then go on to talk about how these notions might be derived from connected objects in categories of graphs.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJan 17th 2018
• (edited Jan 17th 2018)

Please feel invited to expand the entry. I didn’t have any ambition to write an entry on connected graphs. I just wanted it to exist at all so that I could point to it.

• CommentRowNumber6.
• CommentAuthorRodMcGuire
• CommentTimeJan 18th 2018

I’ve edited connected graph to distinguish between strong and weak connectivity.

• I’ve said nothing about how the notion of a strongly connected directed graph might have some definition from a category it appears in.

• the strong definition doesn’t require that a graph be inhabited while the weak one does. I don’t know it this need be pointed out or resolved.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJan 18th 2018

Thanks!