Re: relations on graphs

Is there any literature which discusses different possible notions for relations on graphs?

In any regular category, and certainly any topos, there is a well defined notion of relation, where a relation between two objects is a subobject of their product. These admit a * operation and compose in a well-behaved way; look towards the end of McLarty's category theory textbook for info on this. The category of directed graphs is certainly such a category, being regular. The category of graphs is not a topos, I believe, but might still be regular. Jamie Vicary.