An inhabited graph has two notions of being connected:
weak connected - it cannot be decomposed as the disjoint union of two inhabited graphs.
strong or path connected - each pair of vertices is connected by a sequence of edges or in other words every homset of its free category is inhabited.
If a graphâ€™s edges are undirected these two notions coincide while if directed the stronger condition implies the weaker.
For the various categories of graphs, which of their objects are weakly connected correspond to the general notion of connected objects in these categories.
Last revised on January 18, 2018 at 18:22:32. See the history of this page for a list of all contributions to it.