I have a question regarding networks, I just recently started studying graph theory, and I was wondering for this network below
can I say that a path connecting $B$ and $H$ is B-A-C-D-G-H or B-A-F-E-D-G-H? Like A coming after the B, I know that we usually look for the shortest path like B-C-D-G-H ( 4 degrees of separation).. but I am just wondering does order matter in general when we are dealing with networks?
On
If a problem in a textbook asks you to find a path from one vertex to another, any path will do, including all of the paths you listed, just make sure you do list a path, and don’t repeat any vertices. However, the length might matter in some situations, you might be asked to find a shortest path in some questions.
For this graph: yes, those are all paths connecting B and H. They're not the shortest paths, but it is important to consider them. For instance, if this network represented a roadway system, you'd want to know that you could still get from B to H even if the road from B to C was closed.
Very often, the edges in networks are labeled with arrows to indicate that there is a direction associated with the connection. In that case, you might find that A leads to B but not vice-versa, so you couldn't necessarily make directed paths quite as casually. But undirected networks still have their uses.