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I have a question regarding networks, I just recently started studying graph theory, and I was wondering for this network below enter image description here

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?

Dewton
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    Usually, networks are defined to be directed graphs, and you can't go against the arrows. Your diagram has no arrows. If that's OK for your definition of network, then there's nothing wrong with $A$ coming after $B$. Also, even with directed graphs, one is sometimes interested in all paths (that follow the arrows), not just shortest ones. – Gerry Myerson Nov 14 '19 at 11:54

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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.

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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.

Robo300
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