I know this question sounds silly, but I've been reviewing distance vector tables from this site
Specifically this example where the direct path is longer than an indirect. Is this possible and if so, what are the conditions for this to occur?
closed as off topic by Xavierjazz, terdon, Canadian Luke, Nicole Hamilton, Ƭᴇcʜιᴇ007 Mar 5 '13 at 17:45
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The path is not longer it is more costly. In the example you have posted, the edges are weighted. The table shows the cost of each path. Since the direct edge has a weight of 7, the direct path has a cost of 7. The indirect path has a cost of 4+1=5 so it is less costly even if it is shorter.
I don't know what kind of network you are describing so I cannot know what these weights represent but that is why the cost is cheaper for the indirect path. The weights could, fir example, refer to network speeds. So, if F->D->G takes 5 seconds and F->G takes 7, the indirect path is faster because it goes through a faster network.