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A directed network (or graph) is a network in which each edge has a direction pointing from one vertex to another vertex.

In case of WWW , when we go from one page to another (to be more specific, say in same tab), we can always go back to previous page from the new page, which shouldn't be possible as in directed networks if two vertex are joined by unidirectional edge then there is only single path in between those vertices.

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    We can go back to previous page because we already been there. Do you know what pages linking this web page? – 2017-02-01
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    We "go back" in plenty of applications of directed graphs, for example during a traversal of a tree. The direction of the edge just tells you whether you're going "up" or "down" in that example. But more importantly, who says the WWW is a directed network, and why? – 2017-02-01
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    @DavidK I read that in a book. WWW was given in the examples of directed networks. And suppose an edge is from vertex $1$ to vertex $2$ , then we can only traverse from $1$ to $2$. right? And the only way to come back to vertex $1$ is traveling through other edges(given we have a cyclic network). – 2017-02-01
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    @quicksilver No! and we can't go to vertex $1$ from $2$ although we have already been there(vertex $1$).. – 2017-02-01
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    Direction just means there is a "forward" and a "backward" along the edge. It doesn't mean "can't go backward" unless you _choose_ never to go backward. On the other hand, the "back" button on your browser doesn't actually use the link you came in on; it uses its stored history. The designers of the WWW actually _did_ choose to make the links traversable only in one direction. – 2017-02-01
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    @DavidK Ok so you are saying that directionality of an edge doesn't imply that there is only a single path which can be traversed through(namely that direction)? – 2017-02-01
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    Yes. The direction _plus_ a "don't go backward" rule would imply there is only one way to traverse a link. Anyway, it seems someone was trying to motivate directed graphs with some "real world" examples, and they chose an example that does have a directed graph at least partly involved, but the actual WWW and the way we interact with it is so much more complicated that the example may not really be very helpful. I suggest just moving on to the actual topic. – 2017-02-01
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    @DavidK Ok got it.. If you want you can write your comment as an answer so that I can give you credit. – 2017-02-01

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In a directed graph, the direction plus a "don't go backward" rule would imply there is only one way to traverse a link. The "don't go backward" rule is optional.

On the other hand, the "back" button of your browser does not actually use the link you just followed to go "back," but instead uses its own stored history of your browsing to find the previous page viewed.

It seems someone was trying to motivate directed graphs with some "real world" examples, and they chose an example that does have a directed graph at least partly involved, but the actual WWW and the way we interact with it is so much more complicated that the example may not really be very helpful. I suggest just moving on to the actual topic.

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    Now I am curious about what makes actual WWW is different from directed graph. So could you be more elaborate about it? – 2017-02-01
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    @quicksilver As an example, I frequently compose queries on Wolfram Alpha that may never have been made before, and post links to them in comments or answers on this site. Like a lot of other links, these point not to static files but to responses that will be generated only when the link is followed and are not stored at the "target" site. You _could_ still view these as nodes in a directed graph, but I don't think that's a good way to explain directed graphs to someone who is learning them for the first time. – 2017-02-01