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If 3 routers are connected this way together, is the connection between Router1 and Router2 itself forms a network on its own despite having no stations between them? Similarly, would the connection between Router2 and Router3, and Router3 and Router1 form a network without stations between them?

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In other words, the connection between Router1 and Router2 will require another subnet of IP addresses which is only used for the interfaces connected between Router1 and Router2? Otherwise, what would the IP address of the Interface on the routers that connect between themselves if they don't form an "empty network" between them?

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Sounds homeworky to me. In case you had any doubts, this site isn't for help with homework. We're for professional administrators. Looking back on your question history, you really should get a few good books and some work experience under your belt. –  MDMarra Nov 21 '11 at 18:45

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Normally, yes, you would configure each PtP link with it's own /30 or /31 (depends on software support) network. It's also pretty common for NetAdmins to waste a whole /24 on links if there aren't very many links to begin with.

If it's not an Ethernet link, it could serial for instance, then it depends on the software implementation and possibly on administrator choice. But this is not "normal" on new equipment these days.

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If you have individual routed links between R1 and R2, R2 and R3, and R3 and R1, then yes, every link will require its own set of IP addresses (and subnet to match). Routers don't need "stations" to operate.

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