I want to know what advantages or disadvantages are of adding more routers in network topology?
First example: Topology
Second example: Topology
Is it more secure? If it is, how and why?
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Odd question. You don't add routers (or any device) for the sake of adding them.
When designing a network, you first get your requirements. You usually take into account:
(additional factors may be relevant as well)
There's always many, or at least several possible solutions using various technologies. It is the work of a network architect to design the solution. The solution chosen will dictate the number of devices.
All networks evolve, so you extend them and add devices when there's a need to.
In medium to large setup, you will have a number of routers larger that what is strictly necessary to have things running, to provide redundancy. So if a router is down, either due to a bug, a hardware failure or a planned maintenance, the network is not impacted.