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Could someone please tell me if my understanding is correct?

I created 2 simple networks in Packet Tracer and "wired" them together with router. I have not set up any routing (neither static nor dynamic) for the router. And yet both of my networks can communicate with each other. Is this proper behaviour ? The only thing I can think of is that router knows all networks that are connected to it so within it there is no need for setting up routing protocols. But still, I remember when I was told that for two networks to communicate there is need of a router (and implicitly I assumed routing protocols are required).

topology of network

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    Routing protocols do not route. Routers route, based on what is in their routing tables. Routing protocols are one of three ways routers populate their routing tables. Directly connected networks, and statically configured routes are the other two ways. – Ron Maupin May 1 '18 at 18:57
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Routing protocols are used by routers to communicate their routes with each other.

If you only have one router, there is no one for that router to talk to, and therefore no need for routing protocols.

Don't confuse routing - forwarding based on layer 3 information

with routing protocols -- a method for routers to communicate their reachability.

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router knows all networks that are connected to it so within it there is no need for setting up routing protocols

This is exactly correct: the single router gets an "interface route" for each network it is directly connected to. it doesn't know about anything else unless configured with static routes or a routing protocol to learn the routes. In your example, if the hosts are configured with the router as their default gateware (by DHCP or any other method) then all the hosts will correctly forward to the router.

The following are taken from a real production router with two interfaces and a single static default route:

interface FastEthernet0/0
 ip address 172.30.20.251 255.255.255.0
interface FastEthernet0/1
 ip address 172.31.20.254 255.255.255.0

ip route 0.0.0.0 0.0.0.0 172.30.20.254

show ip route gives the S static route and the two interface routes marked C for connected. L shows the local addresses.

S*    0.0.0.0/0 [1/0] via 172.30.20.254
      172.30.0.0/16 is variably subnetted, 2 subnets, 2 masks
C        172.30.20.0/24 is directly connected, FastEthernet0/0
L        172.30.20.251/32 is directly connected, FastEthernet0/0
      172.31.0.0/16 is variably subnetted, 2 subnets, 2 masks
C        172.31.20.0/24 is directly connected, FastEthernet0/1
L        172.31.20.254/32 is directly connected, FastEthernet0/1
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