Private communications between AWS EC2 instances

I have three EC2 instances.
Each one contains a server.
Each server needs that TCP ports 8181, 2181, 2888 and 3888 are opened on each machine.
Each server should have the possibility to talk with the other servers via these ports.

I created a security group (for example, named : sg-4d775c42) where I put the following rules :

Custom TCP Rule | TCP | 8181 | sg-4d775c42
Custom TCP Rule | TCP | 2181 | sg-4d775c42
Custom TCP Rule | TCP | 2888 | sg-4d775c42
Custom TCP Rule | TCP | 3888 | sg-4d775c42

I thought that these rules mean that each machine in the security group sg-4d775c42 can call the ports 8181, 2181, 2888 and 3888 of the other machines in the same group.

But it seems that it's not the case !

If I open the ports to the world, ie the following rules :

Custom TCP Rule | TCP | 8181 | 0.0.0.0/0
Custom TCP Rule | TCP | 2181 | 0.0.0.0/0
Custom TCP Rule | TCP | 2888 | 0.0.0.0/0
Custom TCP Rule | TCP | 3888 | 0.0.0.0/0

Of course, my servers can talk together.

Moreover, the private communication between these 3 servers is the first step. The second step will be to connect into an other private network this 3 servers ensemble to an other instance.

So my question is the following one :

How can I create (or simulate) a private network where my ports are opened between my EC2 instances ?