Working with the Bitcoin network protocol I am very interested in the p2p protocol used by Bitcoin clients. There are some excellent answers here that describe the way clients connect to the network.


How does the bitcoin client determine the first IP address to connect?
Peer to Peer: Methods of Finding Peers


I want to replicate the peer-to-peer network only without participating in the crypto-currency part. This is for an experiment on peer to peer discovery.

So, can you please show me some code instructions to set-up such a network?
This is a good start point to understand better the code related to peers discovery and management: https://github.com/bitcoin/bitcoin/blob/master/src/net.cpp 
I can't help you directly writing such a code for you but Bitcoin p2p is very similar to bittorrent one or similar. The greatness in Bitcoin is properly the fact that it has such (crypto)currency functionalities, so why should you use the Bitcoin protocol to create a p2p app which has no interest of using the main feature of the original code? 
I think there are different code bases more suitable for your research.