Question: in peer to peer network each computer runs both client and server software

Answer: Yes, A peer-to-peer network is designed around the notion of equal peer nodes simultaneously functioning as both ``clients'' and ``servers'' to the other nodes on the network. This model of network arrangement differs from the client--server model where communication is usually to and from a central server. A typical example of a file transfer that uses the client-server model is the File Transfer Protocol (FTP) service in which the client and server programs are distinct: the clients initiate the transfer, and the servers satisfy these requests.