I want to know about the performance of the Bitcoin Network under various network topology and for which it performs the best. Also what is the current topology being used?
the performance of the Bitcoin Network under various network topology and for which it performs the best
Bitcoin must be secure, foremost, and if it isn't the 'performance' would be totally irrelevant. To given an example, in a world without dishonest parties and failing components a minimal spanning tree rooted at each transaction and block source would be very efficient.. but in reality it would be totally useless since any such topology would be highly vulnerable to any malicious or faulty node.
In practice the Bitcoin P2P network creates a random topology with each peer connecting out to 8 listening nodes and each listening node accepting up to 125 connections. Outbound destinations are randomly selected with the constraint that no two connections will be made to the same /16 (IPv4, /32 for IPv6). User sometimes overlay additional manually configured connections among their own nodes or to other known parties.
Blocks tend to flow along the fastest paths on top of this random topology.