Peer to Peer network
A peer to peer network is one without dedicated server, that is, every computer acts as both a client and a server. This is a good networking solution for 10 or less users that are close to each other. The big problem for a peer to peer network is the security because the people setting permissions for shared resources will be users rather than administrators and the right people may not have access to the right resources. More importantly, the wrong people may have access to the wrong resources, thus, this is only recommended in situations where security is not a big issue.
Client/Server network
Client/Server network is designed to support a large number of users and uses dedicated server/s to accomplish this. Clients need to log in to the server/s in order to run applications or obtain files. Security and permissions can be managed by 1 or more administrators which cuts down on network users "playing" with things that they shouldn't be. This type of network also allows for convenient backup services, reduces network traffic and provides a host of other services that comes with the network operating system(NOS).
Centralized network
Centralized network is also a client/server based model that is most often seen in UNIX environments, but the clients are "dumb terminals". This means that the client may not have a floppy drive, hard disk or CDROM and all applications and processing occur on the server/s. As you can imagine, this requires fast and expensive server/s. Security is very high on this type of network.
