How the nodes are connected together in a P2P network can vary considerably, from a user connecting via a modem from home, to a machine connected via a T3 connection at a university. Consequently the amount of network bandwidth available to a single node can vary considerably.
Ideally a P2P system should be able to operate no matter the connection bandwidth however the choice of network architecture can greatly affect a systems performance. For a decentralised architecture, if two portions of a P2P network are only connected together by a low bandwidth connection, then this could act as a severe bottleneck for peer communication.