A p2p network is a network that allows two or more computers to share resources equivalents. All nodes have equal rights. In the bitcoin network computers do not share their resources (coins) equivalents and nodes do not have equal rights between them.
I don't think you understand what a peer-to-peer network is.
Also, bitcoins are not network resources.
Also, all full nodes are equivalent and have equal rights to braodcast and receive transactions and blocks.
Good point.