If you really want to get into semantics: the P2P network is a graph.
Mike Belshe

SPV thin clients only retrieve a subset of available data from a full-node in order to operate. Fully-validating nodes determine if transactions are valid and blocks are in consensus with the node’s rule set. SPV thin clients do not do this and rely on trusted 3rd-party full-nodes . “He can’t check transactions for himself…” <- in the whitepaper.

*Thin clients are not peers in a peer-to-peer network.*