In recent years, the peer-to-peer paradigm has gained momentum in several application areas: file-sharing and VoIP applications have been able to attract millions of end users, while large-scale distributed computing frameworks, including the Grid, have proven their ability of attacking large scientific problems. We believe, however, that the potential of the P2P approach has not been completely exploited yet. The goal of this position paper is to propose another scientific area where the P2P cooperation paradigm could be profitably adopted: network analysis, i.e. the mathematical characterization of the main graph-theoretic properties of a large-scale network. We discuss the potential issues that must be confronted with when a decentralized approach to network analysisis taken, and we propose a preliminary research plan.