Many emerging applications that use XML are distributed, usually over large peer-to-peer (P2P) networks on the Internet. The deployment of an XML query shipping system over P2P networks requires a specialized synopsis to capture XML data in routing tables. In this paper, we propose a novel eigenvalue-based routing synopsis for deployment over unstructured P2P networks. Based on well-established Cauchy?s Interlacing Theorem, our approach employs multiple eigenvalues as routing synopsis and facilitates query routing process with computationally-inexpensive range inequality checking. Through extensive experiments, we demonstrate the effectiveness of our approach.