This document proposes a graph theoretic model for analyzing and designing community wireless networks (CWNs). It models a CWN as two graphs: a social graph representing community stakeholders and their relationships, and a wireless graph representing the technical network. Node and edge attributes in these graphs capture social, economic, and technical factors. This allows quantification of stakeholder contributions and benefits, and informs decisions around network implementation and operation. The model provides a framework to study CWNs as complex socio-technical systems and solve related problems.