Despite the rich literature on network architecture and communication system design, the current practice of describing architectures remains informal and idiosyncratic. Such practice has evolved based on idiomatic terminology and hence, it is failing to provide a formal framework for representing and for reasoning about network architectures. This state of affairs has led to the overloading of architectural terms, and to the emergence of a large body of network architecture proposals with no clear indication of their cross similarities, their compatibility points, their unique properties, and their architectural performance and soundness. Formalizing network architectural descriptions is therefore a timely contribution, and this paper presents a first step in that direction. The paper builds upon architectural style modeling concepts from the software engineering field, and applies them to the network architecture space. Our approach is presented through a case study detailing a formal model for a common class of network architectures. The model uses a simple declarative language based on relations and first-order logic.