The global market for social robots has grown rapidly, reaching $4.26 billion in 2023, with applications ranging from home monitoring of older adults to patient assistance in care facilities. However, their high connectivity and exposure to sensitive data make them an attractive target for cyberattacks, raising concerns over both safety and privacy. While prior research has primarily focused on the software and hardware of individual robots, the security of the underlying network infrastructure has received comparatively little attention, posing a significant risk as these devices become increasingly widespread. In this paper, we take a first step in defining a secure network architecture for social robots. Building on existing standards in robotics and healthcare, we identify six fundamental security and privacy requirements that such an architecture should satisfy. We then introduce the Secure Social Robot Architecture (SSRA) as a reference model and analyze how it addresses these requirements. Finally, we compare SSRA with related approaches, showing that it combines multiple protections at the data and network levels. This work presents an initial yet comprehensive analysis of the problem space, providing both a concrete architecture and a structured framework to guide future advancements in secure and privacy-preserving social robot networks.