Sensor nodes are usually deployed in adversarial environments in which they are subject to compromise and revelation of critical information rendering the entire network useless. Therefore, secure communication of wireless sensor networks (WSNs) necessitates utilization of efficient key distribution schemes. Over the past few years, several works using probabilistic, deterministic and hybrid methods have been conducted to address key distribution among sensor nodes. In this paper we propose a novel method to deterministically distribute key-chains throughout a WSN utilizing expander graphs based on the Zig-Zag graph product. Given a set of constraints such as network size, amount of storage, radio range and key-chain length, we are able to efficiently construct a resilient yet scalable key distribution graph. The main advantage of the obtained method is providing a more user-adjustable and predictable framework compared to the previously proposed approaches. Simulation results demonstrate the efficiency of our proposed scheme and its general applicability to different network paradigms with diverse requirements.