Key management has always remained a challenging problem for the entire security community. Standard practice in modern times is to agree on symmetric keys using public key protocols. However, public key protocols use heavy computations; rendering them inappropriate for application to low cost devices of Internet of Things (IoT). This led to proposals of various key management strategies for low cost networks; a prominent discovery being key predistribution technique for Wireless Sensor Network (WSN)–a prototype of IoT. Such schemes require several communicating nodes to share the same cryptographic key. This leads to interesting (combinatorial) graphical models and related optimality problems, that get intense for hierarchical architecture. Most protocols meant for hierarchical (low cost) networks employ separate designs for individual levels and/or clusters. Consequently only local optimal values can be computed. We develop a single universal platform using weighted signed graph (WSG) that designs the entire network for a hierarchical setup. This model can be used as itself or clubbed with a key predistribution scheme (KPS) to enhance the latter’s security when applied to a WSN. After generic presentation, we combine our universal model with prominent KPS to facilitate comparative study with existing protocols.