Finding an optimal key assignment (subject to given constraints) for a key
predistribution scheme in wireless sensor networks is a difficult task. Hence,
most of the practical schemes are based on probabilistic key assignment, which
leads to sub-optimal schemes requiring key storage linear in the total number
of nodes. A graph theoretic framework is introduced to study the fundamental
tradeoffs between key storage, average key path length (directly related to the
battery consumption) and resilience (to compromised nodes) of key
predistribution schemes for wireless sensor networks.