There is the paper this paperProperty (T) and Kazhdan constants for discrete groups by ZukAndrzej Żuk, which gives a sufficient criterion for property (T) in terms of some spectral properties of a graph depending on a group $G$ with a generating set $S$. This graph is not the Cayley graph. But maybe it is still in the spirit of the question.
wrote the name of the paper into the post itself, so that a dead link is easier fixable
HenrikRüping
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