  In this paper, we show that every connected signed graph with smallest
eigenvalue strictly greater than $-2$ and large enough minimum degree is
switching equivalent to a complete graph. This is a signed analogue of a
theorem of Hoffman. The proof is based on what we call Hoffman's limit theorem
which we formulate for Hermitian matrices, and also the extension of the
concept of Hoffman graph and line graph for the setting of signed graphs.
