  In a signed graph $G$, an induced subgraph is called a negative clique if it
is a complete graph and all of its edges are negative. In this paper, we give
the characteristic polynomials and the eigenvalues of some signed graphs having
negative cliques. This includes cycle graphs, path graphs, complete graphs with
vertex-disjoint negative cliques of different orders, and star block graphs
with negative cliques. Interestingly, if we reverse the signs of the edges of
these graphs, we get the families of weakly balanced signed graphs, thus the
eigenvalues of wide classes of weakly balanced signed graphs are also
calculated. In social network theory, the eigenvalues of the signed graphs play
an important role in determining their stability and developing the measures
for the degree of balance.
