For a vertex
i of a signed graph, let
![$d_i$](img27.png)
,
![$m_i$](img28.png)
and
![$T_i^-$](img29.png)
denote its degree, average 2-degree and the number of unbalanced triangles passing through
i, respectively. We prove that
where
![$\rho$](img31.png)
stands for the largest eigenvalue. This bound is tight at least for regular signed graphs that are switching equivalent to their underlying graphs. We also derive a general lower bound for
![$\rho$](img31.png)
and certain practical consequences. A discussion, including the cases of equality in inequalities obtained and some examples, is given.