  Let $G$ be a simple graph with $n$ vertices and $\pm 1$-weights on edges.
Suppose that for every edge $e$ the sum of edges adjacent to $e$ (including $e$
itself) is positive. Then the sum of weights over edges of $G$ is at least
$-\frac{n^2}{25}$. Also we provide an example of a weighted graph with
described properties and the sum of weights $-(1+o(1))\frac{n^2}{8(1 +
\sqrt{2})^2}$.
  The previous best known bounds were $-\frac{n^2}{16}$ and
$-(1+o(1))\frac{n^2}{54}$ respectively. We show that the constant $-1/54$ is
optimal under some additional conditions.
