Beta invariant

Crapo's beta invariant $\beta(M) = (-1)^{r(M)} \sum_{A \subseteq E} (-1)^{|A|}\, r(A)$. For $|E| \ge 2$ it equals the coefficient of $x$ (and of $y$) in the Tutte polynomial. It is nonnegative, and for $|E| \ge 2$ it is positive exactly when $M$ is connected. Copied from polyDB (BETA_INVARIANT).