What are $r(\Lambda)$ and $s(\Lambda)$? Proposition 7.2 in Biggs Algebraic Graph Theory book says that $$\det A=\sum (-1)^{r(\Lambda)} 2^{s(\Lambda)},$$
where $A$ is the adjacency matrix of a graph $\Gamma$ and the summation is over all spanning elementary subgraphs $\Lambda$ of $\Gamma$. 
What are $r(\Lambda)$ and $s(\Lambda)$? I swear this Biggs guy has not defined them.

These are the rank and co-rank respectively. If $G$ is a graph with $n$ vertices $m$ edges and $c$ connected components then
$$r(G) = n -c \quad \mbox{and} \quad s(G) = m-n+c.$$
Note that  Biggs actually defines them in his book - see page 25 of the second edition.
