Structure graph of an Alexander system
= Structure graph of an Alexander system
For a filling <Alexander system> $\{\alpha_i\}$, the structure graph is the embedded graph
$$
\Gamma=\bigcup_i\alpha_i\cup\partial S,
$$
with vertices at all curve intersections, arc endpoints, and punctures. Its edges are the curve, arc, and boundary segments between consecutive vertices. A homeomorphism preserving the system induces a graph automorphism.