  A compact graph-like space is a triple $(X,V,E)$ where $X$ is a compact,
metrizable space, $V \subseteq X$ is a closed zero-dimensional subset, and $E$
is an index set such that $X \setminus V \cong E \times (0,1)$. New
characterizations of compact graph-like spaces are given, connecting them to
certain classes of continua, and to standard subspaces of Freudenthal
compactifications of locally finite graphs. These are applied to characterize
Eulerian graph-like compacta.

Combinatorics;General Topology