  The presence of a topologically non-trivial discrete invariants implies the
existence of gapless modes in finite samples, but it does not necessarily imply
their localization. The disappearance of the indirect energy gap in the bulk
generically leads to the absence of localized edge states. We illustrate this
behavior in two fundamental lattice models on the single-particle level. By
tuning a hopping parameter the indirect gap is closed while maintaining the
topological properties. The inverse participation ratio is used to measure the
degree of localization.
