  Representing a scanned map of the real environment as a topological structure
is an important research in robotics. %is currently an important research.
Since topological representations of maps save a huge amount of map storage
space and online computing time, they are widely used in fields such as path
planning, map matching, and semantic mapping. We propose a novel topological
map representation, the Area Graph, in which the vertices represent areas and
edges represent passages. The Area Graph is developed from a pruned Voronoi
Graph, the Topology Graph. The paper also presents path planning as one
application for the Area Graph. For that, we derive a so-called Passage Graph
from the Area Graph. Because our algorithm segments the map as a set of areas,
the first experiment compares the results of the Area Graph with that of
state-of-the-art segmentation approaches, which proved that our method
effectively prevented over-segmentation. Then the second experiment shows the
superiority of our method over the traditional A* planning algorithm.
