  Shortest paths are not always simple. In planar networks, they can be very
different from those with the smallest number of turns - the simplest paths.
The statistical comparison of the lengths of the shortest and simplest paths
provides a non trivial and non local information about the spatial organization
of these graphs. We define the simplicity index as the average ratio of these
lengths and the simplicity profile characterizes the simplicity at different
scales. We measure these metrics on artificial (roads, highways, railways) and
natural networks (leaves, slime mould, insect wings) and show that there are
fundamental differences in the organization of urban and biological systems,
related to their function, navigation or distribution: straight lines are
organized hierarchically in biological cases, and have random lengths and
locations in urban systems. In the case of time evolving networks, the
simplicity is able to reveal important structural changes during their
evolution.
