  The study of network representations of physical, biological, and social
phenomena can help us better understand the structural and functional dynamics
of their networks and formulate predictive models of these phenomena. However,
due to the scarcity of real-world network data owing to factors such as cost
and effort required in collection of network data and the sensitivity of this
data towards theft and misuse, engineers and researchers often rely on
synthetic data for simulations, hypothesis testing, decision making, and
algorithm engineering. An important characteristic of infrastructure networks
such as roads, water distribution and other utility systems is that they can be
embedded in a plane, therefore to simulate these system we need realistic
networks which are also planar. While the currently-available synthetic network
generators can model networks that exhibit realism, they do not guarantee or
achieve planarity. Therefore, in this paper we present a flexible algorithm
that can synthesize realistic networks that are planar. The method follows a
multi-scale randomized editing approach generating a hierarchy of coarsened
networks of a given planar graph and introducing edits at various levels in the
hierarchy. The method preserves the structural properties with minimal bias
including the planarity of the network, while introducing realistic variability
at multiple scales.
