Multiscale Planar Graph Generation

TL;DR

This paper introduces a flexible algorithm for generating realistic, multiscale planar graphs, addressing the need for synthetic network data that preserves planarity and structural properties for infrastructure network simulations.

Contribution

The paper presents a novel multiscale randomized editing algorithm that synthesizes realistic, planar networks while maintaining key structural features with minimal bias.

Findings

Successfully generates realistic planar networks

Preserves structural properties across multiple scales

Introduces variability while maintaining planarity

Abstract

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.