# Topological distance between nonplanar transportation networks

Ahmed Abdelkader,
Geoff Boeing,
Brittany Fasy,
David Millman

October 2018

### Abstract

A key operation in transportation network analysis is to quantify the similarity between networks. This operation, for example, is used to trace the evolution of a street network over time or analyze a proposed subway extension. In order to compare such networks, we must define a similarity measure that takes both spatial proximity and structural similarity into account. Most current approaches, however, are either heuristic in nature or make strong assumptions to provide mathematical guarantees. We propose a layered representation of transportation networks to eliminate common planarity assumptions. The network is modeled as a set of layers, each containing a planar subset of the full network. Thus, the layers allow us to import prior related research on planar graphs into a non-planar setting. In particular, we describe network similarity as a topological distance between layered networks and discuss the construction of suitable layered representations for the purposes of network comparison.

Publication

In *Fall Workshop on Computational Geometry*