Topological Graph Simplification Solutions to the Street Intersection Miscount Problem

TL;DR

This work addresses the pervasive problem of street intersection miscounts arising from nonplanarity, intersection complexity, and curve digitization in street-network data. It introduces reusable, open-source algorithms in the OSMnx package for topological edge simplification and node consolidation to yield parsimonious, topology-faithful graphs. The methods improve key metrics such as intersection counts, street segment lengths, and node degrees, while achieving substantial information compression that speeds downstream graph analyses. Empirical validation across thousands of urban areas demonstrates both the prevalence of miscounts and the potential for substantial bias reduction, albeit with regional variation and parameterization considerations that guide practical deployment.

Abstract

Street intersection counts and densities are ubiquitous measures in transport geography and planning. However, typical street network data and typical street network analysis tools can substantially overcount them. This article explains the three main reasons why this happens and presents solutions to each. It contributes algorithms to automatically simplify spatial graphs of urban street networks -- via edge simplification and node consolidation -- resulting in faster parsimonious models and more accurate network measures like intersection counts and densities, street segment lengths, and node degrees. These algorithms' information compression improves downstream graph analytics' memory and runtime efficiency, boosting analytical tractability without loss of model fidelity. Finally, this article validates these algorithms and empirically assesses intersection count biases worldwide to demonstrate the problem's widespread prevalence. Without consolidation, traditional methods would overestimate the median urban area intersection count by 14\%. However, this bias varies drastically across regions, underscoring these algorithms' importance for consistent comparative empirical analyses.

Figures (5)

• Figure 1: Three causes of intersection miscounts. Lines represent edges, white circles represent true nodes (i.e., intersections/dead-ends), red circles represent false nodes at planar line intersections, redundant/duplicative intersections, or interstitial curvilinear geometry vertices.
• Figure 2: The edge simplification algorithm's six rules to identify a true endpoint node (i.e., an intersection or dead-end). Black circles represent the node in question, white circles represent other nodes, and arrows represent directed edges.
• Figure 3: Before (left) and after (right) running the edge simplification algorithm on an urban street network's graph. Circles represent nodes and lines represent edges.
• Figure 4: Node consolidation algorithm with three different tolerance parameterizations. Red circles/lines are nodes/edges before consolidation, blue are after. Top: too conservative and nodes do not merge (false negative). Middle: appropriate (true positive). Bottom: too aggressive and two separate intersections merge together (false positive).
• Figure 5: Spatially proximate but topologically remote nodes during consolidation. Left: original network. Center: geometric consolidation incorrectly merges unconnected nodes within spatial buffer distance. Right: topological consolidation correctly merges nodes only when they are connected within buffer distance along the network.