Scaling of Geographic Space from the Perspective of City and Field Blocks and Using Volunteered Geographic Information

Scaling of geographic space refers to the fact that for a large geographic area its small constituents or units are much more common than the large ones. This paper develops a novel perspective to the scaling of geographic space using large street networks involving both cities and countryside. Given a street network of an entire country, we decompose the street network into individual blocks, each of which forms a minimum ring or cycle such as city blocks and field blocks. The block sizes demonstrate the scaling property, i.e., far more small blocks than large ones. Interestingly, we find that the mean of all the block sizes can easily separate between small and large blocks- a high percentage (e.g., 90%) of smaller ones and a low percentage (e.g., 10%) of larger ones. Based on this regularity, termed as the head/tail division rule, we propose an approach to delineating city boundaries by grouping the smaller blocks. The extracted city sizes for the three largest European countries (France, Germany and UK) exhibit power law distributions. We further define the concept of border number as a topological distance of a block far from the outmost border to map the center(s) of the country and the city. We draw an analogy between a country and a city (or geographic space in general) with a complex organism like the human body or the human brain to further elaborate on the power of this block perspective in reflecting the structure or patterns of geographic space. Keywords: Power law distribution, scaling of geographic space, data-intensive geospatial computing, street networks

💡 Research Summary

The paper investigates the scaling properties of geographic space by decomposing whole‑country road networks into their elementary closed rings, termed “blocks”. Using OpenStreetMap data for France, Germany, and the United Kingdom, the authors first build topological relationships among millions of street arcs (2.3 M, 8.2 M, and 3.0 M respectively) by assigning directions and linking left/right polygons at each node. A left‑ and right‑traversal algorithm then extracts minimal cycles (blocks) and a maximal outer cycle, while recursively assigning each block a “border number” that records its topological distance from the outermost border.

Statistical analysis of the resulting block areas shows a clear log‑normal distribution for all three countries. Crucially, the arithmetic mean of block sizes serves as a natural threshold that separates the overwhelming majority of small blocks (86–94 % of all blocks) from a minority of large blocks (6–14 %). The authors formalize this observation as the “head/tail division rule”: in any heavy‑tailed variable, the mean partitions the data into a high‑percentage tail and a low‑percentage head. Applying this rule, they find that roughly 10 % of blocks (the large ones) occupy about 90 % of the land area, whereas the remaining 90 % of blocks (the small ones) cover only about 10 % of the land, echoing the classic 80/20 principle.

To delineate urban extents, the authors cluster adjacent small blocks (those below the mean) using a recursive adjacency search that respects spatial autocorrelation (i.e., a small block surrounded by large blocks is excluded). The resulting clusters are then again split by the head/tail rule; clusters larger than the mean are defined as “natural cities”. The size distribution of these natural cities follows a power‑law (P(x) ∝ x^‑α) for all three countries, confirming that city sizes obey Zipf‑like scaling when derived directly from street‑network geometry rather than administrative definitions.

The border number concept provides a topological map of the interior of a country or city. Blocks with higher border numbers lie deeper within the network and are interpreted as “topological centers”. Visualizations reveal that France and the UK have maximum border numbers around 70–80, while Germany reaches 125, indicating a more pronounced interior hierarchy. These centers are not necessarily geometric centroids, highlighting the distinction between geometric and topological centrality.

Methodologically, the study demonstrates a scalable workflow for massive vector data: partitioning OSM files, parallel preprocessing on a 64‑bit, 4‑core machine with 48 GB RAM, and several‑hour to multi‑day processing times (≈5 h for France/UK, ≈63 h for Germany). The algorithmic steps—direction assignment, left/right traversal, maximal cycle detection, recursive border‑number assignment—are detailed in the appendix.

The contributions are threefold: (1) identification of the block‑size mean as a robust, data‑driven delimiter between urban and rural fabric; (2) a vector‑based, raster‑independent method for extracting natural city boundaries that avoids the Modifiable Areal Unit Problem (MAUP); and (3) the introduction of the border number as a tool for visualizing topological centers, offering a new perspective on spatial organization akin to the hierarchical structure of biological organisms.

In conclusion, by treating the street network as a collection of minimum cycles, the authors reveal that geographic space exhibits heavy‑tailed scaling at the block level, that urban extents can be objectively derived from this scaling, and that topological distance metrics can uncover hidden centers within countries. The work bridges data‑intensive geospatial computing, urban theory, and complex‑systems thinking, providing a novel methodological framework for future studies of spatial scaling and city delineation.