Spatial Patterns of Public Transportation Stops: A Spatial Statistical Analysis Using Hexagonal Tessellation in Culiacán, Sinaloa, Mexico
This study employs hexagonal tessellation and spatial statistics to analyze the distribution of public transportation stops in Culiacán, Mexico, revealing a non-random, hierarchical pattern of high-density central cores and low-density peripheral sectors that highlights spatial inequities in urban accessibility.
Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
In any city, the ability to move from one place to another is the lifeblood of daily life. Public transportation is the engine that makes this movement possible for millions, but the system only works if the places where people board and leave the buses are located where people actually need them. Urban planners and geographers have long understood that these stops are not scattered randomly; they are placed to serve specific needs, often clustering where people live, work, or shop. However, seeing these patterns with the naked eye is difficult. A map of individual dots can look like a chaotic mess, hiding the larger story of how the city is organized. To understand the true shape of a city's transit network, researchers need a way to smooth out the chaos and see the big picture, distinguishing between areas that are well-served and those that are left behind. This is where the science of spatial statistics comes in, a field dedicated to measuring how things are arranged across the land and determining whether those arrangements are the result of chance or of deliberate, underlying forces.
In the city of Culiacán, Mexico, a team of researchers set out to uncover the hidden structure of the public bus system. They wanted to know if the bus stops were distributed evenly across the city or if they formed specific groups that revealed how the city functions. To do this, they did not look at the city block by block, which can be confusing because city boundaries are often irregular and change over time. Instead, they covered the entire map of Culiacán with a grid of perfect hexagons, like a honeycomb, where each cell was exactly 500 meters wide. This distance was chosen because it represents a reasonable walk for a person to reach a bus stop. By counting how many bus stops fell inside each hexagon, the researchers turned a scattered list of locations into a clear, organized map of density. They then used a statistical method to check if the number of stops in one hexagon was related to the number of stops in the hexagons right next to it. This process allowed them to see if the stops were truly random or if they were huddled together in specific patterns.
The results painted a very clear picture of the city's transportation landscape. The analysis showed that the bus stops were definitely not scattered by chance. Instead, they formed a distinct hierarchy. In the center of Culiacán, the researchers found a large, dense core where hexagons packed with many bus stops were surrounded by other hexagons that were also packed with stops. This "high-high" cluster represents the heart of the city, where commercial activity, offices, and services are concentrated, creating a high demand for transit. As the researchers moved their gaze away from this central hub, the pattern shifted. The dense clusters gave way to a "low-low" pattern, where hexagons with very few stops were surrounded by other hexagons that were also nearly empty. These areas are located on the edges of the city, in the peripheral neighborhoods where the bus network is much thinner.
The study also found that this pattern was consistent no matter how the researchers defined "neighbors" for their calculations. Whether they looked at hexagons that shared a flat edge or those that were simply the closest four neighbors, the same story emerged: a dense center and sparse edges. There were a few spots that broke the pattern, such as a single hexagon with many stops surrounded by empty ones, or a quiet spot surrounded by busy ones, but these were rare exceptions. The overwhelming evidence pointed to a city where the transportation infrastructure mirrors the city's economic and social structure. The bus stops are heavily concentrated where the city is most active and become increasingly scarce as one moves toward the outskirts. This finding suggests that the current system is built to serve the central business district most effectively, while the outer neighborhoods receive significantly less coverage.
This work provides more than just a map; it offers a new way to look at urban fairness. By using the hexagonal grid, the researchers were able to see the city's structure without the distortion of old administrative lines. They demonstrated that the distribution of bus stops is a direct reflection of how the city is organized, with a clear divide between the well-connected center and the less-connected periphery. The study does not claim to solve the problem of unequal access, nor does it measure how long people wait for a bus or how crowded the vehicles are. Instead, it provides a solid, statistical foundation for understanding where the gaps are. It shows that if a city wants to improve mobility for everyone, it must look beyond the busy center and address the sparse networks on the edges. The researchers suggest that this method of using a honeycomb grid combined with statistical analysis can be used in other cities to reveal similar hidden patterns, helping planners make decisions based on clear evidence rather than guesswork.
Drowning in papers in your field?
Get daily digests of the most novel papers matching your research keywords — with technical summaries, in your language.