From Scalar Rankings to Territorial Structures: A Topological Data Analysis Framework for Regional Competitiveness

For decades, economists and policymakers have tried to measure how well different places are doing. They look at regions, cities, and states, asking which ones are thriving and which are struggling. To answer this, they have traditionally relied on a simple tool: a single number. Imagine taking a complex portrait of a person—their health, their job, their education, their social life—and squashing all of that information down into one score on a test. That is essentially what current methods do for entire regions. They take dozens of different factors, such as how many people have jobs, how much money is invested, and how well people can access the internet, and combine them into a single ranking. This makes it easy to say that one region is "number five" and another is "number fifty." But in doing so, this approach flattens the landscape. It hides the fact that two regions might have the same score but achieve it in completely different ways, or that some regions sit in a messy middle ground that doesn't fit neatly into a line.

This is the problem a team of researchers from Plovdiv University in Bulgaria set out to solve. They argued that regional competitiveness is not a straight line where everyone can be ranked from best to worst. Instead, they proposed that it is a complex, multi-layered space where regions connect to one another in intricate patterns. To see these patterns, they turned to a field of mathematics called topological data analysis. In simple terms, this is a way of studying the shape of data. Instead of just counting points or averaging numbers, this method looks at how the points are arranged in space. It asks whether the data forms a smooth cloud, a set of distinct islands, or a web of loops and gaps. By using this approach, the researchers wanted to see if the map of European regional success looked like a simple ladder or something far more complicated.

The researchers focused on the European Union, looking at 117 specific regions known as NUTS 2 areas. These are the standard units used for regional policy across Europe. They gathered data from 2015 to 2024, but to ensure their map was accurate, they focused on the year 2021, which was the only year where they had complete information for all 117 regions across seven key areas. These areas included how well people were employed, the level of economic development, the ability to invest in new projects, access to the internet, social vulnerability, how much time households spent working, and the level of education and skills in the population. Rather than mixing these seven factors into one score, they kept them separate, treating each region as a unique point floating in a seven-dimensional space.

To visualize this space, the team used a technique called the Mapper algorithm. Think of this process as taking a high-dimensional cloud of data and projecting it onto a flat surface to see its structure. The algorithm groups nearby regions together into clusters, or "nodes," and draws lines between these nodes if they share common characteristics. The result is a network map that shows how regions relate to one another. When the researchers applied this to the 2021 data, the map did not look like a single, smooth hill where you could walk from the bottom to the top. Instead, it revealed a landscape with a central backbone, several branching paths, and distinct clusters.

The map showed that the European Union's regional competitiveness is organized into segments. There was a large central group containing regions from Austria, Denmark, Spain, Finland, and the Netherlands. These regions shared a very similar profile across all seven indicators, forming a coherent core. Nearby, but distinct, was another cluster made up of regions from the Czech Republic, Hungary, and Slovakia, showing a different but equally strong internal structure. Other nodes connected regions from Austria, Denmark, Sweden, the Netherlands, and Spain, while smaller, more isolated nodes held regions from Bulgaria, Romania, and Croatia. Crucially, the map showed that these groups were not just random collections of neighbors. Regions from different countries often ended up in the same cluster because their internal strengths and weaknesses matched, while regions within the same country sometimes ended up in very different parts of the map.

The researchers also checked if this pattern was just a fluke of the year 2021. They ran the same analysis on data from 2018, 2019, 2020, and 2022. In every single year, the map produced a similar shape: a structured network with a central backbone and branching offshoots, rather than a single smooth line. This suggested that the way these regions are organized is a stable feature of the European economy, not a temporary coincidence. The analysis also used a method to test the "holes" and "loops" in the data. It found that the space was not a solid, continuous block. Instead, it had gaps and distinct components, confirming that the regions are not just different in degree, but different in kind.

The findings challenge the old way of thinking about regional success. The study suggests that looking at a single ranking is insufficient because it hides the true structure of the economy. Two regions might have the same overall score, but one might be strong in jobs but weak in digital access, while the other is the opposite. A simple ranking would treat them as equals, but the topological map would show them as occupying very different positions. The researchers found that some regions sit in the middle, acting as bridges between different groups, while others are on the edges, disconnected from the main structures. This matters for policymakers because it means that a solution that works for a region in one cluster might not work for a region in another, even if they have the same rank.

Ultimately, this research offers a new way to see the economic landscape. It does not discard the old rankings but adds a layer of depth to them. By treating regional competitiveness as a complex shape rather than a single number, the study reveals that the European Union is made up of overlapping, recurring patterns of development. These patterns cut across national borders, linking regions that share similar economic DNA regardless of which country they belong to. The work shows that to truly understand how regions compete and grow, we must look at the shape of their relationships, not just the height of their scores.