The methodology of the compactness index

Compactness is an abstract idea — to compare districts, it has to be made measurable. This article shows how the research builds its own, three-dimensional compactness index: what dimensions and indicators it consists of, how differently scaled measures become comparable, and why it is specifically the outer districts that it sets against one another.

1. International methodological roots

International practice typically measures compactness using multidimensional indicator systems. These usually combine density measures (population, housing or job density), land-use measures (functional mix, land-use mix) and transport and accessibility measures (public-transport access, street-network connectivity, conditions for active travel).

Ogrodnik's (2019) compact-city indicator system is built on compactness, accessibility, the transport system, brownfields and community spaces — and stresses that indicators should, wherever possible, be quantitative, spatially comparable and based on available data. In contemporary research, approaches drawing on geospatial and open data sources are playing an ever greater role: Lan et al. (2021), for instance, developed a functional compactness index by integrating geodata, point-based service data and OpenStreetMap-based road-network data.

2. Three dimensions, with two to three indicators

The research's own index connects to these methodological directions but adapts them to the particular features of Budapest's outer districts. The indicator system is built on three main dimensions that together capture the basic conditions of compact urban functioning. The three dimensions and their indicators:

• Urban density — housing density, job density, residential population density.
• Functional mix — land-use mix, jobs-to-housing balance.
• Mobility — stop density, street-junction density, cycling provision.

Each dimension is made up of two or three indicators. The index thus follows the dimensions that appear most frequently in the literature, while being specifically tailored to the available district-level, statistical and geospatial data.

3. Normalisation and aggregation

Measures with different units cannot be compared as they stand — a population density and a street-junction density move on different scales. The research therefore transformed the indicators onto a uniform scale of 0–1 using min–max normalisation, then averaged them by dimension. The simple arithmetic mean of the three dimensions' values yields each district's compactness index.

This structure is what allows a district's relative level of compactness to be expressed in a single, comparable number — while the sub-indices preserve how much each dimension contributes to the result.

4. The "urbanised area" and the two exceptions

For most indicators expressed per unit of area, the calculation used not the district's full administrative area but the urbanised area. This is the combined extent of the land classified by OpenStreetMap as residential, commercial (commercial and service), industrial and retail. The reason for introducing the concept is to give a more accurate picture of the districts' true compactness: it leaves out those areas (e.g. agricultural or disused land) that are not part of everyday city life yet could distort a district's values.

For two indicators the calculation departs from this. For residential population density, only the extent of residential areas was taken into account, because this more accurately reflects the actual spatial concentration of the housing function. For cycling provision, the figure was calculated against the full area, since several cycle routes pass through forest or through land inactive from the standpoint of city life — these do not belong to the urbanised area, yet they can shorten journeys, and recreational use favours the spread of cycling.

5. Why does it compare outer districts?

The aim of the index is not to determine an absolute compactness value but to make a relative comparison of the Budapest districts examined against one another. It is therefore important that only districts in a similar situation are placed in one field. The shared feature of the districts included is their peripheral position — so not every outer district is part of the sample (e.g. Districts 19 and 20). Also left out were those outer districts that touch the "inner zone" element of the zoning system used in the Budapest Settlement Plan, namely Districts 2, 11 and 12.

It is this narrowing that makes it meaningful to read where a district stands among others in a similar peripheral position, and in which dimensions the most important development gaps appear. Where District 18 specifically stands in this ranking is explored by the next part of the series: Compactness results for District 18