In 1736, the mathematician Leonhard Euler published a paper that arguably started the branch of mathematics known as topology. The problem that led to Euler’s work in this area, known as “The Seven Bridges of Königsberg,” is described in the accompanying article “Conundrum Inspires Topology.” More recently, the United States Census Bureau, while preparing for the 1970 census, pioneered the application of mathematical topology to maps to reduce the errors in tabulating massive amounts of census data. Today, topology in GIS is generally defined as the spatial relationships between adjacent or neighboring features.

Mathematical topology assumes that geographic features occur on a two-dimensional plane. Through planar enforcement, spatial features can be represented through nodes (0-dimensional cells); edges, sometimes called arcs (one-dimensional cells); or polygons (two-dimensional cells). Because features can exist only on a plane, lines that cross are broken into separate lines that terminate at nodes representing intersections rather than simple vertices.

In GIS, topology is a collection of rules that, coupled with a set of editing tools and techniques, enables the geospatial data to more accurately model geometric relationships. Topology is defined through a set of rules that define how features may share a geographic space and a set of editing tools that work with features that share geometry in an integrated fashion. A topology is commonly stored in a geodatabase as one or more relationships that define how the features in one or more feature classes share geometry. The features participating in a topology are still simple feature classes—rather than modifying the definition of the feature class, a topology serves as a description of how the features can be spatially related.

*Image courtesy of ESRI*

## I’ve been doing fine up to now, why do I need to use this as well?

As stated above, topology defines rules for the geospatial data and will prevent issues with gaps or overlaps which occur with even the best editing. Both ESRI software and QGIS use topology extremely well, though the documentation for the ESRI software is a little more clear. There is a great poster which ESRI have on their website which you can download here, it might start to help you see how useful topology can be,

Put simply, when you build field parcels, you NEED topology so that fences ALWAYS follow the polygon boundary or that there are never gaps between polygons (fields). You NEED topology when you create urban topography – house must ALWAYS sit within a property boundary, a road MUST ALWAYS meet a field parcel.

It is not only feature creation or survey work where topology is necessary, I am finding a lot more work now requiring the use of spatial analysis based on topology, for example, calculating the number of features touching another feature (this only works properly with features built with proper topology).

## Getting Started

Topology is one of those things, like enabling the “snapping tool” or using the “create faeture from selection” that you don’t realise you need in your life until you start using it.

So to get things started off, depending on whether you are “ESRI” or “QGIS” have a look at one of the tutorials below. Even if you don’t try it, have a look to see what topology could do for you….

QGIS – Feature topology lesson

ArcGIS – Editing shared features with map topology

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## Further Reading:

ArcUser – Understanding Topology

ArcGIS 10.1 Help – Creating a map topology

QGIS (Youtube) – Topology Checker Plugin demonstration

Topology in QGIS 2.0 – Blog by rjhale

Wikipedia – Geospatial Topology