## What is Topology?

#### Short definition:

Topology describes the spatial relationships between adjacent features. Polygon features (cadastre, land use) share edges, line features (street centerlines, rivers) share nodes.

#### Why do we need topologically correct data?

The most important function of a GIS is the analysis of spatial data. The results of the analysis can be only as good as the input data.

• In order to be able to perform network analysis on street or river data, the data should form a network. This requires connectivity between the polylines
• Building polygon features out of polylines requires connectivity between the source polylines
• Performing analysis on land use polygons or cadastral polygons require adjacency (no gaps or overlaps should exist between the polygons.

#### Types of topology:

• Explicit - The adjacency information is explicitly recorded (ArcInfo coverage). Line features are represented by Arcs and Nodes. The Nodes have internal numbers. Each Arc has explicitly recorded "From" and "To" nodes. Arcs are connected to each other if they share a common node. Polygon features are represented as set of Arcs recorded explicitly in the Polygon Arc List. In this fashion there is no duplication of geometries - the common boundary between two polygons is represented by a single Arc.
• Non Explicit - Each feature is stored as a single record (Shapefiles, Geodatabases). Line features (street centerlines) are recorded just as a set of coordinates (vertices). Node information is not explicitly recorded. The connectivity between two or more line features (street intersection) should be enforced by comparing the coordinates. Polygons are recorder in the same way. Two adjacent polygons are represented by two records. The common boundary is recorded twice.