## TOPOLOGY

The topologic model is often confusing to initial users of GIS. **Topology is a mathematical approach that allows us to structure data based on the principles of feature adjacency and feature connectivity. It is in fact the mathematical method used to define spatial relationships.** Without a topologic data structure in a vector based GIS most data manipulation and analysis functions would not be practical or feasible.

**The most common topological data structure is the ****arc/node**** data model.** This model contains two basic entities, the *arc* and the *node*. The arc is a series of points, joined by straight line segments, that start and end at a node. The node is an intersection point where two or more arcs meet. Nodes also occur at the end of a *dangling* arc, e.g. an arc that does not connect to another arc such as a dead end street. Isolated nodes, not connected to arcs represent point features. A polygon feature is comprised of a closed chain of arcs.

I**n GIS software the topological definition is commonly stored in a proprietary format. **However, most software offerings record the topological definition in three tables. These tables are analogous to relational tables. The three tables represent the different types of features, e.g. point, line, area. A fourth table containing the coordinates is also utilized. The *node table* stores information about the node and the arcs that are connected to it. The *arc table* contains topological information about the arcs. This includes the start and end node, and the polygon to the left and right that the arc is an element of. The *polygon table* defines the arcs that make up each polygon. While arc, node, and polygon terminology is used by most GIS vendors, some also introduce terms such as *edges* and *faces* to define arcs and polygons. This is merely the use of different words to define topological definitions. Do not be confused by this.

**Since most input data does not exist in a topological data structure, topology must be ****built**** with the GIS software. **Depending on the data set this can be an CPU intensive and time consuming procedure. This building process involves the creation of the topological tables and the definition of the arc, node, and polygon entities. To properly define the topology there are specific requirements with respect to graphic elements, e.g. no duplicate lines, no gaps in arcs that define polygon features, etc. These requirements are reviewed in the Data Editing section of the book.

**The topological model is utilized because it effectively models the relationship of spatial entities**. Accordingly, it is well suited for operations such as contiguity and connectivity analyses. Contiguity involves the evaluation of feature adjacency, e.g. features that touch one another, and proximity, e.g. features that are near one another. The primary advantage of the topological model is that spatial analysis can be done without using the coordinate data. Many operations can be done largely, if not entirely, by using the topological definition alone. This is a significant advantage over the CAD or *spaghetti *vector data structure that requires the derivation of spatial relationships from the coordinate data before analysis can be undertaken.

**The major disadvantage of the topological data model is its static nature.** It can be a time consuming process to properly define the topology depending on the size and complexity of the data set. For example, 2,000 forest stand polygons will require considerably longer to *build* the topology that 2,000 municipal lot boundaries. This is due to the inherent complexity of the features, e.g. lots tend to be rectangular while forest stands are often long and sinuous. This can be a consideration when evaluating the topological building capabilities of GIS software. The static nature of the topological model also implies that every time some editing has occurred, e.g. forest stand boundaries are changed to reflect harvesting or burns, the topology must be rebuilt. The integrity of the topological structure and the DBMS tables containing the attribute data can be a concern here. This is often referred to as *referential integrity*. While topology is the mechanism to ensure integrity with spatial data, referential integrity is the concept of ensuring integrity for both linked topological data and attribute data.