# Topology

GIS definitions (slightly different from graph theory in mathematics)

• Topology: rules and behaviours for points, lines, and areas that share geometry.  A single point can be part of multiple lines or perimeters, and a line can be a feature like a river and part of the perimeter of a state and a county.
• Edge: a side of a polygon, between to vertices, or a segment of a line between two vertices
• Vertex: point where two edges meet.
 A single line shown in blue is part of three features: the river, the state boundary, and a county boundary.  The river is a line, and the boundaries could be either lines or polygons for perhaps states and counties.  Becasue the lines segments are shared, only the color from the last line drawn will be visible.

Ideally, the common line that appears in multiple features would be digitized and stored once, and all the features would have the exact same coordinates.  Then if the line was edited, the changes would propogate to all the features.  This is not possible with  Shapefiles, but is possible with much more complex data structures.  The simplicity of just storing and rapidly displaying the data outweighs the advantages of saving the topology, since those advantages really only come into play when editinig the data.

Rules for digitizing with topology:

• There must be a node at every point where lines cross; they must meet at the node.
• Lines must hit the node exactly; the GIS program should have a snapping function to insure this.
• Digitize common borders only once.
• Close all areas, with the snapping function so the first and last points of the polygon are the same.

last revised 12/4/2017