GIS the spatial relationships between connecting or adjacent features, e.g., arcs, nodes, polygons, and points —note 1. the topology of an arc includes its from- and to-nodes and its left and right polygons, if the arcs are used to describe polygons —note 2. topological relationships are built from simple elements into complex elements: points (simplest elements), arcs (sets of connected points), polygons (sets of connected arcs), routes (sets of sections that are arcs or portions of arcs), and regions (sets of polygons) —note 3. redundant data (coordinates) are eliminated because an arc may represent a linear feature or part of the boundary of a polygon or part of a region boundary —note 4. topology is useful in GIS because many spatial modeling operations do not require coordinates, only topological information, e.g., to find an optimal path between two points requires a list of which arcs connect to each other and the cost of traversing along each arc in each direction; coordinates are necessary only to draw the path after it is calculated —see arc-node topologyThis definition last updated 10/01/2008