Contiguity

Contiguity is a geographic element of neutral redistricting criteria. In its simplest form contiguity requires that all areas in the district touch the same area, that is there are no separate pieces that make up the district.

Some states place restrictions on contiguity. The most common restriction is to bar point contiguity. Point contiguity exists when an area of the district touches the rest of the district at only a single point. Two same-colored squares that are adjacent on a diagonal of a checkerboard are point contiguous.

Some states require that it be convenient to travel within a district. This requires knowledge of the roads in the state. For example there can be a requirement that all areas of the district be reachable from each other by road. Roads can be limited to public roads, all season roads, and can include ferries. Use of major highways to link larger areas of a district can also encourage districts that represent communities of interest.

The idea of dividing a large area into smaller contiguous pieces allows redistricting to be translated into a problem in graph theory identifying connections or links between geographic units in a plan. A complete set of all possible links define contiguity in the broadest sense. Restrictions on allowed contiguity removes select possible links from consideration.