Connection

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A connection is a link between political units sufficient to form a district with just those units. If contiguity is the only form of connection then districts can be formed that leap bodies of water and mountain ranges with no convenient way to travel from one part of the district to another. This definition of connection avoids that type of district. Connections are also used to measure the erosity of a district.

A political unit can be represented by a node that is the political center of that unit. For a county the node is the county office where the elected officials meet. For a city or town the node is the city or town hall. For a precinct the node is the polling place. Units are connected based on the path that connects their nodes.

Two units are locally connected if there is a continuous path of public roads that allow one to travel between the two nodes without entering any other unit. Local connections can include seasonal public roads. A local connection path can be traced over water without a bridge if there is a publicly available ferry that provides part of the connection. Units smaller than a county must be locally connected within a district.

Two counties are regionally connected if there is a continuous path of numbered state or federal highways that allow one to travel between two nodes without entering any other county. If a node is not on a numbered highway, then the connection is measured from the point of the nearest numbered highway to the node. The path may only use roads that are generally available all year. Regularly scheduled year-round ferry service may be included in the path of a regional connection. Counties must be regionally connected to be connected, except that counties within a cluster are connected if they are locally connected.

There is often more than one possible path to connect to nodes. For both local and regional connections the connection between two units is considered to be based on the path that takes the shortest time as determined by generally available mapping software.

When a chop splits a unit each connection from the whole unit is assigned to one of the fragments that results from the chopped unit. The fragment that has the border containing the connection path is assigned the connection. The fragments are connected to each other if there are local roads that allow travel directly between the parts without going into any other part or unit.

Example 1

Connect5A.jpg

In this example there are 5 geographic units labeled A through E. The nodes are indicated with stars and the roads are shown with heavy lines.

D is connected to both C and E each by a single path.

A is connected to both B and D, each by two separate paths. The shortest one by time would count as the connecting path.

A is connected to C by a single path. The fact that it dips down towards B first doesn't disqualify it since it stays only in A and C.

E is connected to both A and B by virtue of a road that runs along the boundary of A and B.

B is not connected to C. All paths between them cross into other units.

The equivalent graph for this example reduces each connection to a single link between nodes.

Graph5A.jpg

Example 2

Connect4A.jpg

In this example there are 4 geographic units labeled A through D. The nodes are indicated with stars and the roads are shown with heavy lines. The thick shaded area running roughly vertical represents a natural barrier such as a river.

A, B and D are all mutually connected to each other.

C is connected to B, but not to A or D. The path from C to D must go through either A or B. One path from C to A initially goes into A but then goes through D before reaching the node of A.

The equivalent graph keeps the valid connections as links between nodes. For the purposes of the graph, the actual location of the node doesn't matter, so they can be shifted to make the links easier to see.

Graph4A.jpg