Handling Adjacencies

We construct the adjacency graph on our set of precincts (the nodes of our graph) by drawing an edge between any two VTDs that are adjacent.

Note

An adjacency graph is different from the dual graph of the VTD geometries, which we would construct by drawing an edge between two VTDs for each edge that they share. An adjacency graph, by contrast, never has multiple edges between two nodes.

There are two concepts of “adjacency” that one can apply when constructing an adjacency graph.

  • Rook adjacency: Two polygons are adjacent if they share one or more edges.

  • Queen adjacency: Two polygons are adjacent if they share one or more vertices.

All Rook edges are Queen edges, but not the other way around. Many congressional districts are only Queen-contiguous (e.g., they consist of two polygons connected at a single corner).

The names Rook and Queen come from the way Rook and Queen pieces in Chess are allowed to move about the board.

Note

The GerryChain Graph is based on the Graph from the NetworkX library. We recommend consulting the NetworkX documentation to learn how to work with nodes, edges, and their attributes.