Identifying polygons that lie between two polygons using ArcMap

Question

I am working on a single layer which includes an island constructed of multiple polygons (used to represent territories).

I would like to look at dispersal between territories, specifically, how many territories are traversed during dispersal. E.g. on the attached schematic island below, dispersal between territory 10 and 6 would result in 1 territory traversed.

I am using ArcMap 10.6.

Answer 1

Try to think the opposite way! It's basically a graph problem.

Pseudo-code:

1. Get the centroids for each cells. They are nodes.
2. Draw the paths.
3. Count the intersections between each path an cell's borders for each paths (subtract 1). They will eventually sum up if you need to take more than one edge to go from two nodes.

Search for 'dual graph' and you will eventually fall on Getting dual graph from QGIS.