Generate near table for x number of neighbours using arcpy

Question

There are 3 likely scenerios that I am trying to capture near distances for:

1. An interchange subway station, which has 2 or more neighboring stations. That is, the station in question connects 2 or more major routes and has 2 or more neighboring stations.
2. A terminal subway station, which has only 1 neighboring station. This is the station at the end of the line.
3. An inline subway station, which has exactly 2 neighboring stations, one of either approach.

I am attempting to calculate a value one might call "average distance between neighboring stations"

The arcpy.GenerateNearTable_analysis() can handle two options: Distance to closest feature, and Distance between all features.

Does anyone have a clever method for solving for these scenarios? Note that each station is designated as "Interchange", "Terminal" or "Inline" in the attribute table under the field "StationType".

Added:

Here is some psuedo code based on @whuber's suggestion in the comments. I don't have time to figure this out just yet, so if anyone wants to take a stab at it you'll be rewarded with a checkmark! ;)

I have taken a look at the NetworkX library and it seems to work as I want it to.

Given the graph:

A —― B ―― C ―― D
     |
     E

as well as the nodes and links:

Nodes = ["A", "B", "C", "D", "E"]
Links = [("A", "B"), ("B", "C"), ("C", "D"), ("B", "E")]

def myFunction(node):
    identify the links that node belongs to
    count the number of links
    calculate the total link lengths
    divide the total link lengths by the number of links
    return someValue

Answer 1

I beleive your problem, as @whuber, suggested would best be represented in an Adjacency Matrix. That is, if you have the time and inclination to understand the theory behind it, rather than relying on a package to do the job for you.

For a given graph G, with vertices of {v₁, v₂,...,v_n} where _n is the number of vertices, you need to create a matrix of size M_i,j where i = n and j = n. Each vertex is then represented in the _ith row by the number of paths found to adjacent verticies in the _jth column.

Example below:

Given this mildly complex form of representing your relatively simple data, you will need to number your vertices in an arbitrary fashion, not representative of any logical order.

NOTE: Assuming no station loops upon itself, a _kth row will never have a value other than 0 in the _kth column. All definitions below assume this to be true

NOTE: Assuming there are no concurrent lines between the same station, all examples below assume that a cell value will only ever be 1 or 0. The example above also assumes bidirectional travel is permitted.

Rules to identify station categories:

1. Terminal

A terminal would be identified by a _kth row having a single column which does not have a value of 0, and which value is 1. See vertices 1, 2, and 3 in example 1 above.

2. Junction

A junction would be identified by a _kth row having more than two columns containing a value of 1. See vertex 4 in example 1 above, alternatively all vertices in example 3 above.

3. Inline

An inline station is signified by having exactly 2 columns in a _kth row where the value is 1. See all verticies in example 2 above. (Ignore the fact that {v₁, v₃} intersects {v₂, v₄}.)

Answer 2

You might try using Shapely. If you convert your arcpy points to shapely points, you can calculate the distance between individual points.

import arcpy
import shapely

arc_point1 = arcpy.Point(1,1)
arc_point2 = arcpy.Point(5,5)

shp_point1 = shapely.geometry.Point(arc_point1.X, arc_point1.Y)
shp_point2 = shapely.geometry.Point(arc_point2.X, arc_point2.Y)

distance = shp_point1.distance(shp_point2)
print "distance:", distance