Areas of polygon within different buffer overlaps using ArcMap

Question

I have two shapefiles, one with some 100 buffers and one with polygons of which I want to calculate the areas within the buffer overlap areas, but with regards to the adjacent buffers. E.g. the area sum of the polygons within the overlap between 2 and 4, 3 and 2 etc.

So far, I have calculated the overlap zones by using the intersections tool and then intersect those areas again with the polygon shapefile. Summing up manually is a very tedious job, but I cannot get my head around how to achieve this automatically with ArcMap.

Edit: I maintained all the original attributes of both shapefiles (centroid, unique ID etc.) Each buffer has an unique ID, which has been transfered to the clusters as well. I have duplicates within the intersection shapefile depending on the number of buffers which intersect. Same applies to the polygons whose areas I want to calculate.

Answer 1

Approach below is using arcpy Geometry methods and tested on shapefile as a storage.

1. Run Polygon neighbours tool with "Include both sides of neighbor relationship" unchecked.
2. Transfer buffer centroids to above table, and create XY events from it
3. Buffer resulting points using any distance: Their table should look like this:

Run following field calculator on field Shape of layer OUTPUT:

G = arcpy.Geometry()
aDict = arcpy.management.CopyFeatures("BUFFERS",G)
def IsectPairs(fromN,toN):
 A = aDict[fromN]
 B = aDict[toN]
 U = A.union(B)
 SD = A.symmetricDifference (B)
 D = U.difference (SD)
 return  D
#---------------------
IsectPairs( !src_FID!, !nbr_FID! )

OUTPUT:

In theory

D = A.intersect(B,2)

is equivalent of these 3:

 U = A.union(B)
 SD = A.symmetricDifference (B)
 D = U.difference (SD)

But intersect method on polygons does not work in ArvGIS 10.8. It didn't work in all previous versions either. It works in 30+ yo ArcView 3.

1yo UPDATE:

My fault, my apologies to ESRI, because per documentation it should be 4 (!) instead of 2:

D = A.intersect(B,4)

So this is correct expression:

G = arcpy.Geometry()
aDict = arcpy.management.CopyFeatures("BUFFERS",G)
def IsectPairs(fromN,toN):
 A = aDict[fromN]
 B = aDict[toN]
 D = A.intersect(B,4)
 return  D
#---------------------
IsectPairs( !src_FID!, !nbr_FID! )