Spatial - Polygon relationships

[Anudeep_Yalamuru]

Good morning All,

This is a Spatial Challenge. I have around 3000 polygons forming a geography of interest. 

Is it possible to match each polygon to its border sharing polygon and number them?

For e.g. - Polygon 1 shares border with 2,4 and 6. So, they get a number 1, 2, 3. Similarly polygon 2 shares border with 1, 4,5,7. So on and so forth.

Main motto is to get this information to run a catchment of interest but exclude any polygons away from the core of the catchment. 

Attached is a sample catchment. Also image shows primary catchment in Blue and an outlier marked in red.

Please provide your valuable feedback. 

[Qiu]

@Anudeep_Yalamuru 
Maybe I misunderstood your intention, but it seems that a Spatial Match tool can do the work.