How to store bidirectional relationships - database

Question

I am writing some code to find duplicate customer details in a database. I'll be using Levenshtein distance.
However, I am not sure how to store the relationships. I use databases all the time but have never come accross this situation and wondered if someone could point me in the right direction.
What confuses me is how to store the bidirectional nature of the relationship.
I've started to put some examples below, but wondered if there is a best practice for storing this type of data,
Example data
id, address
001, 5 Main Street
002, 5 Main St.
003, 5 Main Str
004, 6 High Street
005, 7 Low Street
006, 7 Low St
Suggestion 1
customer_id1, customer_id2, relationship_strength
001, 002, 0.74
001, 003, 0.77
002, 003, 0.76
005, 006, 0.77
Not happy with this approach as it sort of infers a one way relationship between customer_id1 to customer_id2. Unless of course I include all relationships both ways, but that would double the amount of processing time and the size of the tables.
eg would need to include: 002, 001, 0.74
Suggestion 2
customer_id, grouping_id
001, 1
002, 1
003, 1
005, 2
006, 2

Answer 1

The way to deal with symmetric relations in a relational system is as follows:
choose a canonical form in which the symmetric pairs are stored, e.g. customer_id1 < customer_id2.
Define a view SYMM_TBL as select id1,id2,... from ... UNION select id2 as id1,id1 as id2, ... FROM ...
Decent systems ought not punish you in the performance area when querying this view.

Answer 2

What we have here is a graph in which each node has a relationship (edit distance) with every other node. This is not in the normal range of data models. It is also not a permanent feature of your database (assuming you resolve the business processes which led to the duplicate data) so it isn't worth sweating over the solution which best fits relational theory. What we need is a a practical solution.
Think of it as a matrix. If we go for the optimum processing we won't execute the duplicate scorings. So we score Address 1 against all the other Addresses, we score Address 2 against all the other Addresses except Address 1, we score Address 3 against all the other Addresses except Addresses 1 and 2, etc. And what we end up with is a bit like a football league table:
addr
1 2 3 4 5
addr
1 - 95 95 80 76
2 - - 100 75 72
3 - - - 75 72
4 - - - - 83
5 - - - - -
This data can best be stored in suggestion 1, a table of ID1, ID2, SCORE. Although we do need to pivot the data to get the output looking like that :)
In a proper league table there are two sets of scores - Home and Away - so the table is symmetrical. But that doesn't apply here, as the edit distance for 1 > 2 is the same as 2 > 1. However, it would make querying the results more straightforward if the result set included the mirrored scores. That is, for records (1,5,76), (2,5,72), etc we generate records (5,1,76), (5,2,72). This could be done at the end of the scoring process.
addr
1 2 3 4 5
addr
1 - 95 95 80 76
2 95 - 100 75 72
3 95 100 - 75 72
4 80 75 75 - 83
5 76 72 72 83 -
Of course, this is mainly a presentational thing, so it only needs to be done for display purposes, e.g. exporting the data to a spreadsheet. We can still get all the scores for, say, Address 5 in a readable fashion without miiroring the scores using a simple SQL statement:
select case when id1 = 5 then id1 else id2 end as id1
, case when id1 = 5 then id2 else id1 end as id2
, score
from your_table
where id1 = 5
or id2 = 5
/

Answer 3

As always it depends on what you want to do with the data once you've calculated it.
Assuming it's simply to identify or locate duplicates then your suggestion 1 is what I'd use, i.e. a second table that simply stores the pairs and the strengths. My only suggestion is to make the strengths a scaled integer rather than a decimal.