Social Relationships don't count until they count

There is a game called "the Six Degrees of Kevin Bacon" which tries to link between any Kevin Bacon and any other actor in less than six steps.  This is a popular version of the "small world" thesis put forwards by Stanley Milgram.  In these days of Social Media and "relationships" there is a massive hype around farming these relationships with an implicit assumption that someone with lots of relationships is more valuable than someone who doesn't

The problem is that in reality this is all a version of the Travelling Salesman problem with everyone assuming that every link is of the same value.  The reality is that links have different values based on their strengths so understanding how individuals are actually related is significantly more complex than many social media "experts" would have you believe.

What do I mean by this?  Well my "Obama Number" is 4 as, via my wife, I can trace to Obama in 4 steps with each individual step being reasonably strong.  By reasonably strong I mean that each link has met the previous link several times and probably could put a name to the face.  Now the variability of strengths on these links is huge, from my wife (hopefully a strong link) to people who move in similar social circles and then into the political sphere where the connection to Obama is made.

I've a Myra Hindley number of 2 as I have a friend who met her more than once (before her conviction).

So for Republicans and Tea Party nut-jobs this means that its 6 steps max from Obama to a child killer.  Does this mean there is a relationship worth knowing or caring about?  Nope.

So how to weight relationships and how to weight each step within the graph?  Well this is actually pretty simple.  Lets say A has a relationship to B via a social network, lets call that a score of 0.0001.  Lets say that B (who is the person) has a score of 1.0.  So for each interaction between two individuals you then look at the strength from A to B.

1. How many times does A post to B?  If  > 10 then add 0.0001
2. How many times does B post to A?  If > 10 then add 0.001 (i.e. B connects to A, hence more likely to be mutual) for each multiple of 10
3. How many times does B indicate that they are at the same place as A? If > 10 then add 0.001 per 10
4. How many times does a voucher provided to A get used by B? If  > 10 then add 0.1 per 10
5. Are they directly related or married? If cousin or less then add 0.5
6. Do they work closely together? If within 1 reporting hop add 0.2
7. How many times have they met? If > 10 then add 0.05 per 10

What I'm saying is that its actually the interactions that matter to back up the social experience rather than the existence of a social link.

So while from Obama to me is 4 steps I'd say that overall its pretty weak (0.8 * 0.2 * 0.2 * 0.2 =  0.0064) a .64% link which really means I'm not worth lobbying to get influence over the US president.

This is where the combination of Big Data analytics could really deliver value, by understand the true weightings on individual relationships and from that determining the real genuine paths to the maximum possible market for the minimum effort.

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