What Social Networks can tell you

I’ve been browsing through Nicholas Christakis et al’s book entitled Connected: The Surprising Power Of Our Social Networks, and it inspired me to resume fiddling about with D-Wave's quantum computing software, Orion.

Here's a problem I formulated:

Let's say you have a class with 7 students, who have the following Names and Student Numbers:

You know the following about these students:

• Mary gossips with Josephine and Johnetta.
• Johnetta gossips with Peter.
• Peter gossips with James and Judas.
• Judas gossips with Isaac.

From that information you can construct the information network / grapevine below:



In the grapevine above, the blue vertices represent the males, the pink ones represent the females. The numbers represent the respective student numbers of each vertex (which represents a student), the lines connecting the vertices represent 'gossip relationships'. From the network above, we can tell that girls generally gossip together and guys generally gossip with other guys. As you can see from the chart, Johnetta is the bridge between the girls network and the guys network, and Peter is the bridge between the guys network and the girls network.

Analysis of this graph yields these metrics (never mind what they mean):



Now, lets say that you want to find the largest clique in the gossip network, and its respective constituents.

You would go to Orion, and enter this problem matrix (to be solved by the Clique Problem Solver):

P edge 7 8
e 1 2
e 1 6
e 2 6
e 2 4
e 4 7
e 4 3
e 7 3
e 7 5

And you would get a result that looks like this:

1100010 3

What this basically means is: The largest clique in the gossip network is comprised of three individuals; Mary, Johnetta and Josephine [1]. Generally, members of this cohesive subgroup will tend to share information, have homogeneity of thought, identity, beliefs, behavior, even food habits and illnesses.
Now, here is the beauty of this whole exercise, if you entered the same problem matrix in Orion and selected the Maximum Independent Set solver, you'd get this output:

1010100 3

This basically means that the greatest possible set of unrelated individuals will consist of 3 people; Mary, James and Isaac. These people basically don't have direct 'gossip relationships', and will exhibit the most differences from each other in terms of thought, identity, beliefs, behavior, even food habits and illnesses. If you want to form the most diverse workgroup from the gossip network, it would be made-up of those individuals [2].

What can this information be used for:

• Word of mouth marketing campaigns.
• Finding out who the real leaders of a group, like a terrorist cell, are.
• And whatever your imagination can conjure.

 I guess that you get the gist of it.

[1] Geordie Rose, the CTO of D-Wave Systems, the Quantum Computing Company, gave me a pointer on interpreting Orion's output. Thanks Geordie!
[2] Diverse workgroups are the best at solving complex problems.