So you have social graphs and networks aced?
So you understand social graphs and social networks? If you do, please check this and educate me and together we can pass our knowledge on to others.
If not, I’ve set up an A/B test for you here. I can guarantee that by the time you have played Social Chocolate, read the short tutorial, and played Social Chocolate a second time that you will radically improve your ability to influence your network.
Play Social Chocolate
To test your initial knowledge of social graphs, play Social Chocolate. Your goal is to complete 12 quests, or levels, and be given the key to the secret wall.
It’s hard. You have to persist. And of course, note your start and finish times! You want to beat your time next time you play!
Tutorial in social graphs
Even after playing Social Chocolate a few times, I was still struggling with a few quests. So I looked up the theory.
Connections of a node, vertex, or person in a social graph or network
The number of connections to any node or vertex or person is a measure of popularity.
We all understand that. How many followers do we have on LinkedIn, Facebook or Twitter?
Closeness of a node, vertex, or person in a social graph or network
Mathematicians calculate our closeness in a network as the shortest path to reach everyone
The person with the lowest closeness can reach everyone the quickest. If they put out a message , it will reach everyone in the shortest route.
Obviously, if the routes are short, there is not only a time & cost saving. The network is also less prone to failure and messages are less prone to distortion.
Interestingly, closeness is not equal to connections and the reason is that social networks are not homogenous in shape or density.
Someone with a high profile is connected with part of the network – but may have distant ties to other important parts of the network. A big fish in a small pond phenomenon.
Closeness means a short path to a lot of people not just having a lot of first degree connections. Think 150x150x150 not 450 x 50 x 15 x 10.
Betweenness in a social graph
A person has a high betweenness rating links two otherwise unconnected groups. Simply, if you take the person away, two people would no longer be able to reach each other.
Betweenness ratings are actually calculated, like the closeness rating, to reflect the shortest paths in the network. We have a high betweenness rating if a lot of people reach each other in the shortest way through us.
A person who is not particular “popular” within a group may be a valuable connection to a world over the group’s natural horizon.
The question to ask is whom do we connect who could not reach each other without us.
Eigenvector of a node, vertex, or person in a social graph or network
The eigenvector that most of us is familiar with is Google Pagerank. An eigenvector sums up not only the number of our links but the quality of the links to us.
A web page has a high page rank if other highly ranked pages connect to it.
Likely closeness, eigenvector isn’t everything. Betweenness adds unique value and tells us about the edge and the potential of our network.
Which role do you play in your network and which role do you prefer? Close knit, between or eigenvector connecting to powerful players?
Clustering or cliqueness in social graphs and networks
And of course, we have cliques. We know cliques from high school because they are unwelcoming and dismissive of outsiders.
What we don’t always grasp as teenagers is that cliques are redundant. If Jane tells everything to Mary and to Elizabeth, and they do the same, one of the three girls is actually redundant. As teenagers, we understand this vulnerability to exclusion and intuit why cliques are such bitchy groups. Now we know why in mathematical terms.
We need to note the cliques in our network but why belong to a group with redundant connections? The network is putting a lot of effort into duplication where they could be spreading out and connecting.
Most of us are still scared of being rejected by a clique but they only matter if they are very well connected to other people too. While that is possible on paper, it is less possible in real life where time is a real constraint. Because cliques are closed to other members, they can often be lost without damaging the network as a whole Contrast this with the damage of losing the mediation value of someon with “betweenness” or the contagion value of someone with “closeness”.
Taking action with knowledge about your social graph
When you draw your social graph on paper, you are probably concerned with the most obvious feature – how many connections do I have?
What you also want to know is
- What is the shortest path to everyone in the network? Who is contagious?
- Who connects to whom through me, and who connects me to others? What is my mediation value and who are the mediators in this group?
- Where are the cliques and are they useful cliques or neurotically redundant?
- Where is the shortest path between powerful players? It is quite possible that a relatively “unclose” or “unbetween” player connects two powerful players!
Test B: Replay Social Chocolate
Now replay Social Chocolate.
Even allowing for your earlier experience of the game, are you playing it any better? Are you more thoughtful and controlled?
I did the whole game in 7 minutes this time. How about you?
Comments
And comments for me? How can we improve the tutorial so that people develop an thoughtful approach to their social graph?
