# Tag: social graph

### 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.

#### 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”.

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?

And comments for me?  How can we improve the tutorial so that people develop an thoughtful approach to their social graph?

# What can I count on?

Yes,”count on”, “depend upon”, “know that you will do as surely as the sun rises and sets”.  And you ask the same question of me.  What am I 100% committed to doing for you?  That is the foundation of our relationship.

Our relationship may be more. It will include

• What do we do together?
• What do we celebrate together?
• How important is our relationship compared to other relationships?  What priority does it have?
• How relevant is our relationship to coping with the trials and tribulations and  developing the opportunities already present?

Most people only look at the priority of a relationship.  They want total loyalty – which is unrealistic.  Blood is thicker than water, after all.  What counts is the essence.

What, what is it that I can count on you to do?

## Disciplines study trust from different angles

• Economists use game theory to look at our interests and the constraints that lead us to be quite predictable.
• Politicians look at our interests and the alliances we make with others to pursue them.
• Poets urge us to put “ourselves inside the river” – to pay attention to the story unfolding around us
• Clinical psychologists measure our self-efficacy – how do we rate our competence to achieve something that seems hard
• Educational psychologists have championed collective efficacy – how do we rate the competence of our colleagues?
• Positive management scholars ask “what do we do well” and “what will we do more of”?
• Toyota management specialists tell us to take our ideas and run a formal experiment – find out what matters and respect it.

## Do we understand the nature of our commitment to each other?

Collective efficacy, the tool used by educational psychologists, illustrates well where I am going.  Collective efficacy  is measured by the specific question: “how good is X at his or her job?”  Questionnaires and simple ratings are neat and tidy.  Cool stuff – we get a number and the higher the number, the better the school.  Important to know and understand.

It’s also important to put our finger on the nub.  Can we describe our relationships in simple, accurate and concrete language?

• What is it that we are totally committed to do for the people around us?  In what way are we utterly dependable to others?
• In what way are they utterly dependable to us?
• In what way is this, our reciprocated commitment, important to our lives?
• And are we talking about “what is” rather than “what isn’t”?  Are we talking about the relationship as it is, rather than as we want it to be?

## Do we understand the network of commitments that are important to the good life?

I’ve always felt that there are 10 or so people in my life whom I need to trust entirely.  They include my banker, my mechanic, my butcher and my baker.   When 3 or 4 are unreliable, my life becomes miserable indeed.

I am magnificently happy though when I am surrounded by people who share a mutual commitment to me.  It may be a small commitment. It may be a relatively small circle.

But that sense that we are competent, dependable and principled is very important.

(As opposed to fickle, corrupt and inept – a phrase I heard on BBC.)

Our lives are as big and as magnificent as our sense that people around us are good people.

Celebrating that goodness will boost your sense of well-being.

• It’s worth putting our finger on the small contribution each person makes to our lives.
• It’s worth putting a name to its essential essence – not to what we want to change – but to what will never change because it is the essence of the person and what they will do for us.
• It’s worth hearing the words of others as they see what about us is predictable and counted upon (because they’ve observed our essence and don’t try to change us).

When we have mapped our network, or social graph, of commitments, when we begin with what is rock solid, how do we feel?  How much energy have we liberated?

I’d be interested to know how you approach these questions.  Have a great weekend.

## Facebook is “who knows who” in London?

If you want to find someone in the UK, go to Facebook.  1/3 of the country is there and more than 1/2 of our internet users are there.   3/4 of Londoners are there.

Because so many Londoners are on Facebook, it is also London party.  Just over a quarter people in the UK live in or close to London, but nearly half of Facebook members are Londoners

Almost everyone who uses Twitter is on Facebook.  Its easier to say that 1 out of 7 Twitter users do not use Facebook.

But as 6 out of 7 of their Twitter friends will be on Facebook, they are well connected!

The question is whether you can find the other 2/3 of UK residents through your Facebook network.  It would be work a try, wouldn’t it?  Can you find and meet anyone of the 61 million people beginning with your Facebook network?

## The numbers

I made the diagram using the online chart maker, Chartle, using the numbers below, some of which I got from Google Adplanner on 2 August 2009 and some of which I got from Wolfram Alpha.

1.  People in the UK : 60.8 million
2.  Internet users in UK : 40 million (66%) (2006 – probably higher now)
3.  People in the work force before the credit crunch:  29 million (almost 50%)
4.  Young people 13-16, 16-18 and 18-24 who are not in the workforce but who are active internet users: Unknown (do you know?)
5.  Retired people who are not in the workforce but who are active internet users : Unknown (do you know?)
6.  People in the London : 7 million  (about 13.5% of  UK residents)
7.  People in the wider London metropolitan area : 13 million (about 27% of UK residents)
8.  People who use Facebook in UK : 22 million ( about 35% of UK residents and 55% of UK internet users)
9.  People who use Facebook in the wider London metropolitan area: 10 million (77% of residents, 25% of UK internet users, 17% of UK residents, 45% of Facebook users)
10.  People who use Twitter in UK: 3.5 million (6% of UK residents and 8% of UK internet users)
11.  People who use Twitter and Facebook in UK: 2.9 million (7 % of UK internet users, 13% of Facebook users and 83% of Twitter users)
12.  People who use Twitter and not Facebook in UK:  0.6 million (17% of Twitter users and 1.5% of UK internet users)
13.  People who use Twitter in the wider London metropolitan area:  1.8 million (18% of London internet users)
14.  People who use Twitter and Facebook in the wider London metropolitan area : 1.5 million (15% of London Facebook users)
15.  People who use Twitter and not Facebook in the London metropolitan area : 0.3 million (3% of London internet users)