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So It's a Small World--So What?

Dick van Vlooten
Netherlands
6 February 2004

Did you know that you could reach anyone in the world within an average of six steps? That is, a friend of a friend of a friend of a friend of a friend knows the president of the United States, or the queen of the Netherlands, or the president of France?

Amazing, isn't it? But then again, so what? How is this knowledge going to help you in your quest for information, funds, a job, or housing? Well, somebody out there has the answer that you are looking for. And the fact that it is a small world implies that you can reach that person, if you only knew how.

Reaching the world in six steps

In 1967, sociologist Stanley Milgram[1] came up with the famous concept of six degrees of separation: the notion that every American is connected to every other American by a chain of some six people. The concept of the "small world" was born.

Last year, Peter Sheridan Dodds, Roby Muhamad, and Duncan J. Watts reported the results of the Columbia Small World Research Project[2]: More than 60,000 e-mail users tried to reach one of 18 target people in 13 countries by forwarding messages to acquaintances. Out of 24,163 chains, only 384 reached their targets--just 1.6%.

Shorter chains had a very much higher success rate than longer chains, and further analysis showed that lack of interest or incentive was by far the most important reason for chains failing to reach the target.

What do we learn from these figures? That you can reach any person within six steps on average. But it is not easy!

Somehow, that feels intuitively right. In all honesty, I don't think that I personally could reach President George W. Bush with just a few e-mails. But then again, I do have a cousin in Utah. Who knows whom she knows?

Hubs, connectors, and cliques--how small is small?

Social networks are cliques. They consist of groups of individuals that are closely interconnected and connected with other cliques. Some cliques are fairly isolated; others have more connections to other cliques. And groups of cliques form islands.

For instance, I'm passionate about playing golf, and therefore my personal clique--see Figure 1--is my own golf club. (As a matter of fact, the high handicap chapter ... but that will change and I will amaze Tiger, someday!).

Figure 1. Personal clique

This clique very easily connects to another golf club when I play a competition game with someone. If we have a nice day, and a laugh, we have become acquaintances. And I am a connector (Figure 2).

Figure 2. Connecting cliques, with me as connector

And because my new golfing friend knows other golf clubs, courses, and players too, together we form the island of golfers who play in clubs.

Which in itself is a section of "all golf players," another, and bigger, island. That in turn could be seen as a subset of all sports-minded people. And so on and so forth (Figure 3).

Bear in mind that not all networkers are equal or equally connected. Not even close! Whereas most people have some 200 to 300 contacts, Franklin Delano Roosevelt's appointment book had about 22,000 names in it. So the average number of connections that people have and the extreme are very far apart. As a matter of fact, if you start looking, you will find people with 15,000 links, some with 10,000, and very, very many with about 250.

Figure 3. Interconnecting cliques and islands

This is a structural characteristic of networks. Albert-László Barabási[3] showed that the relation between the number of links an individual has and the number of people having that specific number of links is exponential. In Figure 4, you can see what that means.

Figure 4. Exponential differences in numbers of connections

People like FDR are known as "hubs." A hub connects many other people, by virtue of that person's enormous address book. And we will need hubs to connect to people far away from our cozy little daily life.

So connectors are people who connect cliques, and hubs connect lots and lots of cliques. The opportunities to connect are there, on average, in six steps, but how to find our way?

To the rescue--identities

Watts, Dodds, and Newman[4] introduce the notion of identities:

"Individuals in social networks are endowed not only with network ties, but identities: sets of characteristics that they attribute to themselves and others by virtue of their association with, and participation in, social groups." And they say, "people divide the world into a hierarchical classification." For instance, take sports and golf.

Level 1: Sports-loving people

Level 2: Golf-loving people

Level 3: Golf-playing people

Level 4: Golf club members (you don't have to be a member of a golf club to play golf!)

Level 5: Competition-playing golf club members

Level 6: Me and the other competition-playing golf club members in my club

What's more, identities are multifaceted (see also Dana Boyd[5]).

Take me, for instance. I don't only play golf. No sir! I also live in Deventer in the Netherlands (geographical class), am interested in networking and publish on that subject (and so am findable through the Internet), am a father of two sons and active in school. ...

So, if you were looking for me and you knew about my love of golf, this is how you could find me, through this golf cascade. If you know more about me, there are more search chains.

Here is the same exercise the other way around, using two classifications: For me to connect to President George W. Bush, I personally would start with the geographical classification and then with a professional one. Or in plain English: First find someone in the United States, and then someone in the Civil Service.

Another example: Let's suppose you are going to an international seminar and you want to speak to one of the other delegates, a celebrity from South Africa, that rather well-known lawyer, ex-convict, and great leader Nelson Mandela.

What routes could you think of? Think first, then read on. ...

Some possibilities:

• Geographical—first, find a contact in South Africa, then take the next steps closer to Nelson. Maybe you are into wines and can get in touch with a wine importer who does business in South Africa.
• Professional--find another statesman. (That could be a very short chain if you are politically involved yourself.)
• Through the occasion--talk to someone on the organising committee, if you are not already a member of it.
• Through Amnesty International--they have done a lot for him. And of course you just happen to be an active AI member?
• Through artists--there are artists who have good connections to Mr. Mandela. And you are in a band yourself.

Which chain will work best is unpredictable. This is partially because you are depending on what happens on next steps and partially because it depends on where you can start asking, on your own cliques.

What cliques are you in?

When addressing students from INFORMS (the Institute for Operations Research and Management Sciences) in 2003, Michael Trick[6] of Carnegie Mellon University compared the social activities of students in 1970 and 1995. As Figure 5 shows, these days, people apparently spend their time working, studying, eating, and watching TV! The trouble with having best friends who are soap actors is that they don't mail back. ...

Figure 5. Declining participation in social activities

Wayne Baker[7] names at least eight different possible categories of social groups that you could be active in: professional, work, political party, religious institution, charity work, sports, arts, and personal development. Most people, he suggests, are involved in two groups, besides that pertaining to their work or study, and their family.

This is a moment of truth: How many social groups are you active in? Through what cliques could you start a search for Mr. Mandela or President George W. Bush? One, two, or more?

And now: finding

We've covered the basics:

• There is a "small world" with at least the possibility to reach people within a reasonable number of steps.
• People have identities and characteristics with which you can distinguish them.
• There are connectors that connect different groups of people that know each other rather intimately.
• There are even hubs, people who know a lot of others and therefore are great connectors.
• And you are an active member of (I don't know how many) social groups or cliques.

Here are two easy-to-remember principles that will help you to apply this knowledge.

Principle 1--Short chains work

Let's suppose you are looking for a house. You consider your friends. Who would know where you could find somewhere to live? You call the most likely friend and ask if he knows of any nice houses in a certain neighbourhood which are for sale. He might say: "Yes, of course." Or, more probably: "No, why? Are you looking?"

After explaining why you are looking for a house, when you want to move, and discussing the pros and cons of the area you want to move to, the next question you're likely to ask is: "Do you know somebody who might be able to help?" You have started a chain. Now your friend starts thinking--who do I know who would know this? And am I willing to name him?

So you get the name. You thank your friend (ALWAYS) and carry on.

You go to the friend of your friend. You introduce yourself, you mention the mutual acquaintance, do the small talk, and again ask: "Do you perhaps know a house in the neighbourhood XYZ?" And when the answer is no, you ask the same second question: "Do you happen to know ... ?" Same ritual. Thanks a lot. Carry on.

This stops after friend number three.

Why? Because you are now starting to have a long chain. The social distance is getting very long. The friend of a friend of a friend does not know you, nor your friend. So you are starting to get lower and lower on the ladder of the five modes of human interaction. You haven't built up a relationship with this person.

And here you have a problem. Your chain stopped, and you still are living in a camper van. In the winter. And it's cold.

Or not. If you applied:

Principle 2--Create multiple chains

You wouldn't have started just one search chain, would you? Oh no, you'd have asked in other directions as well! Because you are in more then one clique. Your identity is multifaceted. And so is that of the person owning the house that you would love to buy.

Conclusion

Human networks form structures that allow for the fast finding of information. But the structure alone is not enough! At the very least, to exploit this structure, you need to be active in multiple cliques and search them in a variety of ways.

References

1. J. Travers and S. Milgram, Sociometry 32, 425 (1969).
2. P. S. Dodds, R. Muhamad, D. J. Watts, "An experimental Study of Search in Global Social Networks, Science 301, 827 (2003).
3. A. Barabási, Linked (Plum, 2003).
4. D. J. Watts, P. S. Dodds, M. Newman, "Identity and search in social networks," Science 296, 1302 (2002).
5. Dana Boyd, Faceted Id/entity: Managing representation in a digital world, Thesis, MIT media lab.
6. M. Trick, Making a Career in OR: You are not alone!, October 2003, presentation at INFORMS, Carnegie Mellon University.
7. Wayne Baker, Achieving success through social capital (Jossey-bass, 2001).

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