Is Your ‘Small World’ Network Too Small?

If you are new to this blog, you may not know that Tim and I are business school academics with a particular research interest in networks (person to person) and innovation. We have a few other research interests but this is where we spend most of our time with our doctoral students and industry collaborators. In 2008 we were awarded a substantial research grant from the Australian Research Council on how social network structures affect innovation performance in firms.

Over the past few years we have collected data from a global mining company, engineering companies, high-tech services and local government and we have made some conclusions about a class of network called a ‘small world’. This phrase has entered popular culture and I am sure you have had several small world experience when a new work colleague from another town turns out be a married to a friend from school (or something like that).

As we have said before on this blog, this ‘small world’ experience has also been called ‘six degrees of separation’ and it has been puzzled social scientists for decades. Many years ago, a US sociologist by the name of Stanley Milgram popularized the six-degrees idea by getting people to send a letter to someone they had never met in another US city. The senders had to do this by sending the letter to people they knew who might know the final receiver. The amazing finding was that the average number of steps was a little over 6- hence the six degrees of separation.

The Milgram experiment has been repeated internationally with similar findings and the Kevin Bacon game works on the same principle. The fact that small worlds ‘work’ is a bit harder to explain. We don’t have that many contacts and we mostly prefer to be with people who are culturally or professionally similar to ourselves. This would suggest that the world is organized into distinct clusters of people and yet we have this idea that we are six network steps from anyone on the planet. Surely both clustering and few steps through the network can’t work together? Or can it….

One of the really interesting breakthroughs in network science over the past 10 years is an understanding of why small worlds work – and this has some pretty big implications for managing innovation (which I’ll explain later). Most of what follows here is taken from Six Degrees: The Science of a Connected Age by Duncan Watts. This is a really interesting account of networks and the six degrees problem and it’s very readable.

Watts introduces small world networks as being in between highly structured networks with organized clusters and networks with completely random links

The ‘regular’ sample network is highly structured with everyone connected to their immediate neighbors but count how many steps it takes to get from one side of the network to the other. On the other hand, the random network has few steps between anyone in the network but has no organization to it. The small world trick is that a few random connections across clusters in the network creates shortcuts and turns an organized (silo) structure into a small world. It turns out that this structure is very common in many social networks and this is a real map of a small world network of project engineers within a large multinational business. I have indicated a person who acts as a ‘connector’ by putting a red circle around them.

Collaboration Network of Engineers

Now, I suspect that many of you are thinking about the possibility of having organization structures together with an efficient way of transferring ideas and expertise. The small world network shows us that this is possible and there is a lot of good evidence that it can support innovation. I won’t go into great detail (and you can read a more technical review from Tim and me here) but my favorite evidence comes from the Broadway Musical industry. Using collaboration networks of score-writers, choreographers and librettists, this study showed that block-buster musicals were more likely to occur in the small-world environment.

So far, so good but can your world become too small and too connected? Another really interesting finding from the Broadway study was that too much small worldedness (e.g more clustered and less connected overall) correlated with decreased musical success. This is interesting and we think that there are two things going on here.

A highly connected cluster of people is like a goldfish bowl. Everyone knows everybody else and knows the same thing. Like a goldfish, talking around the network just makes us see the same things and hearing the same information. There is a very strong chance that group think and rigidity will set in when this network structure occurs. Another way of looking at it is that there is nowhere that different ideas can emerge.

The brokers in ‘hyper’ small worlds can get overloaded. When the clusters get too big and overall connectivity relies on a handfull of people they get overloaded or even use their position to selectively filter information for their own benefit. One study that Tim and I have done shows and engineering collaboration network that looks like a small world but the role of the connectors in that instance was to filter rather than pass on information. This small world network resulted in decreased collaboration performance on the project.

Small worlds can help innovation but look out for signs that groups are getting too inwardly focussed on their own work and watch for the overloading of connectors.

Thanks to Sam Macaulay for help with the network data.

Please note: I reserve the right to delete comments that are offensive or off-topic.

10 thoughts on “Is Your ‘Small World’ Network Too Small?

  1. John,

    Whit all due respect to you and Tim, I think you have it exactly wrong here.

    The problem isn’t that networks are too connected or that hubs are too big, that’s just a symptom. The problem lies with dynamics. The network isn’t making new links.

    As networks age, triads tend to close and clusters form. If newer links aren’t introduced, you get exactly the situation you described (I faintly remember reading about that Broadway study, I think in Christakis and Fowler).

    I point this out not to be a dick, but because from the way you wrote it seems that people would not want to make too many connections to form a “Goldilocks network” that’s just right. In fact, just the opposite is true, you should keep making new links, just make sure they’re not all in one network.

    In reality, you don’t have to do much to form a small world network.If you look at Duncan Watts original paper (published as “Small Worlds”) you’ll see that when he evaluates the randomness variable (Beta), he needs to use a logarithmic scale. While it takes just a small amount of mixing to make a small world network it takes a whole lot to ruin it.

    (I make the same point and plagiarize his charts here

    So what you want to do is prevent unnatural barriers to making new connections. This is a major problem because both formal and informal barriers to building new links in professional networks are very common and extremely pervasive.

    Sorry for a long and somewhat pissy comment. But, hey! This is the Internet after all..

    – Greg

  2. Hi Greg:

    thanks for the note. It’s not pissy, it’s thoughtful and valuable. I agree with your point about dynamics and I haven’t considered that in this post. What made me write the post was a recent research paper in “Organization Science” that looks at the dynamics of small worlds. I’ll do a translation of that paper in next week’s post. The finding from that paper was that small worldedness goes in pulses. The small world quotient in social networks rises and falls as it becomes unstable with too much or too little small worldedness. The lack of new connections in clusters means that redundant information ciculates in these parts of the network as more triangles are formed (as you say).
    I do disagree woith your point about a lot being needed to ruin small worlds. There was a paper published in Nature by Barabasi that looked at this using simulations and world wide web data. Here, the small world was highly tolerant of random node deletions, but highly susceptible to targetted deletions of the high degree nodes. Degree distribution is ‘long-tailed’ (non-gaussian) and some nodes matter a lot more than others.
    I wholehearted agree with your final conclusion, though I still think that network analysis helps us to understand if we are overly clustered or not. At least that is the feedbck we are getting from firms who are working with us.
    Thanks for the comment. We really like critical comments because they force us to think things through. The academic review process is supposed to work the same way (and often it doesn’t).

  3. John,

    Thanks for replying. I think a lot of the problem is presentation. Although you didn’t come out and say it (and I’m sure you didn’t mean it), your post could be taken to mean “make some connections, but not too many or you’ll ruin your network”.

    I’ve read the Barabasi paper and, as important as that paper is, I think it’s a little bit off point. He wasn’t writing about small worlds, but what it would take to sabotage networks with different structures and I don’t think he had social networks in mind, but technical networks (i.e. internet).

    So while I do agree with your central point, that overly clustered networks stifle creativity and performance, I don’t think the connecting behavior of people in the networks is the right way to approach it. As a rule, people should always make connections when they can.

    There is, however, a lot to be improved in how collaboration networks are managed. In my own experience running companies, I’ve found three practices to be helpful:

    1. Training programs: Having training programs on general industry principles improves connectivity dramatically if people within the company are pooled into a general group. After the training is completed, they go to different parts of the company but maintain ties to their training class.

    2. Best Practice Programs: Holding monthly meetings across departments for people to show off their best work not only encourages knowledge transfer but gets people to mix and helps develop weak ties.

    3. Forced Switching: Another, more difficult, practice is to force people to switch departments and functions.

    Incidentally, one Industry that has a problem with collaboration is the marketing services industry, which tends to have extremely clustered networks. There are four major types of agencies: Creative, Media, Digital and PR. Amazingly, although functions overlap considerably, switching between sub industries is almost nonexistent.

    A while back, I was asked for give input into a “Creating Value Over the Next Decade” committee at one of the major global holding companies. I suggested that they institute a rule whereby executives would have to work in at least two functional or geographical areas in order to get promoted beyond a certain level.

    My suggestion was, of course, ignored. However, due to the “colorful” way I expressed it, I seem to have done my career some good.

    Maybe you could do some research into the “jackass” effect in networks?

    – Greg

    P.S. Thanks for including the Broadway musical paper. I’ve been trying to track that one down!

    P.P.S. I probably will do a post on this stuff, giving you and Tim no credit of course:-)

  4. Very interesting discussion gentlemen :-). Enjoyed reading it.

    Of course, I am a fence sitter on this one. I believe networks need to grow continuously to keep the juices flowing in terms of new information, new mental models, new pathways but also believe that when attacking a problem or trying to loop in a solution, the right nodes need to click to form the “small world” relevant to that particular context. “Small worlds” are efficient but they dynamics become stale if the membership in it is static.


  5. Hi Greg and Ned:

    You’ve both raised the critical point of trying to focus on the dynamics rather than static structure of the network. This tends to get less attention from network researchers as the analysis is harder to do.
    One thing that we do know about social networks is that they are normally sparse with connections. The connections are not costless and making new connections can be risky. As you say, creating the conditions to foster connections is a valuable excercise. We’ve got a PhD student working on network connections and social risk in a prominent MNE and he is coming up with some very interesting results.
    You are right is saying that the details matter and are hard to cover in a short post. In addition to Brian Uzzi’s study of Broadway collaborations, there are a couple of notable studies linking small world structure to innovation. We have reviewed them is a 6000 word article that was accepted for publication last week. The hyperlink to an earlier version of the article (and the details of the references) is the “here” mentioned in the post.
    Thanks for the conversation. Others seem to be enjoying it too.


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