Six degrees of separation and super nodes

COMMENTARY--The past year has seen the resurgence of the "six degrees of separation" theory. Journalists across the planet have variously trumpeted the "amazing" fact that any two individuals are separated by no more than six acquaintances. The reality, though, is there's absolutely nothing amazing about it.

Interesting? Sure. Mind boggling? Never. It is simple to understand at a basic level but gets rapidly more complex as we delve deeper. To get a picture of the mechanisms at work, let's look at a few unusual populations.

First, take the case of a Pacific island some 500 years ago with a stable population of around 3,000 people who had arrived by canoe several generations back and since that time had no outside contact. Such societies were highly interdependent and tightly bonded and thus everyone could know everyone else--everyone was connected by a single handshake, or one degree of separation.

Today sociologists reckon we each average 300 acquaintances and may know between 200 and 5,000 individuals by name. So on an acquaintance basis, each individual is linked to 300 people who are each linked to a further 300. This gives a range of 3002= 90,000 people, which is beyond the scale of the island population. This indicates the island dwellers could be connected by only one or two degrees of separation. But their connectivity to the rest of the planet is zero--a therefore an infinite degree of separation.

Second, consider a much bigger (hypothetical) island with a population of 100 million in an evenly distributed society where everyone knows on average around 300 people. The worst-case population connectivity is again defined by 300n, where "n" is the degree of separation. So the question is what value of "n" will span the population?

You will not be amazed to see that 3003= 27 million, which is more than a quarter of the island's population, whilst 3004= 8.1 billion, which is 81 times greater than required for full connectivity. We might therefore conclude that today's worldwide population of six billion could be spanned by just four handshakes. This would be the case if the population were evenly distributed. If not, then the degree of separation is bigger. Before we had national and international travel, and of course telecommunications, none of this was quite so obvious or indeed quite so true. Today we have nearly one billion people with access to a telephone, mobile phone and the Internet, plus millions of regular and irregular travelers. So it is feasible that four degrees of separation has been established within this community and five (or six) might be the number when we include a further five billion disenfranchised people outside the modern world.

In reality, however, populations are not evenly distributed; they are hierarchical and clustered around the physical resources of water, food and terrain. The theory now becomes trickier. The good news is this clustering condition is seen not just with people but with flora, fauna and even computer networks--it's both biological and electronic. In every arena, the degree of separation turns out to be very small despite the size of the population.

As far as I can tell, the first recorded thinking on the "six degrees of separation" theory started in Budapest around 1929. That's when Frigyes Karinthy wrote a short story entitled "Chains" in which he postulated that one billion people had only five degrees of separation. He was not a mathematician, scientist or engineer but a poet and writer, so where the number five came from remains unclear.

Later, in 1967, the sociologist Stanley Milgram conducted the first recorded experiments on social connectivity using post cards in the United States. Despite the crudity of the experiment, and the tardiness of the participants, he recorded a median number of 5.5 degrees of separation. Round up and we see the start of "six degrees of separation."

More recently computer simulations, mathematical studies and Internet experiments--plus observations on biological brains and organisms--have served to confirm further the apparently universal separation number.

The most revealing discovery related to this theory has been that of the "super node." It seems very few networks offer even or homogenous structures. They are almost always clustered assemblies that concentrate around a smallish number of super nodes.

For us such a node might be a manager who knows thousands of people, or an ISP that links directly to an international hub, which in turn connects to all the major cities on the planet. When connecting to others via a super node, the degree of separation is four. If we count our connections to others via a "standard" node--say, our manager's manager or an ISP without the direct international link--then we quickly move up to six.

Now here is the fun part: it turns out these super node-based networks are incredibly resilient. Should a node or super node fail or become damaged, the rerouting is super efficient. In most cases, such a failure will see little or no change in the degree of separation. This is a primary reason that Internet failures, brain damage and other biological malfunctions can often be overcome. It is also why companies can often achieve great success despite pockets of disastrous management.

I have been witnessing all of the above on the net for over a decade. My practice is to delete contact information from those people who do not reply to my e-mail, or who are so tardy to be ineffective. I also delete web pages and hyperlinks if I don't use them often. It really works. With well over 1,000 e-mail addresses of proactive people and even more websites, reference papers and documents on my laptop, I am now super efficient compared to 10 years ago.

So have I become a super node? I have no idea. Apart from the flood of e-mails generated by this column, I still only process around 50 messages a day--although I do find myself linking up people, and thousands visit my home page without contacting me. The tragedy is those who could be super nodes but choose not to be and instead become rapidly isolated. Seems to me on the net we are separated by three or four degrees, while across the planet its closer to five or six.

This column was written during a day of meetings in and around Ipswich and dispatched to silicon.com from a free Wi-Fi hot spot provided knowingly or otherwise by a local business park.

biography
Peter Cochrane is a co-founder of ConceptLabs CA, where he acts as a mentor, advisor, consultant and business angel to a wide range of companies. For more about Peter, see: http://www.cochrane.org.uk/. He writes a regular column for silicon.com that is archived here.