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Peter Cochrane's Uncommon Sense: Six Degrees And Supernodes
How interconnected are we? Perhaps even more so than cliché leads us to believe...

The past year has seen the periodic resurgence of the 'remarkable six degrees theory'. Journalists across the planet have variously trumpeted the 'amazing fact' that any two of us are only separated by no more than six people. The reality is - there is absolutely nothing amazing about it! Interesting? For sure. Mind boggling? Never. It is simple to understand at a basic level but gets rapidly more complex as we peel back the layers of sophistication. To get a picture of the mechanisms at work let's do a couple of mind experiments.

First, let's take the case of a Pacific island some 500 years ago with a stable population of around 3000 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 it is obvious that everyone could know everyone else - everyone was connected by a single handshake.

Today sociologists reckon we each average 300 acquaintances and may know between 200 and 5,000 individuals by name. So on an acquaintance basis, the worst case would be each individual linked to another 300 and on to a further 300. This gives a 300^2 = 90,000 people span possibility, which is beyond the scale of this island population. So all the inhabitants are connected by only one or two handshakes - namely a separation of two or less. But their connectivity to the rest of the planet is zero - a therefore an infinite degree of separation!

Second, let us consider a much bigger (hypothetical) island with a 100,000,000 population in an evenly distributed society where again everyone knows on average around 300 people. The worst-case population connectivity is again defined by 300^n, where 'n' is the degree of separation or number of people linking any two. So the question is what value of 'n' will span the population?

You will not be amazed to see that 300^3 = 27,000,000; which is more than a quarter of the population; whilst 300^4 = 8,100,000,000 which is 81 times greater than required for full connectivity. We might therefore conclude that today's 6,000,000,000 population of planet earth could be spanned by just four handshakes. And this would be the case if the population were ideally related and evenly distributed. If not, then the 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 1,000,000,000 people with access to a telephone, mobile phone and the internet, plus millions of regular and irregular travellers. 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 5,000,000,000 disenfranchised people outside the modern world. But we have to start talking probabilities as we have to assume that there are still lost tribes somewhere - and six degrees most likely spans 99 per cent of humanity.

In reality our societies and populations are not flat and evenly distributed, they are hierarchical and clustered around the physical resources of water, food, terrain and organisations. The theory now becomes trickier. But the good news is that this clustering condition is generic to most networks: flora, fauna, people - 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. I'm pretty sure that the Chinese, Greeks and Romans thought through and used elements of all this in their military and society.

As far as I can tell the first recorded thinking started in Budapest around 1929 when Frigyes Karinthy wrote a short story entitled 'Chains' where he postulated that 1,000,000,000 people had only five degrees of separation. He was not a mathematician, scientist or engineer but a poet and writer, so where '5' came from remains unclear. Much later, in 1967, the sociologist Stanley Milgram conducted the first recorded experiments on social connectivity using post cards and the US population. Given the crudity of the experiment, and the tardiness of the participants, it is amazing that he recorded a median number of 5.5. Rounding up saw the start of the six degrees of separation mystery.

More recently computer simulations, mathematical studies and internet experiments - plus observations on biological brains and organisms - have served to confirm further the apparently universal small separation number. But the most revealing discovery has been that of the supernode. It seems that 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 can bridge the organisation we work in from one side to the other and by-pass thousands of people, or it might be our ISP that links directly to some international hub linking all the major cities on the planet. In such cases the degree of separation is four. If on the other hand we have to go via our manager's manager, or an additional ISP node, then we quickly move up to six.

Now here is the fun part! It turns out that these networks based on super nodes are incredibly resilient. Should a node or supernode 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.

In an oblique methodology I have been witnessing all of the above on the net for over a decade. My practice is to delete all of those who do not reply to my email, or who are so tardy to be ineffective, and similarly web pages and hyperlinks. And it really works! With well over 1000 email addresses of proactive people and even more websites, reference papers and documents, all on my laptop, I am now super efficient compared to 10 years ago.

So have I become a supernode? I have no idea. Apart from the flood of emails generated by this column, I still only process around 50 emails a day but I find myself linking and connecting people and thousands visit my home page to help themselves.

The tragedy is that there are those who could be supernodes but they choose not to be and they rapidly become isolated and moribund and mostly don't seem to notice. Seems to me that on the net '3' or '4' wins, and across the planet '5' or '6' is very close behind.

This column was typed during a break during a day of meetings in and around Ipswich and despatched to from a free Wi-Fi site provided knowingly or otherwise on a local business park.