Read more: 鈥�Mind maths: Five laws that rule the brain鈥�
If you stretched out all the nerve fibres in the brain, they would wrap four times around the globe. Crammed into the skull, this wiring looks like a tangled mess, but in fact mathematicians know its structure well 鈥� it is a form of the 鈥渟mall-world network鈥�.
The hallmark of a small-world network is the relatively short path between any two nodes. You鈥檝e probably already heard of the famous 鈥渟ix degrees of separation鈥� between you and anyone else in the world, which reflects the small-world structure of human societies. The average number of steps between any two brain regions is , and .
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That may be because a small-world structure makes communication between different areas of a network rapid and efficient. Relatively few long-range connections are involved 鈥� just 1 in 25 nerve fibres connect distant brain regions, while the rest join neurons in their immediate vicinity. Long nerve fibres are costly to build and maintain, says at the University Medical Center in Utrecht, the Netherlands, so a small-world-network architecture may be the best compromise between the cost of these fibres and the efficiency of messaging.
The brain鈥檚 long-range connections aren鈥檛 distributed evenly over the brain, though. Last year van den Heuvel and Olaf Sporns of Indiana University Bloomington discovered that clusters of these connections form that shuttles traffic between a dozen principal brain regions (see diagram). The backbone and these brain regions are together called a 鈥渞ich club鈥�, reflecting the abundance of its interconnections.
No one knows why the brain is home to a rich club, says van den Heuvel, but it is clearly important because it carries so much traffic. That makes any problems here potentially very serious. 鈥淭here鈥檚 an emerging idea that perhaps schizophrenia is really a problem with integrating information within these rich-club hubs,鈥� he says. Improving rich-club traffic flow might be the best form of treatment, though it is not easy to say how that might be achieved.
鈥�12 hyper-connected hubs that help direct traffic flow鈥�
What is clear for now is that this highly interconnected network is the perfect platform for our mental gymnastics, and it forms a backdrop for many of the other mathematical principles behind our thoughts and behaviour.
This article appeared in print under the headline 鈥淪mall world, big connections鈥�
