In 1999, Albert-László Barabási, a physicist at the University of Notre Dame, and one of his students, Réka Albert, published a landmark paper in the journal Science. Arising from work on the structure of the Internet, they saw a pattern in the world of networks that astonished them.71
The two physicists started to construct maps of the Internet, where each website was a point, with lines depicting the links to other hubs and to users. A popular hub, such as Yahoo, would have a huge number of lines converging on it, whereas your website or mine would have very few. The picture, then, was one of dense concentration in a few places, and wide open spaces or just a few lines in others. It looked a bit like a map of population concentration in the United States: a few hubs had a tremendous number of links to the other hubs or to individuals in the network; on the other hand, the great majority of hubs in any system had very few links.
The scientists went on to count how many hubs had at least two connections, then four, sixteen and so on, up to millions. They found that, in any small area they inspected, there was a regular pattern: every time the number of links doubled, the number of hubs having that many links declined by roughly five times. So, there might be five thousand hubs with two connections, but only about a thousand hubs with four connections, two hundred hubs with eight connections, and so on.
This is known as a power law distribution, where a few hubs hog nearly all the links. Power laws often follow an 80/20 pattern, where 80 per cent of phenomena or results belong to 20 per cent of people or causes. We might hypothesise, for example, that 80 per cent of society’s wealth belongs to 20 per cent of citizens. And, indeed, the true figure is remarkably close to this: the richest 20 per cent of Americans own 86 per cent of America’s wealth; and the richest 20 per cent of people in the world own 85 per cent of global capital. On the Web, Google is millions of times more connected to other sites and pages than the ‘long tail’ of almost all other sites–which are very poorly connected in comparison.
In other words, networks tend to concentrate, to have a few hubs that really matter, while most hubs hardly matter at all. Connectedness in networks, Barabási and Albert concluded, was not random or democratic, not spread about or widely shared. It was monopolistic.
The lopsided distribution of networks is completely different from the ‘bell-curve’ distribution that we are told is ‘normal’, where most observations are quite close to the average. Human height, for example, follows a normal distribution. Most men are only a few inches above or below the average height of five feet, eight inches, and there are no real extremes of height. You’ll never find a hundred-foot giant in the normally distributed world of human height. But you might if height behaved as most hubs do.
With power law distributions, the typical pattern is one of extreme potential variation, where a few observations can be hundreds, thousands or even millions of times greater than the average. For instance, Bill Gates is a million times richer than the average American.
The dominant few can be so large that they change the shape of the whole system. With power laws, the top performers are so important to the total that the large majority is actually below average, below the ‘arithmetic mean’. With human wealth, the ‘average’ net worth is distorted by the few billionaires and multi-millionaires, so the average is much higher than the median–that is, the level most people enjoy. Imagine ten people who have, on average, £50,000 in the bank–a total of £500,000. But if two of them own 80 per cent of the money, they account for £400,000, leaving just £100,000 for the other eight people–£12,500 apiece. So the average wealth might be £50,000, but eight of the ten people–80 per cent–are a long way below that average. When this is the case, the concept of average stops making intuitive sense. This is what happens with money; and it is what happens with networks.
Barabási and Albert were stunned when they found the world of man and nature riddled with networks with this same power law distribution of links to hubs. A few hubs hogged nearly all the connections, so the ‘average’ hub scarcely got a look in. And this applied not just to Internet hubs, but seemingly to almost anything that was connected in a network–the US power grid, the neurons in a worm’s brain, IBM computer chips, the distribution of book sales, the number of people’s sexual partners, even the way actors are linked to co-stars during their movie careers.
Hollywood, for example, is a closely connected network. Tom London might have been in a movie with Rod Steiger, who might previously have acted with Christopher Lee, connecting London and Lee. But some actors have many more links than others. On average, every actor in Hollywood has twenty-seven links to other actors. But because this is a network, with a power law distribution of contacts, that average means little. For instance, Robert Mitchum didn’t have 27 links–he had 2905, meaning that he played alongside that many different colleagues. John Carradine had four thousand links. Yet, more than 40 per cent of actors have fewer than ten links. Mitchum and Carradine were superconnectors, and a handful of others occupy that role today. Without them, Hollywood would not be a small world. One or two enormously connected hubs typically dwarf all the rest–the winner takes most, and sometimes almost all.
It should be said that not all hubs follow this pattern. For instance, with airports, the advantages of size, beyond a certain point, are outweighed by the time it takes to arrive at the airport or leave it. But the vast majority of human and other networks do mimic the Internet’s pattern of hub connection–a few mega-hubs and masses of tiny ones.
Of course, these large hubs are superconnectors: they do the hard work in terms of linking their ‘customers’, the people who connect to them and therefore are connected to everyone else as a result. For whatever reason–ease or convenience, saving time or energy, superior information or experience–most people or other nodes link to the dominant hub. We don’t stop to consider the thousands of search engines to which we could connect; without thinking, we plump for Google or Yahoo!
And when it comes to large and powerful hubs, there is a strong tendency for the big to grow, the rich to become even wealthier. They tend to concentrate further as time passes. The most connected hubs today are likely to be connected to an even greater extent tomorrow. For example, having taken the lead in the betting-exchange market, Betfair’s market share keeps rising. Network scientists have explored how this might work in theory, and have even shown how wealth could become increasingly concentrated without the rich having any superior abilities. But we don’t need computer simulations–the explanation is simple. In a network, everyone wants to connect to the hub to which everyone else connects–the network is more valuable simply because it is bigger. As long as it’s a network–be it a restaurant, marketplace, social network, real or virtual sports league, computer system, mobile-phone network, business directory, or electronic exchange–popularity breeds popularity.
There is another explanation why markets concentrate, especially in network businesses. Back in 1973, Bruce Henderson made this rather papal pronouncement: ‘The dominant producer in every business should increase its market share steadily.’ Bruce’s logic was that the market leader should have lower costs, and ‘at least part of that superior cost position should be passed on to the customer in lower prices or better quality’. A virtuous cycle should therefore ensue–with a better deal for the customer, more customers should be attracted to the market leader, which in turn should give the top firm even more business and therefore even lower costs, leading to an even better price or higher-quality product for the customer. ‘Failure of an industry to concentrate is failure to compete,’ Henderson concluded, meaning that if the leader’s market share didn’t keep rising, that was an indictment of the firm’s management.71