LINKED: Network science and the diffusion of innovations

Physicist Albert-Laszlo Barabasi's new book Linked: The New Science of Networks demolishes many of the assumptions about networks--human, computer, and biological--that have prevailed, often unconsciously, for a long time.

Networks consist of nodes and links. In social networks for example, people are the nodes, and relationships are the links. That networks consist of a more-or-less random arrangement of nodes and links is often assumed.

With a random network, the number of links per node follows the bell curve, like a highway map might suggest--each city or town has approximately the same number of highways leading in and out. There is variation, but it aggregates strongly around an average value.

Barabasi shows that most networks follow a mathematical expression known as a power law rather than a normal curve. Rather than a highway map, the power-law distribution resembles the airline flight system--many nodes have only one or a few links, but some nodes have a tremendous number of links. If you were to imagine such a distribution in human height, most people would be of average height, but there would be a few 100-foot-tall people, and maybe someone who was a mile high. This power-law distribution is common in social, economic, computer, and biological networks--for example the metabolic reactions of proteins in a cell or organism. Many molecules interact with three or four others, but some, such as ATP, have a high number of reactions with other molecules.

The upshot here is that the hubs, the nodes with an exceptionally high number of links, are all-important. If the diffusion of computer viruses, for example, was merely a question of virulence versus distribution, once a virus was identified and an antidote supplied, we would expect it to disappear because of reduced virulence, hence lower rate of infection. Barabasi tells an intriguing story of the Love Bug virus, which continued to reappear and infect computers for a long time because of the topology of the network itself--which was not random, but consisted of a high number of links to and from hubs.

According to Barabasi, classical diffusion-of-innovations theory, with its emphasis on threshold/susceptibility and virulence, misses the point about the structure and properties of power-law networks.

This book has strong implications for those seeking to manage wholes, which have network properties. The marginal reaction guideline, for example, asks what actions will make the most out of time, energy, and money toward your holistic goal. Barabasi suggests focusing on the hubs. With ecosystem process, this could mean the organisms that have the highest number of foodweb or ecological relations with others. In social or economic networks or wholes, we should concentrate on those people, organizations, or companies with the highest connectivity. In halting the spread of AIDS, suggests Barabasi, we should concentrate treatment on the most promiscuous segment of the population. Giving treatment to those less likely to spread the disease will do little to damp the epidemic. (Though Barabasi recognizes a possible ethical dilemma here, he's done the math.)

Though Holistic Management makes a lot of sense to a lot of people, many of us are constantly reinforced in linear decision making through hubs--the universities, the media, most large organizations. We can get an antidote by attending a workshop but it's common to become "reinfected" on return to everyday life, with frequent contact through these major hubs.

Linked: The New Science of Networks by Albert-Laszlo Barabasi on

See a good illustration at