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

Review by Andreas. Contact me at andreas@andreas.com

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Albert-Laszlo Barabasi's book Linked: The New Science of Networks (Plume, 2003) on the theory of networks shows that networks (social network of friends, the web's five billion websites, the biological food chain, business and commerce, the growth of cities, intra-cellular proteins, and so on) share the same properties, which means they can be quantified and described with mathematical laws. By understanding how networks function and grow, one can develop strategies to take advantage of that growth.

Origins of Network Theory

In the 1780s, Leonhard Euler invented network theory. A network is made up of nodes and links and mathematicians assumed the links between the nodes were randomly distributed. If there are, say, 10 nodes and 50 links, they assumed the distribution would be random and each node would get, on average, five links. Mathematicians explored the properties of these random-distribution networks. However, for most of the last two hundred years, network theory remained a form of abstract mathematics because it was difficult to study large networks with millions (or billions) of nodes and links.

The Social World as a Network

If one applies random distribution in networks to the social world, then six billion humans (the nodes) should each have generally the same number of friends (the links). However, sociologists and economists realized that real-world networks were not randomly distributed.

Stanley Milgram in the late 60s performed his famous six-degrees-of-separation experiment. The popular understanding of Milgram's experiment is that anyone can be linked to anyone else on Earth through only six links. In fact, Milgram discovered:

Three Links of Separation: Some people have such good links that they can connect to someone far away with only three links.

100 Links of Separation: Others may require a hundred links or more to reach someone. This also means the people within those hundred links are also poorly linked.

No Links: Milgram also found that many people have such poor links that they can't establish a connection to distant others. These people are isolated into small islands. They are cut off from the rest of society.

In the late 60s, Mark Granovetter, a sociologist who is now the head of sociology at Stanford, studied how people found jobs. Whereas it was generally assumed that society was homogenous, sociologists realized that society is made up of groups of people, which is now known as clustering. Granovetter showed that weak contacts were twice as effective (28%) as strong contacts (17%) for finding a job. Casual connections were more likely to lead to a job.

This seems counter-intuitive. It would seem your close friends would be better for job leads. But if you think about it, we tend to gather within groups of similiar interests. If a tennis instructor wants new students, there's no point for her to ask her friends because they are all tennis instructors. She will find more students by asking people in clusters that have nothing to do with tennis, such as church groups, knitting clubs, and so on. Those clusters (church groups and so on) probably lack tennis instructors. So if you are creating networks for job hunting, sales, and so on, make lots of casual acquaintances to groups outside of your normal interests. Better yet, make contacts to the leaders of those clusters, because leaders know everyone in their cluster.

There's another kind of distribution in social networks. In the early 1900s, Vilfredo Pareto, an Italian economist, discovered the 80/20 Rule:

20% of landowners own 80% of the land.

20% of workers do 80% of the work.

20% of salespeople make 80% of sales.

20% of criminals carry out 80% of crime.

20% of websites get 80% of the traffic.

20% of the customers create 80% of the calls to techsupport.

The Internet as a Network

The Internet was originally designed to be randomly distributed in order to create a communications network that can survive an attack. In the 90s, physicists began studying the web because it was a network in which all nodes and links could be tracked. Computer scientists quickly realized the Web was not randomly distributed. Maps of the web showed that some nodes had huge numbers of links while most nodes had only a few links.

The Nature of Networks

Barabasi, a physicist, discovered that networks use logarithmic distribution, highly-linked nodes grow faster, and networks undergo phase transitions.

Logarithmic Distribution: Instead of random distribution or bell curve distributions, the distribution of links in a network is determined by logarithmic power laws. If you remember log tables from math, log numbers increase by powers of ten. Log 2 is ten times larger than log 1, log 3 is 100 times larger than log 1, and so on. If we apply logrithmic power laws to nodes and links, this means some nodes have all the links and most nodes only have a few links.
Earthquakes are measured by log numbers: A magnitude 2.0 is ten times more severe than a magnitude 1.0, a 3.0 is 100 times stronger, and so on.
On the web, the top websites have ten times more links than the next set, 100 times more links than the third set, and 1,000 times more links than the fourth set. Google's original idea of Page Ranking is based on log distribution. A website with Google PageRank 5 (PR5) is ten times bigger than a website with PR4, 100x a PR3, 1,000X a PR2, and 10,000X a PR1 website.
This means the third link at Google is only going to get 1/1,000th the number of visits compared to #1. If you continue down the list, #10 will get hardly any traffic. This works with practically everything on websites: a few keywords get most of the searches, a few pages of a website get most of the visits, and so on. They are all based on log number distributions.
For example, if you are using Google Adwords for advertising, then you must bid enough to be in the top three positions. If your ad appears lower than that, you will get very little traffic.

Big Nodes Grow Faster: As new nodes enter the network, they are more likely to link to highly-linked nodes than low-link nodes, because the highly-linked nodes are easier to reach, because they are highly linked, so they'll get more links. This feedback loop gives preference to large nodes. Namely, the rich get richer. Networks grow according to the 80/20 rule. Barabasi calls this preferential linking.

Phase Transition: Networks undergo phase transition. This means that when a critical threshold (the tipping point) is crossed, the all of the nodes undergo a phase transition and starts acting as a single entity. The property of the network is shared among all nodes in the network. For example, when you boil a pot of water, the water acts like ordinary water as it heats up. But at some point, all of the water suddenly starts to boil. There is no "low temperature boiling" or localized boiling. In terms of the web, in the beginning of a new market space, a number of startups sell the same thing. At first, the various websites will have different features and offers. But when the market niche crosses a certain size, a few of the dotcoms become very large (the 20%), the remainder (80%) stay small, and they all take on the properties of the group: they all adapt the same general standards. (Incidentally, in the early 90s, I wrote about this as the "Law of No #2."

Incidentally, this also shows why networks (social, biological, computer, and so on) easily survive most attacks. If a computer virus spreads into a network and destroys perhaps 10% of all nodes, that's not really a problem, because 80% of nodes have low value, so losing many low-value nodes will not affect the network as a whole. However, an attack that targets the large nodes (the 20%) can be catastrophic. The entire network collapses and reverts in a phase transition to an earlier state.

These mathematical laws apply to many kinds of networks: the Internet, wealth and property distribution, membership on corporate boards, intra-cellular protein molecules, and so on.

Companies that pursue a "business is war" model will be at a self-inflicted disadvantage. They create few links, newcomers don't link to them, business cycle downturns leave them stranded, and so on.

Companies that embed themselves into the social network of an industry by creating lots of contacts (links) to other companies, suppliers, industry magazines, customers, government, and workers will grow, because the node with the most links will get more links. At some point, the industry (the network) will undergo a phase transition from "just a bunch of separate companies" into an industry. The core companies become institutionalized and they own the industry. Their standards become the industry's standard. Pareto's 80/20 Rule applies and the 20% will get 80% of the revenues. Due to the law of preferential linking, newcomers will be effectively locked out of the industry.

One can read the previous paragraph carefully and realize that it applies to many endeavors: international politics, real estate sales, personal networks, and so on.

Barbarasi doesn't seem to know about geodemographics. Sociological clustering shows that American society is made up of some 62 clusters. He also does not seem to be aware of the fields of artificial life and concepts of swarming. These fields have developed mathematical models that describe how populations develop and interact.

Links

Linked: The New Science of Networks. By Albert-Laszlo Barabasi (2002)