By Simon Bond

Say a lily pad starts in the middle of a pond on day one, and overnight, it doubles in size. This happens every night. If the pond is covered on day 10, how big was the lily pad on day nine? The answer is half. While the lily grows imperceptibly all summer long, only in the last week of the cycle would most bystanders notice its “sudden” appearance. And so goes the network effect.

In other words, as the number of nodes in a network increases arithmetically, the value of the network increases exponentially. Facebook figured out earlier than most, that adding a few more members can dramatically increase the value for all members. 

This scenario is not hard to visualise. Take four acquaintances; there are 12 distinct one-to-one friendships among them. If we add a fifth friend to the group, the friendship network increases to 20 different relations; six friends makes 30 connections; seven makes 42. As the number of members goes beyond 10, the total number of relationships among the friends escalates rapidly. When the number of people (n) involved is large, the total number of connections can be approximated as simply n × n, or n2. Thus, a thousand members can have a million friendships.

A network’s tendency to explode in value mathematically was first noticed by Bob Metcalfe, the inventor of a localised networking technology called Ethernet. During the late 1970s, Metcalfe was selling a combination of Ethernet, Unix, and TCP/IP (the internet protocol), as a way to make large networks out of many small ones. Metcalfe says, “The idea that the value of a network equals n squared came to me after I failed to get networks to work on a small scale, despite many repeated experiments.”

He noticed that networks needed to achieve critical mass to make them worthwhile. But, he also noticed that as he linked together small local networks here and there, the value of the combined large network would multiply abruptly. In 1980, he began formulating his law: value = n × n.

In fact, n2 underestimates the total value of network growth. As economic journalist John Browning notes, the power of a network multiplies even faster than this. Metcalfe’s observation was based on the idea of a phone network. Each telephone call had one person at each end; therefore the total number of potential calls was the grand sum of all possible pairings of people with phones. But online networks, like personal networks in real life, provide opportunities for complicated three-way, four-way, or many-way connections. You can not only interact with your friend Charlie, but with Alice and Bob and Charlie at the same time. The experience of communicating simultaneously with Charlie’s group in an online world is a distinct experience, separate in its essential qualities, from communicating with Charlie alone. Therefore, when we tally up the number of possible connections in a network we have to add up not only all the combinations in which members can be paired, but also all the possible groups as well. These additional combos send the total value of the network skyrocketing. The precise arithmetic is not important. It is enough to know that the worth of a network races ahead of its input.

This tendency of networks to drastically amplify small inputs leads to the second key axiom of network logic: the law of increasing returns. In one way or another, this law undergirds much of the strange behaviour in the network economy. The simplest version goes like this: The value of a network explodes as its membership increases, and then the value explosion sucks in yet more members, compounding the result.

An old saying puts it succinctly: Them that’s got shall get.

A new way of saying it: Networks encourage the successful to be yet more successful. Economist Brian Arthur calls this effect “increasing returns.” “Increasing returns” he says, “are the tendency for that which is ahead to get further ahead; for that which loses advantage to lose further advantage.” In the industrial economy success was self-limiting; it obeyed the law of decreasing returns. In the network economy, success is self reinforcing; it obeys the law of increasing returns.

We see the law of increasing returns operating in the way areas such as Silicon Valley grow; each successful new start-up attracts other startups, which in turn attract more capital and skills and yet more start-ups. Each additional member increases the network’s value, which in turn attracts more members, initiating a spiral of benefits. (Silicon Valley and other high-tech industrial regions are themselves tightly coupled networks of talent, resources, and opportunities.)

At first glance, the law of increasing returns may seem identical to the familiar textbook notion of economies of scale: The more of a product you make, the more efficient the process becomes. Henry Ford leveraged his success in selling automobiles to devise more productive methods of manufacturing cars. This enabled Ford to sell his cars more cheaply, which created larger sales, which fueled more innovation and even better production methods, sending his company to the top.

That self-feeding circle is a positive feedback loop. While the law of increasing returns and the economies of scale both rely on positive feedback loops, there are two key differences. First, industrial economies of scale increase value gradually and linearly. Small efforts yield small results; large efforts give large results. Networks, on the other hand, increase value exponentially—small efforts reinforce one another so that results can quickly snowball into an avalanche. It’s the difference between a piggy bank and compounded interest. 

Second, and more important, industrial economies of scale stem from the herculean efforts of a single organization to outpace the competition by creating value for less. The expertise (and advantage) developed by the leading company is it alone. By contrast, networked increasing returns are created and shared by the entire network. Many agents, users, and competitors together create the network’s value. Although the gains of increasing returns may be reaped unequally by one organisation, the value of the gains resides in the greater web of relationships.

These positive feedback loops are created by “network externalities.” Anything that creates (or destroys) value which cannot be appointed to someone’s account ledgers is an externality. The total value of a telephone system lies outside the total internal value of the telephone companies and their assets. It lies externally in the greater phone network itself. Networks are particularly potent sources of external value and have become a hot spot of economic investigation in the last decade. A parade of recently published academic papers scrutinize the fine points of network externalities: When do they arise? How do they break down? Are they symmetrical? Can they be manipulated?

One reason increasing returns and network externalities are garnering attention is because they tend to create apparent monopolies. Huge amounts of cash pour toward network winners such as Amazon, Apple, AirBnb, Facebook, Microsoft and Uber to name a few, and that makes everyone else nervous.

Are network superwinners in fact monopolies? They are not like any monopolies of the industrial age. When antitrust hearings are conducted today, the witnesses are not customers angered by high pricing, haughty service, or lack of options—the traditional sins of a monopolist. Customers have nothing to complain about because they get lower prices, better service, and more features from network superwinners—at least in the short term. The only ones complaining about superwinners are their competitors, because increasing returns create a winner-take-most environment.

But in the long term, the customer will have reason to complain if competitors pull back, or disappear. The new monopolies are different in several ways. Traditional monopolies dominated commodities. In the new order, as Santa Fe Institute economist Brian Arthur points out; “Dominance may consist not so much in cornering a single product as in successively taking over more and more threads of the web of technology.” Superwinners can practice a type of crossover where control of one layer of the web leverages control into others.

Industrial monopolies exploited simple economies of scale for their own benefit. Network effects are not about economies of scale, they are about value that is created above and beyond a single organisation—by a larger network—and then returned to the parts, often unevenly. Because some portion of the value of a network firm so obviously comes from external sources, allegiance is often granted to external sources.

We see this in the way network effects govern the growth of Silicon Valley. Silicon Valley’s success is external to any particular company’s success, and so loyalty is external, too. As AnnaLee Saxenian, author of Regional Advantage, notes, Silicon Valley has in effect become one large, distributed company. People job-hop so frequently that folks “joke that you can change jobs without changing car pools. Some say they wake up thinking they work for Silicon Valley. Their loyalty is more to advancing technology or to the region than it is to any individual firm.”

Network organisations experience small gains, while their network is being seeded. Once the network is established, explosive growth follows with relatively little additional genius and the next thing you know, they are everywhere. Just look at the recent results from Amazon, Facebook and Alphabet AKA Google. 

Technology has now become our culture and our future is less "stuff" and more networks.