Key Points

  • Metcalfe’s Law is one of the foundational principles of network economics.
  • Metcalfe’s Law observes that any network’s value is a proportion of the square of the network’s total number of connected nodes.
  • When Metcalfe first came up with the idea, he indicated that the formula for a network’s value worked best as an exponential function of its total number of nodes.

What Is Metcalfe’s Law?: Complete Explanation

Metcalfe’s Law is one of the foundational principles of network economics. It suggests that as a network grows, its value grows much faster than its user base.

The idea behind Metcalfe’s Law is that, while a network’s cost generally grows as a direct proportion of its total number of nodes, its value grows in proportion to the square of that number. Network value grows fast because it’s related to the number of connections between nodes rather than the number of nodes. Metcalfe’s idea implies that node connectivity is the real source of utility in a network.

The word node comes from a Latin word that means knot. In this context, we use it to mean any endpoint in a network. Telephones, computers, train stations, or individual people can all act as nodes in different kinds of networks.

A network with 10 of these nodes might cost about 10 times the price of one node, but Metcalfe’s Law suggests that the network’s inherent value will be closer to 100 times the value of one node. If you add a node, the cost will jump to 11, but the value will jump to 121, the square of 11. In mathematical terms, network cost grows linearly, but network value seems to grow nonlinearly as an exponential function of the total number of nodes in the network.

Metcalfe’s Law isn’t a physical or perfect law of network value. Just like economics has the idea of supply and demand that works perfectly only under perfect conditions, Metcalfe’s idea of network effects is more of an approximation rather than an exact formula. It’s most useful as a conceptual model that you can use to think about network economics in general terms.

Metcalfe’s Law: An Exact Definition

Metcalfe’s Law observes that any network’s value is a proportion of the square of the network’s total number of connected nodes.

How Does Metcalfe’s Law Work?

The mechanics of Metcalfe’s Law are simple. If a network gains new nodes that can connect with all its existing nodes, then the amount of connections grows much quicker than the number of nodes. Every single new node adds as many connections to the network as there are existing nodes.

Square or Log

When Metcalfe first came up with the idea, he indicated that the formula for a network’s value worked best as an exponential function of its total number of nodes. He and other researchers like Bob Briscoe later scaled it back, calculating that the network value was closer to a logarithmic function of its number of nodes.

In 2013, data analysts from the Netherlands released a broad study of seven years of internet use across 33 European countries. They concluded that the growth patterns of smaller and newly launched networks do seem to follow Metcalfe’s exponential estimation. As a network grows, however, the growth of its value seems to taper off into a logarithmic rather than exponential function of its number of nodes.

Other recent studies involving data from the past decade from Facebook, Tencent, Bitcoin, and Ethereum networks also indicate that these networks seem to fit Metcalfe’s observation in their initial phases and then slow down as they reach widespread adoption.

Recent data studies suggest that Facebook, Tencent, Bitcoin, and Ethereum networks fit Metcalfe’s observation in their beginning stages.

Direct or Indirect

The network effects of this value escalation tend to be both direct and indirect.

We call network effects symmetric or direct when a node increase provides direct utility to the other nodes. We can see direct network effects in social networks like Twitter or Tinder, where additional users joining directly improves the user experience of the existing users, giving them the possibility of more followers or matches.

We call networks effects asymmetric or indirect when there is more than one type of node and a node increase provides indirect utility to other types of nodes. Indirect network effects show up in networks like Uber or Airbnb, where more drivers and hosts indirectly improve the experience of the riders and guests, and vice versa. Indirect effects often look like increased supply encouraging increased demand, which then encourages even more supply.

Node Value

Metcalfe’s Law seems to work best when all the nodes in a network have equal value and provide equal benefit. Nodes with fewer connections are less valuable than highly connected nodes.

Many networks don’t match Metcalfe-style growth because some new nodes don’t create connections with all existing nodes. This can happen when, for instance, new users of a network speak different languages or have interests and expertise in areas that don’t overlap.

To estimate network effects accurately, we have to take into account not only the number of nodes but also the affinity between nodes. If a network’s cost per user is fixed and later users use the network less than the trailblazers, the newer users will be less valuable to the network, and the network will become less efficient.

ethereum vs bitcoin
Ether is the native cryptocurrency of the Ethereum platform.

©Photo by Kanchanara on Unsplash – License

While experts in network economics and computer science continue to battle over whether the correct formula for calculating network effects should be exponential, logarithmic, or some other function, Metcalfe’s general point is clear. A network’s overall value tends to grow much quicker than its size.

How Do You Use Metcalfe’s Law?

In business, Metcalfe’s Law can help show you where to focus your efforts to increase the value of your product and company. It implies that the more people use your product, the more valuable your product will be to its users, even if the product itself doesn’t change. A better product just starting in a marketplace is usually less valuable than a slightly inferior product with a bigger user base.

This means that new businesses looking to attract investments from new customers should focus on specialized market niches where competing products with big user bases don’t exist. Rather than just thinking about product design and sales, small businesses should draw new users into their network by providing unique value and connections that their early adopters can’t get from any existing network.

Once you start to get some initial traction, then you can start planning to gradually expand into different or more generalized markets. As you expand, you should make sure that your business model continues to provide unique value to each new set of users. Attracting investments of money or time from new users in new markets will probably require a different marketing strategy for each new user group.

You’ll also want to make sure that your product or platform encourages the creation of complementary products that others can add to yours. Once you get the ball rolling with complementary add-ons from others, you start to create a snowball of network value that inspires even more users, investments, and add-ons.

If you want to continue to benefit from Metcalfe’s Law, besides attracting new users, you’ll need to keep your older users and customers. Many startups choose to lower their short-term profits in exchange for massive growth in business over the long term.

Finally, to stay in business as you grow, you also need a stable network model that can handle expansion and continue to provide good customer service to all your users without getting bogged down as you scale up.

Who Discovered Metcalfe’s Law?

Robert Metcalfe was an American entrepreneur and engineer. While working at Xerox PARC in the 1970s, he co-invented Ethernet, a technology that uses cables to connect computers in a local area network.

The PARC complex built and used some of the earliest personal computers. Metcalfe and fellow engineer David Boggs designed Ethernet when they were asked to come up with a networking system to connect the PARC computers.

In 1979, Metcalfe resigned from PARC and co-founded his own company, 3Com Corp, which would focus on building compatible systems of networking hardware and software. He visited the top technology companies of the time, including Xerox, Intel, and Digital Equipment Corporation, to promote his system and managed to convince them to accept the Ethernet standard.

In 1980, while working to promote Ethernet, Metcalfe came up with the idea that you could reach an approximation of the value of a network by squaring its total number of nodes. The basis of his idea was that the more connections a network could create between compatible communicating devices, the more valuable the network would be.

In 1985, the Institute of Electrical and Electronics Engineers accepted the Ethernet standard, but it wasn’t until 1993 that George Gilder, an American author and economist, put Metcalfe’s idea into the neat formula that we know today as Metcalfe’s Law. Later, as the internet exploded, computer scientists and network economists found that the idea seemed to apply broadly to many different kinds of networks and nodes instead of just the Ethernet standard.

What Are the Applications of Metcalfe’s Law?

Metcalfe’s Law of network effects seems to have the strongest applications in these four main kinds of networks:

  • Physical networks
  • Protocol networks
  • Personal networks
  • Market networks

Physical Networks

Physical networks are composed of physical nodes connected by physical links. These include electrical grids, roads, railroads, sewer systems, and broadband internet services.

Thanks to Metcalfe’s Law, it’s not uncommon to see these physical networks grow so powerful that they overwhelm smaller competing networks and turn into monopolies or duopolies. When that happens, governments tend to nationalize them and call them utilities.

Protocol Networks

Protocol networks are standards of use for digital or communications networks. They layout sets of rules for how nodes in a network must format and process data.

Nodes in protocol networks are generally digital devices rather than humans, so you can think of protocol networks as computer languages. Just like a human language, once a protocol network has been widely adopted, it’s nearly impossible to replace.

Ethernet is an example of a protocol network. When Metcalfe and Boggs came up with the Ethernet standard, other local area network protocols existed. Thanks to Metcalfe’s Law, however, the more market share Ethernet captured, the less valuable the competition became until it dwindled to almost nothing. More recent examples of protocol networks include Bitcoin, Ethereum, and other cryptocurrencies.

Personal Networks

A network is considered personal when the nodes are people. Human nodes may be anonymous or may have their real identities tied to their usernames.

Personal networks generally grow when real-life people find value in them and influence their inner circles to join as well. When a large number of people who you like and respect are using a network, you’ll usually find a lot of value in joining it too.

Examples of personal networks include TikTok and Facebook.

Facebook is a leading tech company in California, with headquarters located in Menlo Park.


Market Networks

Market networks take the identity-based format of personal networks and combine it with the transactional focus of marketplaces to facilitate mass transactions from many buyers and sellers. Instead of optimizing for quick transactions, market networks generally encourage long-term projects that allow users to improve their reputation with each successful purchase or sale.

Market networks provide value in both directions, from the sellers to the buyers, and vice versa. In double-sided systems like these, the value is derived from the network connectivity not from the specific system itself. Once a market network is established, the two sides tend to cement the network in place. To get users to move, you have to find a way to provide more value to both sides at once than what they’re getting from the existing network.

Examples of Metcalfe’s Law in the Real World

The internet is one of the prime real-world examples of Metcalfe’s Law. Its comprehensiveness and connectivity provide so much value to its users that creating a second internet sounds almost laughable. Here are a few more examples.

Ridesharing Apps

The fewer drivers a ridesharing app has, the longer the wait time will be for the users. This makes it difficult for new ridesharing networks because no matter how cheap their prices are, almost no one is willing to wait half an hour for a ride.

The bigger a ridesharing network gets, the shorter the wait time becomes. Once a ridesharing network has enough drivers to get wait times down to five or 10 minutes, its value to riders reaches a tipping point, and the network can become almost ubiquitous.

Ridesharing apps like Lyft and Uber have a better rider outcome when the driver count is up.

Stock Exchanges

One of the main determinants of the cost of a transaction on a stock exchange is market liquidity. Fewer sellers and buyers on a stock exchange mean less liquidity, which creates a bigger difference between what sellers are willing to accept and what buyers are willing to pay.

The more participants a stock exchange has, the more shares will be traded daily. This increased liquidity brings down transaction costs, attracting even more participants.

Auction Sites

Auction sites like eBay need a lot of users to make the auctions competitive. The more users an auction site gets, the more people bid on the products, which pushes the prices up. Higher prices bring more sellers to the site, which pushes the prices back down until market equilibrium is reached.

Next Up…

What Is “Metcalfe’s Law”, and Why Does it Matter? FAQs (Frequently Asked Questions) 

What does Metcalfe's Law say?

Metcalfe’s Law says that a given network’s value increases as an exponential function of the network’s total number of connected nodes.

What is the difference between Metcalfe’s Law and Eflactem’s Law?

Eflactem’s Law is a corollary of Metcalfe’s Law that describes what happens to a declining network’s value. It says that as a network loses nodes, its value decreases exponentially.

If a number of users don’t find value in a network, some of them will exit. Their exit will leave the network with a bit less value, which may cause another group of users to exit. This effect can escalate into a death spiral and collapse a once-powerful network.

What impact does Metcalfe's Law have on how we do business online?

If a network’s value is directly aligned with its number of users and possible connections, then online businesses can create a massive advantage over the competition by focusing on building their network instead of just improving their product. A good product combined with a large network benefits from greater product awareness, better supply chain control, and more product utility as the network changes users’ habits and attracts more users.

What is the Metcalfe effect?

The Metcalfe effect is the raw idea that Metcalfe’s Law tries to put into actual numbers. The idea is that networks gain value not just from their number of nodes but from the number of possible connections between nodes.

Is Metcalfe's Law proven?

Various recent studies involving European internet use, Facebook data, and cryptocurrencies like Bitcoin and Ethereum have indicated that the value of small networks really does increase in proportion to the square of their participants. For larger networks, the effect tends to fall short of exponential but still comes surprisingly close.

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