Metcalfe's law

 

The London Underground is a dense, connected network, which makes it extraordinarily valuable
 to London and Southern England. 

From History-Computer

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

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.

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.

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.

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.

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.

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 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 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.

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.

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.

I'd never heard of Metcalfe's Law before I read this article, but I realise now that I'd always understood it without being aware of it.  

In particular, I thought of it as it applies to public transport networks.  Think of the extraordinary network of the London Tube, including the Underground, the Overground, the new Elizabeth line (Crossrail), the tram network, and mainline trains and airports, where almost every line connects with several other lines.  

In Victoria, the tram (light rail) and transit networks don't connect very well.  There are connections at the main downtown termini, but in the suburbs, because the tramways and railways were owned by different companies, their stops at the end of the line are sometimes far apart.  It has been suggested to the public transport authorities that tram lines should be extended to the nearest railway station to improve network connectivity.  Alas, this still hasn't happened.  Although the Labor government has committed to a new outer circle rail line, which will connect all the radial suburban branch lines.  Predicatbly, the LNP opposition doesn't want it.