In the early years of networking, Bob Metcalfe set forth his famous law of networking that points out that the total value of a network grows by the square of the number of nodes (people or devices) that connect to it.

As time went on, networks grew, the dot-com world worked itself into a frothing frenzy, and Metcalfe’s Law seemed to promise utopia. Armed with hindsight, which is inherently unfair, the issue with any network value statement is that the potential value of a network increases at an unknown rate for each node added and, even if there is real value, the potential may not be realized either for the node or the overall network.

Additional nodes and networks added to an existing network do not necessarily guarantee value – positive or negative. A node could be silent, stealing value due to maliciousness or serviced by multiple networks wherein there are multiple logical addresses but only one physical device or service causing redundancy and the potential for overstatement in the real world.

Looking at the potential value of networks is interesting but an exact answer about value is impossible – only guesstimates are possible for a variety of reasons. The intent of this article is to spend a few minutes and examine the potential value of networks.

If you can bear with some math for just a moment, Metcalfe’s Law promised that the value of a network was n^{2}-n, where "n" is the number of nodes. In the late 1990s, David Reed suggested the value was really 2^n. In 2005, Andrew Odlyzko and Benjamin Tilly suggested a formula of n log(n) because they viewed the previous two formulas as overstating value. Now, with reality setting in, we can look at these formulas through a different lens.

First, connections, value, price and cost are three fundamentally different concepts. Connections address how many different ways nodes can be connected – paths if you will.

Value is something that is assigned by a buyer of a good or service. It is subjective and fluctuates with time and the whims of the market.

Costs are outlays, both in economic and accounting terms, associated with running a business/organization and providing products and services. Lastly, price is what a product or service is attempted to be sold at and, like value, will fluctuate with the market.

Despite the rhetoric, there simply isn’t a direct correlation between nodes and value. There are too many real-world variables that enter in to accurately estimate value.

When we look at the network value formulas, we are not truly seeing value, price or cost – only potential connections. If we have 2^32 connections and all lack value, then the value of the total network is still only zero, but the potential could hold promise over a relatively smaller network of 2^16 connections given that all nodes have positive value.

Therein lies the first issue – value is cumulative. One high-value node can be far more worthwhile than several other nodes combined and a small network with relatively high-value nodes can be cumulatively worth more than a larger network of relatively lower-value nodes.

For that matter, we can safely assume that for any network, only 20% of the nodes will create 80% of the value. Conversely, we can also assume that the majority, or 80%, of the nodes will contribute very little value – perhaps 20%, if the 80/20 rule holds true.

While possible connections and potential values are interesting to contemplate, any formula aimed at ascertaining theoretical network potential value (NPV) can only go so far in the real world due to factors that impair incremental value or even create negative value for each additional node added.

This latter part is very concerning because of the possibility that some or all of the total value created could be destroyed following a curve more like a logistics growth curve that reaches an asymptotic peak with diminishing returns, but as the threats overwhelm the value, the tail end of the curve begins to fall at a rapid rate.