The Value of Networks
The “worth” or value of networks is often expounded upon across a wide variety of subjects from the world wide web to the value of digitally-related companies. The bone of contention that arises mainly is, how can this be quantified with a mathematical base. There are a few empirical laws which try to do so and one the earliest such to emerge was from Robert Metcalfe, the inventor of Ethernet in the 1980s. Metcalfe’s law attempts to quantify the value of any network as being proportional to square of connected users of a system.
The foundation of Metcalfe’s law is based on the observation that in a communications network with n members, each can make (n –1) connections with other participants. If all those connections are equally valuable — an important assumption— the total value of the network is proportional to n (n –1), that is, approximately , n^2. So if, for example, a network has 11 members, there are 110 different possible connections that one member can make to another. If the network doubles in size, to 22, the number of connections does not just double, to 220, it grows to 462— it approximately quadruples, in other words.
Metcalfe’s law is often used to illustrate the crossover point in networks where, when the costs of the network are assumed to increase linearly, is the point at which a positive Return On Investment (ROI) is achieved as shown below.
There are however certain limitations with regards to Metcalfe’s law which critics claim are not valid, such as the assumption of equal importance for all nodes. Also in the case of computer networks, Metcalfe’s law does not account for service degradation as the number of users and/or data consumption grows, but the network bandwidth (the throughput of the medium of communication between nodes) does not.
In order to account for this another alternative law was proposed known as Beckstrom’s law by Rod Beckstrom.
Beckstrom’s law teaches us that to account for the value of a network (for example, a computer network), we need to account for all transactions from all devices and sum their value. If the network j goes down for whatever reason, what is the opportunity cost to the users for example ? This is the impact any real world network brings and is a more representative real-world attribution of value. The most difficult variable or attribute to model in the equation would be the benefit of a transaction B as this could be time variant across the network and possibly not constant.
