Mark Cuban at Blog Maverick

At Blog Maverick, in a post titled "Metcalfe's Law and Video," Mark Cuban discusses a different perspective on network value, specifically with a view towards the intensity over time of connectivity. He comments that "the more people that see content when it is originally "broadcast," regardless of the distribution medium, the more valuable the content." Although that can be demonstrated by simple net present value calculations, he is talking about emergent effects, such as emotional attachment and the social value from real or virtual simultaneous participation.

He also hypothesizes that not only is there greater value from simultaneous delivery, but also that there is greater cost. His argument is that networks that are designed for large scale simultaneous delivery of content cost more than those that are less ambitious.

To me, this is arguable. For example, there are inherent economies in using a broadcast, content distribution network, or IP multicast to distribute content simultaneously, than to keep redelivering it on demand and sequentially. If the capital expenditure for a scalable and feature-rich network has been made, broadcast and multicast technologies and architectures actually reduce cost per bit delivered per person.

If you combine his viewpoint on the value add of "live" and simultaneous events, with my observation that such events can actually cost less, that means that there is a sweet spot, if the network is engineered properly, in delivering live simultaneous content versus delayed and on-demand content.

This conclusion is actually not surprising, since traditional broadcast TV and movie theaters were only economically viable (in their day) due to the cost reductions inherent in broadcasting program content to a large simultaneous audience rather than unicasting it asynchronously. Of course, today's technology has now reduced the marginal cost of unicasting to be an infinitesimal fraction of a customers willingness to pay for such content.

Or so it would seem. In reality though, for the foreseeable future there will be content that is too bandwidth-hungry for widespread acceptance. Maybe YouTube videos don't have that property right now, but what about HDTV to your laptop screen? How many people are willing to pay for mobile bandwidth sufficient to deliver it in real time, say for 1080p video conferencing? If not that, how about digital cinema quality images?

For the next 5 to 10 years, there will always be that dilemma. After that, perhaps not, because we will have the ability to deliver enough bandwidth to each user, whether fixed or mobile, to equal or exceed the limits of human perception. At that point, until we evolve or bio-engineer our visual cortex and other sensory modalities to become Human 2.0, any additional bandwidth will be overkill, at least for the purposes of entertainment.

And What About Web 2.0 and Social Networks

Buko Obele, in a blog post at discipline and punish called "The Tragedy of Web 2.0," observes that the lack of mergers between social network providers is yet more evidence of the lack of applicability of Metcalfe's Law in this environment. He points out that the objectives of social network service providers may not be exactly aligned with the objectives of the users, and that this misalignment prevents consolidation and, in some cases, feature enhancement.

This corresponds to Odlyzko and Tilly's analysis "A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections." Although, as I've observed, there are many cases when network connectivity value may only be linear, even if it is n log (n), as discussed by Odlyzko and Tilly, there still may be relatively weak incentives for consolidation.

Nick Carr and Customer Lifetime Value

Nicholas Carr, author of "Does IT Matter," refers to an interesting analysis regarding Customer Lifetime Value (CLV) and the Network Effect, on his blog, Rough Type. Specifically, he addresses a paper by three professors, one at Harvard Business School, regarding "free" customers. These are customers, such as buyers of real-estate or at on-line auctions, who don't pay a service provider, such as a realtor or auction house, directly. The professors are able to, for a specific unnamed real-world auction house, identify the economic value of each seller, (roughly $500), and an economic value for each buyer (roughly $550). The main -- and somewhat counterintuitive -- point of the paper is that "customers" who don't spend money can be worth more than those who do. However, a hidden impact of the analysis, which took into account numerous factors including word-of-mouth recommendation value and discount rates and Lagrangian multipliers and Jacobi-Bellman conditions and many other elements that most of us have never heard of, is that the value of each customer is essentially a constant. The implication is that, in a network of buyers and sellers, the total value generated by the network, and therefore revenue to the service provider intermediary, is linearly proportional to the size of the network. Again, this provides support for the hypothesis that network value can be linearly proportional to the size of the network.

Linked by Albert-Laszlo Barabasi

Dr. Barabasi's book "Linked" is very readable overview of the math underlying a variety of network architectures, with many real-world examples in a variety of contexts. Briefly, three main types of networks are addressed. One, a random network, where links between nodes are created at random. Secondly, a "small-world" network, where most nodes are linked to nearby "neighbors," and a few links span across clusters. As studies by Watts and Strogatz, these types of networks lead to six degrees of separation types of architectures, where any node can reach any other node in a small number of hops.

However, he points out that neither type of network represents the type of structure one might find in, say, a telecommunications network or the World-Wide Web. Therefore a third type of network, a "scale-free" network, comprising a few larger hubs and many smaller hubs and endpoints is introduced. His research indicates that the node degree distribution matches the power-law distribution of many real-world structures, including neural networks and the World-Wide Web.

These real-world networks arise when two phenomena are present: one, growth, and two, preferential attachment for these growing networks. Also, implicit in the model is that each new node links to a fixed number k of existing nodes. Based on these assumptions, where a new node will tend to prefer to connect to existing nodes with more connections, a scale-free architecture emerges.

Interestingly, if we define the value of a link as a constant when it exists and as zero when it doesn't exist, the overall connectivity value of any of these networks is provably linear, based on the assumptions.

On Metcalfe's Law

I recently wrote an article addressing Metcalfe's Law and related analyses from Reed and Briscoe, Odlyzko, and Tilly of network value. The summary of my analysis is that a number of factors can cause real world networks to have value substantially less than n squared. One factor is convergent value distributions, where each connection does not have equal value. Instead, if the distribution of connection values from each node converges to a limit, that drives the total network value to be only of order (n), in other words, linearly proportional to the size of the network.

Another factor is limits of consumption that are intrinsic to the type of network. If each user can hit an upper bound in money or time spent extracting value from the network, then the value of the network is also just linear. The actual article was published in Business Communications Review, but is available here as a pdf.

The analysis also applies indirectly to Reed's 2^n valuation of Web 2.0 networks based on their group-forming capabilities. Briefly, while it is true that there are 2^n (2 to the nth power) subgroups of a network, it is unlikely that they are all equally valuable. This makes the total value substantially less than 2^n.

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