美国波音公司工业工程师，笔名“Graytrain”，是区块链和加密货币的忠实拥护者。他致力于将复杂的区块链技术简单化，以便大众更好地学习和理解。他对区块链技术深入的解读，使得他的文章在海外一直备受好评，拥有众多忠实的粉丝。

I recently came across an article from MIT Technology Review titled How Network Theory Predicts the Value of Bitcoin. Now I am well aware of Technical Analysis and the hand-wavy techniques used to “determine” market trends and future price and I generally try to steer away from such speculation as they are often wrong as many times as they are right. So when MIT published an article saying they were able to predict 94% of Bitcoin price movement using Metcalfe’s law, my interest was piqued. I figured it would be an interesting exercise to use it to look at the impact of predicted future IoT network growth.

First introduced in 1980, and attributed to Robert Metcalfe (co-inventor of Ethernet), the law states that the value of a network (V) is proportional to the square of the number of connected users of the system (n²). This first was applied to not users, but compatible connected devices like fax machines and phones in the days before the Internet.

Put simply, the more people use a network, the more valuable it is. If a network is composed of 2 computers, it has less value than one with 10 computers and lesser still than one of 50 computers. It turns out that the increase in value grows faster than the growth of the network.

This assumes that each user or device is of equal value which in certain cases may not be true. If one fax machine serves 50 people in a workplace, the value of that one machine is higher than that of one that serves only 2.

It is important to note here that it is not equal to the number of users but proportional to the number of users by a Metcalfe’s coefficient (a) that has to be empirically found for a given network. This coefficient approaches stability the larger the n. Metcalfe’s law then becomes:

Proving the validity of this proposed law has only been a possibility with the recent growth of social media and large scale data sets. The most significant of which was an independent study (Zhang et al., 2015) on the value of Facebook and Tencent, China’s largest social network company. They found that over a 10 year period, the value of these companies grew not linearly with the growth of the user base but as the square as predicted by Metcalfe’s law.

They reported a Metcalfe’s function for Tencent and Facebook of: 

More recently, cryptocurrencies have drawn the attention of curious network scientist and financial experts as the dawn of a new internet of value approaches. These networks present another interesting case of large, ever-growing user base with a network of known market value.

Several economists from ETH Zurich and the Swiss Finance Institute released a paper in March of this year which used Metcalfe’s law to predict bitcoin’s bubbles and crashes (Wheatly et al., 2018). They outline in great detail how they went about constructing this model for bitcoin valuation using daily active users by counting unique addresses used in a given day.

Plotting market capitalization versus active users reveals a remarkable correlation between the two and when fit with a line formulated by Metcalfe’s law, collections of points above the line correspond to times before crashes and points below the line correspond to times of buying opportunity [Fig. 1]. (remember linear in log scale means exponential in linear scale)

As shown in the chart on the right, the growth of daily active users of the network correlates almost perfectly to the market cap at that time.

This is remarkable. This is the only example I could find of hard data that correlates to value of a cryptocurrency. I couldn’t stop here, I had to try it for myself. So I pulled the data for Ethereum from Etherscan.

Now we can expect to not see as great of a fit because there was some expected valuation at the start of this project and so it’s market cap didn’t grow naturally from zero like it did with bitcoin. Also we don’t have the same timelines to deal with so sample size is not as big.

Putting the data together and correlating it like was shown in the study above, we see the same relationships. Charting the active users of the network over time with the market cap overlaid we can see the remarkably direct correlation between the two [Fig. 2]. Action in user activity directly results in corresponding market valuation movement.

Charting market capitalization versus daily active users shows a linear in log relationship that can be fit with a formula based on Metcalfe’s law [Fig. 3]. What is interesting is that the network doesn’t grow proportional to the square of the users but to n^(1.43). This is in line with the Zhang et al. study reported with bitcoin’s growth exponent being n^(1.69). This is because not everyone in the network is connected to each other and the network is more like a cellular network of collections of nodes with collections of users connected to each other. The complete Metcalfe formula was found to be:

When the market cap vs active user data is fit with a line formulated with the above Metcalfe’s law, we see the same correlation between relative position of a collection of points and the over or under valuation that lead to drastic market movement [Fig. 3]. First we can see that the network was valued over what would be expected from number of active users until late 2016. At this point the network was growing faster than the market cap which lead into the large summer of 2017 spike in price where the data shows points on the top side of the line indicating over-valuation. What is interesting to me is the fact that the network grew so fast in late 2017 and through 2018 which has yet to be reflected in the market cap. The 2018 bubble which is seen in bitcoin is not as present in Ethereum.

Going back to the core of Metcalfe’s law which states the network value is proportional to the square of users, how would this apply to an IoT network, where every user could potentially have multiple devices connected to the network? If the number of active users grow similar to a netoid function shape, which we see in Ethereum [Fig. 4] and NEO [Fig. 5], then this would have an effect on the steepness and height of the exponential portion of the curve before leveling off.

Since no IoT network is developed enough with sufficient device participation to make a model of, we will have to make some assumptions around impacting variables and develop a model based upon them.

What do we know? INT is a Chinese project with a minimal amount of communication, lesser still to the western world, developing something that currently has no competing architecture for the given application, which has yet to release a main net and is not yet on any major US accessible exchanges.

This all takes me back to NEO, when people had to translate what little information was out there about a project that’s only (only) competition was Ethereum that fit a niche in China’s market.

Understanding that the cryptoeconomy is in much a different place than it was then, with many more investors involved and many ideals changed, the impact or growth of these variables may be different. Hype may have less impact, FOMO may not occur, or actual technical ability may have no impact on valuation and communication and hype may create all value, that much we cannot determine. So for this exercise, let’s assume the growth of this network is similar to that of NEO.

NEO’s network is currently 1/35th that of Ethereum at just over 1,000,000 addresses with an average daily activity of even less (1/100th of Ethereum’s daily activity) [Fig. 5].

Unfortunately, we don’t have address creation history for INT since it is still an ERC-20 token but we do know that there is currently ~80,000 addresses holding INT. Looking at NEO’s address creation chart, this corresponds to August 2017 when Antshares re-branded to NEO and when NEO’s main net had already been live for almost a year. That kind of highlights the difference between the cryptoeconomy of one year ago and now.

Based on this, I don’t think it is fair to compare where INT is now to where NEO was when it had this many addresses. Instead, lets use the percentage growth seen after Antshares re-brand as what may happen when INT releases main net and gets on a bigger exchange (4Q 2018). Looking at current unique address activity, averaging ~50–100 addresses a day, this pushes back the timeline to about March 2017. I feel like this is more fair to the timeline of INT’s development and what they have coming in the latter part of this year. INT will also not likely see the spike from a re-brand compounded with NEO’s 2017 run up but that growth may be seen on INT’s main net launch so we will match up the timeline there. I know we are really compounding our error bars here by making so many assumptions but what the heck.

In doing so we get an INT-NEO proportionality that we can apply to NEO’s active address history and model a potential INT network activity into the future. This gives us predicted network activity out ~1.5 years to March 2020.

In order to use this to find INT’s proposed market cap correlation to this predicted network activity, we have to first find the Metcalfe coefficient (the slope of the line) to NEO’s dataset and renormalize it to INT’s starting point market cap. This gives us a Metcalfe function similar to that of Ethereum of:

You can see that the slope of this line is MUCH higher than Ethereum. I believe this is because of the age of speculation that we are in that drives value without real world usage. This basically means that every user adds more value to the network than a user on Ethereum. Now this may be true for a data based network as in IoT, where the users are not just transacting value exchange but are also transacting data that may have value. Applying this formula to INT’s predicted dataset, we get:

So where does that leave us? What price at what time? We can use the above Metcalfe’s formula to predict the market cap at a given time [Fig. 7].

This data shows INT at $10 around January 2019 and oscillating between there and $15 before a big run up in the summer of 2019, peaking at $50 before consolidating back down to the ~$20 level.

Now this is totally and absolutely a collection of guesses and estimates with a healthy dose of speculation but it is modeled on real world data and fit to a valuation formula that is proven to accurately predict network value based on number of users. This might even be an underestimate based on the fact an IoT network may have more immediate real world use (and therefore higher user growth) than a smart contract based network real world adoption. INT has already specified several projects and partnerships that will drive that use.

This also assumes:

• INT will have no major market growth before main net release. This would change the starting point for all growth and shift the pattern up.

• The circulating supply which determines the price is held steady at 300 million throughout. If we assume that number becomes larger in the 1.5 year timeline shown, that may have some impact on overall price.

• The user activity will grow regardless of market conditions. Basically stating that this network will have more real world usage that will drive network activity, not just the speculative buying and selling activity. This adds another variable to growth independent of market speculation. This implies that even in market slumps, the value of the network will rise.

• AND THE BIG ONE. The overall market growth in the coming year is going to have the same cycle like what was seen in late 2017. This correlates to the spike shown in mid-2019 in the above chart and was reflected in the network activity in active users. If this does not happen, active user count will still continue to grow and drive the market price, continuing to be proportional to the active users in a more linear fashion instead of the spike shown.

I will continue to track this user growth through main net release and market expansion and release updates on how the real world data reflects this model. Based on the partnerships currently underway with INT and the data that is available from other projects, network growth is bound to occur and the number of active addresses will reflect that, maybe more so than what was shown in NEO. Even if we assume a slower growth and a much less steep network activity to market cap relation like that of Ethereum, $10 INT is more of a “when” instead of an “if”.

You can go much deeper into this analysis by fully modeling network growth and taking into account number of active users and daily transaction volume. To have a more in-depth look at this method, read these articles and papers: