How to Understand Value in Networks: A New Framework

“Try not to become a man of success, but rather a man of value.” — Einstein

Each of us are nodes in a vast human network of interconnectivity and interdependence. The entire living human network (7.4+ billion nodes) is comprised of subnetworks of nations, cities, communities, villages, and so on. These physical human networks and our vast realm of digital (human and machine) networks function similarly from the standpoint of how we understand network effects. Einstein urges us to strive to be valuable people, so what does it mean to be valuable in an interdependent network of people?

We simply don’t have the right framework to properly scrutinize the behavior and psychology of networks of people. Without which, you won’t know which nodes/users are truly the most valuable and why. You won’t know which behaviors and non-behaviors to optimize and incentivize for. In short, you won’t be able to best optimize the network.

The performance of a human network depends entirely on the depth to which you model and understand it, and how well you execute on insights gained from this scrutiny to improve it.

I hope to add clarity to how we model the flow of value in human networks.

If you’re a startup founder, tech investor, employee at a tech company that employs network effects, or just interested in the understanding and optimization of group formation, this analysis is for you.

In this essay I’ll deconstruct why the the most common law for modeling value in networks (Metcalfe’s Law) is mis-applied to the tech world, propose a new theory for quantifying value in networks, and explore the implications of this new framework for startups and society.

Quantifying Interdependence

Because of how fundamental network effects are to the functioning of communities and companies, we must have robust models for understanding and quantifying them. The incumbent model is Metcalfe’s Law, which unfortunately is anything but robust, and gets frequently mis-applied to the tech world.

Metcalfe tried to quantify this observation that there is tremendous value in group formation and interdependence. But how much value, and what kind of networks are we talking about?

Metcalfe’s Law proclaims that the value of a network is proportional to the square of the number of connected devices.

Metcalfe’s Law, circa 1980.

Note the word “devices” and not “people”[1]. Metcalfe was the inventor of Ethernet, and when he proclaimed this around 1980, he was describing connected devices like printers and telephones. In these networks, each node fundamentally behalves exactly the same and are of equal value. The central fallacy is assuming this observation applies to human networks.

Metcalfe’s Law is for connected devices, not connected humans.

The assumption that all nodes are of equal value is simply no where near true in human networks (users or customers of a service). Humans consume and provide value within a peer-to-peer network asymmetrically. User segmentation is common practice today; defining and understanding your power users, average users, lurkers, and other user segments are absolutely critical to growth strategy. Some basic network questions that companies try very hard to answer are, what are the characteristics of an engaged user? How many users are highly engaged? How does user retention vary across different segments? Variables like how a user was acquired, initial experience, how much content consumed vs. created, how many invites sent to others, etc, have to be taken into account in order to understand the basics of your user base and what is working well and what isn’t. What’s the value distribution of the nodes in the network? Power law? Flat? Linear?

Metcalfe’s Law answers exactly none of these questions, yet it’s espoused as a foundational concept in the tech world in 2016. It’s a complete misapplication of his law, and it baffles me how many people blindly propagate it. It’s taken as received wisdom among investors, entrepreneurs in and out of Silicon Valley. Even Andreessen Horowitz mentions it in their comprehensive analysis of network effects, calling it a “common law for assessing the value of communication networks” like Facebook. It is a common law. The problem is, it shouldn’t be. And it will continue to be a common law the more people who champion it out of context. [2]

Device laws don’t pertain to human users. It’s like trying to apply general relativity to the quantum world. They both operate on totally different premises. With actual scientific theories, we are usually well aware of the bounds of applicability. We’ve been extremely sloppy in this case.

It’s not that Metcalfe’s Law is reductionist or outdated. It’s that it simply wasn’t ever meant to describe human networks. So, what we need is a theory not for “connected devices,” but for “connected people.” Basically, a Metcalfe’s Law for people.

Here are my proposed assumptions that a new law must take into account:

1. All nodes are not equal

As far as humans are concerned, content creation and consumption are highly asymmetric. We aren’t printers, who’s behavior is highly defined, and is the same as other printers. Human behavior is all over the place, and growth teams at companies exist because to navigate this terrain.

2. The contribution of any node in a network has to be measured in terms of value received by the other affected nodes.

From the quote at the top, Einstein knew that in our interdependent world, being valuable is more important than personal success. To be a valuable person implies you’re providing value to others, and the exact same is true for online networks of users.

This is a critical point in understanding node value, as well as how to think about ourselves in the context of a broader society. Essentially, you measure your own contribution by the total amount of value received by others from you.

It’s also worth mentioning that value received != value transmitted. Value sent means nothing if it’s never received. If I send 10 emails, but they never get noticed or opened, the action wasn’t valuable and shouldn’t be interpreted as such.

Each node must be understood within the broader context of its externalities — the consequences it has on the overall network.

Since all nodes aren’t equal, to understand the value that each node brings, we have to ask this simple question: from the network’s perspective, how consequential is each particular node?

How should you model “value received”? Two proposals…

Level 1 Analysis

Measure node value in terms of value received by all other nodes, but generalize the receiving value. Assume received value per node is equal, for the sake of simplicity.

Example — Youtube. 10M YouTube views vs. 2.5M. Total value = number of viewers, assuming each person received the same value from watching the video. This is simplest way to understand which users are most valuable in the network.

Example — VillageDefense. In a VillageDefense network, users can send real-time crime alerts to others nearby, participate in a live chat, and invite others. These are three ways a user can add value to the network. This is a simplistic analysis, but that’s the point. I can send 5 real-time crime alerts to people nearby, but if only 10 people receive it each time, that’s less value than if they were being received by 100 people each time. Again, we‘re making an implicit assumption that alerts received are valuable at all, and equally valuable for each recipient.

In addition to direct content creation, one of the most valuable things a user can do in a network is to grow it. This word of mouth growth is represented by K, the viral coefficient (# invites sent * conversion rate). By definition, organic network growth relies on users bringing others along, and we can quantify the value this brings to the network when a user does this.

Here’s a sample equation showing how to make this calculation to assign a “value score” on a per user basis, summing up the total value received by everyone else in the network as a result of your actions.

Level 1 analysis of a VillageDefense network. The summation of the value of the content received by the network, raised to the Kth power (viral coefficient), is a simple way to define the value of a given user.

Level 2 Analysis

Break down value received by each node on a transactional basis.

In this deeper analysis, we don’t make the assumption that all nodes receive value equally as we did previously. Just as nodes don’t transmit value equally, they don’t consume it equally either.

Here’s how to break down value received.

(1) List all the ways (transactions) in which users consume value from other users. 
(2) List any proxies you can think of that are indicators of value received.
(3) Measure value received by each node, per transaction, based on your value attributes.

Example — YouTube. Give each YouTube viewer of a particular video a score to approximate value received (perhaps looking at % of the video watched, whether or not the user subscribes to the channel, # of shares, comments, repeat views, etc).

Example — Medium. Look at how far each user scrolls down in a given article, combined with the amount of time on the page, to give some kind of approximation for how much value each particular reader consumes (Surprise! Medium’s top line metric is time spent reading). If you aggregate all these value received scores from each user of a particular author, you have real data on which to compare the value of that author to others. Who are the most valuable contributors on Medium? That analysis would answer that question. (Not Metcalfe’s Law, page views, or any other “common” network law).

Ev Williams makes this very case as he outlines Medium’s level 2 analysis, arguing that companies and investors should shift from only caring about shallow metrics like active users to metrics that do a much better job at quantifying depth of engagement and value received.

In summary, given that all nodes are very unequal in value, quantifying that value in any network HAS to be in terms of value received by others, not transmitted, however measured. The better you can approximate value received on a per node basis, the more accurate your model will be. Growth teams and engineers must develop a system for tracking and analyzing this. A better understanding of your network totally depends on it.

Precision wins, but start somewhere

Level 1 is simpler and easier to get started, but involves generalizations. Level 2 is much more precise and robust, but much more involved from an engineering and analytical standpoint. The more precise you can get in quantifying value received, the more accurate your overall node comparison will be. Ideally, every network effect based software company should strive for a Level 2 analysis.

Putting all this together, here’s what I propose is a network’s true value…

The total value of a network is proportional to the square of the number of nodes in the network, multiplied by the sum of the value received by each node.
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Keep in mind it’s not important whether these value equations perfectly match some objective measure of reality which may not even exist. The point is that you have a thoughtful framework you can use to discover how your nodes are performing individually, compare and rank them in relation to one another, and see how strong your network is overall. All while tracking change over time. This is a framework for approximating and comparing the value of your users, and ultimately, understanding the value of your whole network.

How this affects software startups:

To even do these analyses, the data you need must be accessible by your growth team. Taking time to define a value equation for comparing users will directly impact how engineers store user information and events in your database (and the retrieval process). Especially in the case of a Level 2 analysis, very conscious engineering and data science is required.

As a growth team, if you’re not analyzing the value of your users, especially your power users, by their combined and detailed effects on the rest of your user base, you’re doing it wrong.

If you’re not analyzing and segmenting your user base based on this value comparison, you’re doing it wrong.

You HAVE to know how the individual actions of your power users affect the rest of your user base. Otherwise, you simply won’t know what actions are valuable and therefore UI optimization are impossible, or at best, a shot in the dark.

How this affects society

Societies are organisms, strengthened or weakened by certain collective attitudes. If you define success solely from your standpoint, it makes sense to strive for personal success. However, if you switch your perspective to that of the overall network of people, it becomes apparent that individuals contributing to the whole is necessary to build a stronger society.

Let’s be valuable people.

Think about your our own value as the sum of all value received by everyone and everything else that you’ve affected. The more you optimize life for value received by others, the stronger and more valuable our entire society is.

Within this framework, you can start to ask questions like, what kind of value do I want to provide others? What kind of value do I love providing? If we want to contribute to building the strongest, most flourishing society we can, we have to maximize the value that others receive from our existence. This perspective actually can help define and clarify our life’s purpose.

Notes:

[1] Metcalfe proposed his theory around 1980 as it pertains to “compatible communication devices.” Fax machines, printers, ethernet switches. Not people, not users. At some point, journalists mistakenly added the word “users” when they were reporting the law.

[2] My theory for why people constantly bring up Metcalfe’s Law, even though it’s being mis-applied, is that a) our brains like shortcuts to answers vs. questioning premises and re-analyzing from first principles, and b) it is the only “law” available that we can point to in our quest to convey why network effects are so powerful (availability bias).

[3] Even though I use this word in the essay, “user” isn’t a good word to refer to network participants. Inaccuracy of our words begets inaccuracy of our models. “Using” implies is a one-way stream of value. In networks, there is complex value exchange. It’s alive and dynamic. You interact and collaborate. I don’t collaborate with my toaster, toilet, or sunscreen. Only looking at daily active users (a good snapshot for size of network), ignores the complex value exchange happening. The term “node” is an abstraction, but at least it conveys multi-directional value exchange, or interdependence.