Summary

Metcalfe's Law is a formula describing network effects, which holds that the value of a network is proportional to the square of its number of nodes. However, in the Web3 AI economy, this formula is no longer suitable for the value manufacturing network in which multiple nodes participate. In a multi-dimensional network environment, Metcalfe's law needs to be expanded and revised. We analyzed the reasons why the Web3 AI economy can no longer be established, and considered the weight, complexity, and internal and external value factors between nodes in the multi-dimensional network, and extended and revised Metcalfe's law as V=K×f( N, W, C, I, E), tentatively named FlerkenS Law of Multidimensional Network Value, and used this formula to evaluate some networks in the Web3 AI economy and find out the highest value network. Finally, we concluded that V=K×f(N,W,C,I,E) FlerkenS multidimensional network value law is a new tool for the digital economy driven by Web3 architecture and AI.

Introduction

The development of Internet technology can be divided into three stages: Web1.0, Web2.0 and Web3.0. Web1.0 is the stage of static web pages and information retrieval, and users can only receive information passively; Web2.0 is the stage of dynamic web pages and social media, users can actively create and share information; Web3.0 is decentralized and intelligent In the contract stage, users can control and exchange information autonomously.

Among these three stages, Metcalfe's Law is a commonly used formula to describe network effects. Metcalfe's law holds that the value of a network is proportional to the square of its number of nodes, that is, V=K×N², where V represents the value of a network, N represents the number of nodes in the network, and K represents the value coefficient. This formula assumes that the connection between each node is uniform and the same, and that the value of the network depends only on the number of nodes.

However, in the Web3 AI economy, these assumptions may no longer hold because:

· Nodes in the network may have different types, attributes, functions and behaviors, such as users, devices, data, smart contracts, AI models, etc. Connections between these nodes may have different qualities, strengths, directions and meanings, such as social relations, data flow, transaction records, trustworthiness, etc.

· The value in the network may not only depend on the number of nodes, but also on other factors, such as data quality, user satisfaction, community activity, innovation ability, etc.

· The value in the network may be dynamic, changing as the network structure, environment and needs change.

Therefore, in order to adapt to the more complex and flexible network structure and value creation methods in the Web3 AI economy, Metcalfe's Law may need to be extended or revised to consider the following aspects:

Connection weights between nodes: Connections between nodes of different types and attributes may have different weights, reflecting the importance and influence of connections. For example, in a social network, the connection weight of close relations may be higher than that of unfamiliar relations; in a data network, the connection weight of high-quality data may be higher than that of low-quality data.

Connection complexity between nodes: Connections between nodes of different types and attributes may have different complexities, reflecting the diversity and depth of connections. For example, in an AI network, the connection between AI models may include data input and output, parameter sharing, model fusion, etc.; in a smart contract network, the connection between smart contracts may include call relationships, dependencies, authorization various forms of relationship.

· Value factors inside and outside the network: There may be many factors that affect the value of the network inside and outside the network, reflecting the matching degree of the network with the environment and needs. For example, in the Metaverse network, the internal value factors of the network may include user experience, content quality, creative level, etc.; the external value factors of the network may include market demand, competitive advantage, social influence, etc.

We will expand or modify Metcalfe's Law based on the above aspects, and use this formula to evaluate some networks in the Web3 AI economy and find out the highest value network. We tentatively named this formula the FlerkenS Law of Multidimensional Network Value, and summarized it as a new tool for the Web3 architecture and AI-driven digital economy.

Method

We took the following approach:

According to the characteristics of the network structure and value creation mode in the Web3 AI economy, Metcalfe's law is extended or revised, and V=K×f(N,W,C,I,E)FlerkenS multi-dimensional network value law is obtained.

· Select three representative networks in the Web3 AI economy as examples, namely Botto (a generative art community governed by DAO), Mawari (a decentralized 3D and XR content delivery platform designed based on Web3 principles) and Trusta labs (an on-chain data analysis company).

· Evaluate each network and calculate its value based on the number of nodes, connection weight, connection complexity, internal value factors and external value factors of each network.

· Compare the value of the three networks and identify the highest value network.

Result

FlerkenS multidimensional network value law

According to the characteristics of the network structure and value creation mode in the Web3 AI economy, we have extended or revised Metcalfe's law and obtained the following formula:

Among them, V represents the value of a network, N represents the number of nodes in the network, W represents the connection weight matrix of the network, C represents the connection complexity matrix of the network, I represents the internal value factor vector of the network, and E represents the network The vector of external value factors, K represents the value coefficient, and f represents a nonlinear function.

This formula can be interpreted as:

· The value of a network is proportional to the combined influence of its number of nodes, connection weight, connection complexity, internal value factors and external value factors.

· Connections between nodes of different types and attributes may have different weights, reflecting the importance and influence of connections.

· Connections between nodes of different types and attributes may have different complexities, reflecting the diversity and depth of connections.

· There may be various factors inside and outside the network that affect the value of the network, reflecting how well the network matches the environment and needs.

· The value coefficient is a constant that reflects the base level of network value.

· The nonlinear function is an unknown function, which reflects the law that the network value changes with various factors.

We tentatively name this formula the FlerkenS Law of Multidimensional Network Value and use it to evaluate networks in some Web3 AI economies.

Network assessment

We selected three representative networks in the Web3 AI economy as examples, namely Botto (a generative art community governed by DAO), Mawari (a decentralized 3D and XR content delivery platform designed based on Web3 principles) and Trusta labs (an on-chain data analysis company).

We evaluated each network and calculated its value based on its number of nodes, connection weight, connection complexity, intrinsic value factor, and extrinsic value factor. Due to the lack of specific data and parameters, we can only conduct qualitative analysis and assume that both K and f are constant. The specific evaluation is as follows:

The value of Botto mainly depends on N (number of nodes), W (connection weight) and I (internal value factor). N includes users participating in community governance, AI models for generating artistic images, platforms for minting and auctioning NFTs, etc. W includes voting weight between users, data sharing weight between AI models, transaction weight between NFT platforms, etc. I includes users' artistic preferences, the innovation of AI models, the scarcity of NFT, etc. Therefore, the value of Botto can be expressed as:

Among them, Nu represents the number of user nodes, Na represents the number of AI model nodes, Np represents the number of NFT platform nodes; Wu represents the user connection weight matrix, Wa represents the AI model connection weight matrix, Wp represents the NFT platform connection weight matrix; Iu represents the user's internal value factors Vector, Ia represents the internal value factor vector of the AI model, and Ip represents the NFT internal value factor vector.

The value of Mawari mainly depends on N (number of nodes), C (connection complexity) and E (external value factors). N includes users, devices, apps, etc. that provide and consume 3D and XR content. C includes multiple connection forms between users, devices, and applications, such as data input and output, parameter sharing, model fusion, etc. E includes market demand, competitive advantage, social impact, etc. Therefore, the value of Mawari can be expressed as:

Among them, Nu represents the number of user nodes, Nd represents the number of device nodes, Na represents the number of application nodes; Cu represents the user connection complexity matrix, Cd represents the device connection complexity matrix, Ca represents the application connection complexity matrix; Eu represents the user external value factor vector , Ed represents the vector of external value factors of equipment, and Ea represents the vector of external value factors of application.

· The value of Trusta labs mainly depends on N (number of nodes), W (connection weight) and C (connection complexity). N includes users, data, smart contracts, etc. that provide and use on-chain data analysis services. W includes trust and influence between users, data, and smart contracts. C includes multiple connection forms between users, data, and smart contracts, such as call relationships, dependencies, authorization relationships, etc. Therefore, the value of Trusta labs can be expressed as:

Where Nu represents the number of user nodes, Nd represents the number of data nodes, Nc represents the number of smart contract nodes; Wu represents the user connection weight matrix, Wd represents the data connection weight matrix, Wc represents the smart contract connection weight matrix; Cu represents the user connection complexity matrix, Cd represents the data connection complexity matrix, and Cc represents the smart contract connection complexity matrix.

Network comparison

We compared the value of the three networks and identified the highest value network. Due to the lack of specific data and parameters, we can only make qualitative comparisons and assume that both K and f are constant. The specific comparison is as follows:

The value of Botto is relatively low because it has a relatively small number of nodes and only involves content generation and transactions in one field; its connection weight is relatively low because its user voting and AI model data sharing may not be active enough and Fair; its internal value factor is relatively low, as its user preferences and AI model innovation may not be diverse and prominent enough.

The value of Mawari is relatively high because it has a relatively large number of nodes and involves content delivery and sharing in multiple fields; its connection complexity is relatively high because it has multiple connections between users, devices, and applications The interaction and integration of data and models; its external value factors are relatively high, because it faces great market demand, competitive advantages, and social influence.

The value of Trusta labs is relatively moderate, because its number of nodes is relatively moderate, and it involves data analysis and evaluation in a field; its connection weight and connection complexity are relatively moderate, because its users, data, and smart contracts have a certain There are also certain invocation relationships, dependency relationships, and authorization relationships.

In summary, we consider Mawari to be the most valuable network among the three networks because it has advantages in terms of number of nodes, connection complexity, and external value factors.

In conclusion

We have extended or modified Metcalfe's law, obtained V=K×f(N,W,C,I,E) FlerkenS multidimensional network value law, and used this formula to evaluate some networks in the Web3 AI economy , the highest value network is found. We summarize the following points:

· Metcalfe's law is no longer suitable for the value manufacturing network in which multiple nodes participate in the Web3 AI economy. In a multi-dimensional network environment, Metcalfe's law needs to be expanded or revised.

V=K×f(N,W,C,I,E) FlerkenS multi-dimensional network value law is a formula that considers the connection weight between nodes, the connection complexity and the internal and external value factors of the network, which can be more A good description of the characteristics of the network structure and value creation methods in the Web3 AI economy.

· V=K×f(N,W,C,I,E) FlerkenS multi-dimensional network value law is a new tool of Web3 architecture and AI-driven digital economy, which can help us better understand and evaluate various networks in Web3 AI economy the value of.

Disclaimer: The intellectual property rights contained in this article belong to FlerkenS Labs, and any reposting or misappropriation of the original work without a note is deemed an infringement.

References

: Cutting Through The Web3 Hype: AI In The Decentralized Web. Forbes. https://www.forbes.com/sites/forbestechcouncil/2022/08/04/cutting·through·the·web3·hype·ai·in·the ·decentralized·web/

: Metcalfe's law. Wikipedia. https://en.wikipedia.org/wiki/Metcalfe%27s_law