Formulæ for β & deep-dives

2. Betweenness (β)

In practical terms, the Betweenness of an individual in the Web3 ecosystem represents how well connected they are, and how "central" an individual is for their connections. It's based on a simple, progressive score, that quantifies this "social score" based on how close everyone is to all the others they are connected to.

It's simply calculated by using this formula:

$$β_j = \displaystyle \sum_{(C, w) = 1}^{N = 4} (w_{\tiny N} \times C_{\tiny N}) \times \frac {100} {C_{\tiny N}}$$

Where:

• $\beta$ is the Betweenness of j, based on the amount of connections they have with their peers, weighed by the Proximity Level of those connections

• N is the number of Proximity Levels, in this case, 4:

  • $C_{\tiny 1}, C_{\tiny 2}, C_{\tiny 3}, C_{\tiny 4}$ are the number of connections at each Proximity Level (PL)

  • $w_{\tiny 1}, w_{\tiny 2}, w_{\tiny 3}, w_{\tiny 4}$ are the weights corresponding to each Proximity Level,

    • with $w_{\tiny 1} > w_{\tiny 2} > w_{\tiny 3} > w_{\tiny 4}$,

    • and a weight of:

      • $w_{\tiny 1} = 1.00$

      • $w_{\tiny 2} = 0.75$

      • $w_{\tiny 3} = 0.50$

      • $w_{\tiny 4} = 0.25$

• $C_{N}$ is the total number of connections across all levels

Deep-dive: Proximity Levels & Markets

Proximity Levels (PL)

• PL 1: same Role a Secondary Node is in the same Hub AND in the same Role as the Central Node

• PL 2: same Hub a Secondary Node is in the same Hub BUT NOT in the same Role as the Central Node

• PL 3: same Market a Secondary Node is in the same Market BUT NEITHER in the same Hub OR in the same Role as the Central Node

• PL 4: have an ĀutID a Secondary Node owns an ĀutID BUT NEITHER is in the same Market, in the same Hub OR in the same Role of the Central Node

Markets

1. 🧑‍💻 Open-Source & Infra

2. 💲 DeFi & Payments

3. 🍀 ReFi & Governance

4. 🎲 Social, Gaming & Art

5. 🆔 Identity & Reputation