Formulæ for β & deep-dives

2. Betweenness (β)

βj=(C,w)=1N=4(wN×CN)×100CNβ_j = \displaystyle \sum_{(C, w) = 1}^{N = 4} (w_{\tiny N} \times C_{\tiny N}) \times \frac {100} {C_{\tiny N}}

Where:

  • β\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:

    • C1,C2,C3,C4C_{\tiny 1}, C_{\tiny 2}, C_{\tiny 3}, C_{\tiny 4} are the number of connections at each Proximity Level (PL)

    • w1,w2,w3,w4w_{\tiny 1}, w_{\tiny 2}, w_{\tiny 3}, w_{\tiny 4} are the weights corresponding to each Proximity Level,

      • with w1>w2>w3>w4w_{\tiny 1} > w_{\tiny 2} > w_{\tiny 3} > w_{\tiny 4},

      • and a weight of:

        • w1=1.00w_{\tiny 1} = 1.00

        • w2=0.75w_{\tiny 2} = 0.75

        • w3=0.50w_{\tiny 3} = 0.50

        • w4=0.25w_{\tiny 4} = 0.25

  • CNC_{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

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