# Formulæ for β & deep-dives

### 2. Betweenness (β)

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 NodePL 2: same

**Hub**a Secondary Node is in the same Hub BUT NOT in the same Role as the Central NodePL 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 NodePL 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

🧑💻 Open-Source & Infra

💲 DeFi & Payments

🍀 ReFi & Governance

🎲 Social, Gaming & Art

🆔 Identity & Reputation

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