1. Centrality ($\alpha$)

The Centrality represents how needed/relevant is a Contributor to a Hub, comparing it directly to all other Contributors. In fact, if on one side, multiple Contributors can have a positive Participation Score - on the other, the Centrality parameter measures how high is someone's participation respect to all other top contributors. This both shows the true dedication / workload of a member to bootstrap the Hub, and helps Operators to understand who is making the heavy lift to bring the Hub to the next level, and can reward them accordingly.

To calculate a Contributor's Centrality ( $\alpha$ ) within the Hub, we can use this simple formula:

where:

• $\alpha$ is the Centrality of j’s Participation in each one of their Hubs.

• $cPS_{(j, \tt H \cdot)}$ is the absolute centrality of j’s PS in all their local Hubs $[\tt h \cdot]$ in the Set $[\tt H \cdot]$

• $[{\tt H \cdot}]_{j}$ is the Set of all Hubs $[\tt h \cdot]$ to which j contributes.

• $max(PS_{[1, …, n], \text{ h}})$ is the highest PS value of any participant in Hub $[\tt h \cdot]$.

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:

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

Initial Parameters for $\upsilon$

Initially, we will be using three (3) main parameters for evaluating an individual’s Peer Value (Global Reputation):

• The Centrality ( $\alpha$ ) of the contribution of a Participant across their Hubs.

• The Betweenness (Interconnection) ( $\beta$ ) of a Participant respect to their peers.

• The Variety ( $\gamma$ ) in the Contributions delivered by a Participant across all their Hubs.

On a concrete level, they also identify the main "archetypes" of a value-contributor:

• The Pillar ( $\alpha$ )

• The Socialite ( $\beta$ )

• The Polymath ( $\gamma$ )

From these archetype we can extract a compound parameter, called Peer archetype ( $\mathring{a}$ ):

where:

• $\mathring{a}_{j, \tt N \cdot}$ is the Peer archetype of Participant j across all their Hubs $[\tt h \cdot]$ in the set $[\tt H \cdot]$.

• $\alpha$ is the Centrality of j's Participation Score (PS) in all their Hubs.

• $\beta$ is the Interconnection (Betweenness) of j with their peers.

• $\gamma$ is the variety of j’s contributions across their Hubs

The dominant parameter will determine the Archetype of the Contributor j.

3. Variety ($\gamma$)

The concept of Variety is quite intuitive: it calculates how "diverse" are someone's contributions across all the different Hubs they are part of. This keeps into consideration the Role of the individual in each one of their Hubs, as well as the Market in which each Hub operates, and the different Contributions they commit to complete, and actually submit. In one sentence: someone's Variety score is based on the amount of "unique" contributions (= contributions which do not repeat) they deliver across all their Hubs, divided by the total amount of Contributions submitted (= how many of the Contributions submitted are different from the others).

It's calculated using the formula:

where $r\gamma$ is the "credible relative variety" of j’s contribution at the local Hub’s level.

Once we have $r\gamma_{j, h} \text { } \forall \text { } \tt h \cdot in \text { } \tt H \cdot_{j}$, then we can calculate $\gamma$ as: