Formulæ for α & deep-dives

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:

$$\displaystyle \alpha = \frac {cPS_{\tiny {(j, \tt H \cdot)}}}{|H_j|} \times 100$$

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 $[\tt h \cdot]$.

Deep-dive: calculating local $cPS$

As a reminder, the Local Centrality of j’s Participation Score in a Hub is calculated as:

$\displaystyle cPS_{j, \tt h \cdot} = \frac{PS_{j,h}}{\max(PS_{[1, ..., n],h})}$

To obtain $\alpha$ (the “absolute centrality”), we can calculate all the local cPS of the Participant across their Hubs:

$\displaystyle cPS_{j, \tt H \cdot} = \sum cPS_{j, \tt h \cdot}$

and divide it by the total amount of Hubs $[\tt H \cdot]$ of which j is a Participant:

$\displaystyle \alpha = \frac {cPS_{\tiny {(j, \tt H \cdot)}}}{|H_j|}$