Formulæ for α & deep-dives

1. Centrality (α\alpha)

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

where:

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

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

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

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

Deep-dive: calculating local cPScPS

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

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

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

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

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

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

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