Betweenness Centrality

Betweenness centrality is a measure of a node's importance in a network, based on its role as a bridge between other nodes. It is calculated as follows:

$$C_B(v) = \sum_{ \substack{ s\neq u\neq t\in B_v }} \frac{\sigma_{st}(v)}{\sigma_{st}}$$

where V is the set of nodes in the network, o, st is the total number of shortest paths from node s to node t, and Ost(w) is the number of those shortest paths that pass through node v. The Betweenness centrality of a node is therefore the sum of the fraction of all pairs of nodes in the network that pass through that node.

In Bond Oracle betweenness centrality can be used to identify and reward users who play a crucial role in connecting different communities or groups. By quantifying the importance of nodes in the network, the platform can design reward mechanisms that incentivise users to contribute to the growth and sustainability of the network.

For example, users with high Betweenness centrality scores could be rewarded for their contributions to the network's overall connectivity, helping to create a more cohesive and resilient social ecosystem.