2.2.2. Betweenness Centrality

This study uses betweenness centrality to determine the comparative importance of TIs in the graph of shale petroleum technologies [31].

$$\mathcal{C}\_{B}(k) = \sum\_{\substack{\upsilon \neq k \neq w \\ k, \upsilon, w \in K}} \frac{\sigma\_{\upsilon w}(k)}{\sigma\_{\upsilon w}},\tag{6}$$

In Equation (6), *CB*(*k*) is the betweenness centrality of TI *k*. *k* is an element of *K*, a set of whole TIs. Each TI is a node in the graph, which comprises TIs and their similarities. σ*vw* denotes the number of shortest paths from nodes *v* and *w*. <sup>σ</sup>*vw*(*k*) denotes number of shortest paths through node *k*.
