Table 2 Summary of complex network metrics
Network metrics | Definition | Equation | Remarks |
|---|---|---|---|
Betweenness centrality | The number of times a node acts as a connecting point along the shortest path between two other nodes is measured by betweenness centrality. Out of a number centrality measures, betweenness centrality of node k is the sum of the fraction of all-pairs of shortest path that pass-through node \(v\) (Brandes 2001, 2008; Brandes and Pich 2007) | \({C}_{B}(v)=\sum_{a\ne k\ne b \in Z}\frac{{\upsigma }_{ab \left(v\right)}}{{\upsigma }_{ab}}\) | Where Z is the set of nodes \((v)\) in the graph, \({\upsigma }_{ab}\) is the number of shortest paths from node a to b, and \({\upsigma }_{ab}(v)\) is the number of paths that pass-through nodes other than (a, b) |
Edge betweenness centrality | Compute betweenness centrality for edges. Betweenness centrality of an edge e is the summation of the fraction of all-pairs shortest paths that pass-through e (Brandes 2008) | \({BC}\left(e\right)=\sum_{x,y \in Z}\frac{\theta (x, y |e)}{\theta (x, y)}\) | where Z = number of nodes, \(\theta\) (x, y) = quantity of smallest (x, y) routes, and \(\theta\)(x, y |e) = number of routes which traverse to link e |