Betweenness centrality captures the geographical distribution of attractive travel paths between each pair of nodes across the network. It shows concentrations of ‘movement energy’ generated by the travel opportunities the network provides, or in other words, to what extent an activity node is located ‘at the crossroads’ of public transport supply. This index is weighted by the catchment size of activity nodes as well as their proximity (travel impediment), following the logic that larger nodes and nodes more accessible to each other generate more travel opportunities between them than smaller nodes and nodes with greater spatial or network separation. The scale of this indicator is arbitrary but is kept constant for easy comparisons with future scenarios or between cities. It is shown for each node as well as aggregately across the network. Higher values indicate greater centrality.
Betweenness Centrality is separated into two separate indicators, Nodal Betweenness and Segmental Betweenness. The only difference between the two indicators is that in the formula below the 'i' in segmental betweenness stands for 'segment' instead of 'node'
Betweenness centrality
where:
Bk = Betweenness centrality of node/segment k
Pij(k) = Paths between nodes i and j that pass through node/segment k
acti = Number of residents and jobs in catchment area of node i
actj = Number of residents and jobs in catchment area of node j
Lmin,ij = Minimum cumulative impediment between nodes i and j
Bg = Global betweenness index
N = Number of activity nodes in the network
Betweenness Centrality is separated into two separate indicators, Nodal Betweenness and Segmental Betweenness. The only difference between the two indicators is that in the formula below the 'i' in segmental betweenness stands for 'segment' instead of 'node'
Betweenness centrality
where:
Bk = Betweenness centrality of node/segment k
Pij(k) = Paths between nodes i and j that pass through node/segment k
acti = Number of residents and jobs in catchment area of node i
actj = Number of residents and jobs in catchment area of node j
Lmin,ij = Minimum cumulative impediment between nodes i and j
Bg = Global betweenness index
N = Number of activity nodes in the network
Global betweenness
where:
Bg = Global betweenness index
acti = Number of residents and jobs in catchment area of node i
actj = Number of residents and jobs in catchment area of node j
Lmin,ij = Minimum cumulative impediment between nodes i and j
N = Number of activity nodes in the network
where:
Bg = Global betweenness index
acti = Number of residents and jobs in catchment area of node i
actj = Number of residents and jobs in catchment area of node j
Lmin,ij = Minimum cumulative impediment between nodes i and j
N = Number of activity nodes in the network
