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Network Science Based Quantification of Resilience Demonstrated on the Indian Railways Network

Fig 1

Node removal and recovery process in the representative network with N = 6.

Nodes X and Y are selected randomly for removal at time, T = 1 and T = 2, respectively. A. (i) The SCF = 1 at step T = 0 (pre-hazard). Node X (red) is selected for removal at step T = 1. (ii) Removal of node X results in reduction of the size of the Giant Component (GC), which sets SCF = 0.5. Dashed nodes (edges) means that nodes (edges) gets detached from the GC and hence incapacitated. Node Y (blue) is selected for removal at step T = 2 (f = 1/6, meaning one out of the six nodes is targeted for removal). (iii) The GC ceases to exist after the removal of node Y. B. To highlight the asymmetric nature of recovery process, nodes are restored to their full functionality in the same order these were removed (i.e. node X followed by node Y) from the network. (iv) Node X (yellow) is selected for restoration to full functionality in the first step of the recovery process. (v) This results in the recovery of the node X to full functionality (f’ = 1/6, meaning one out of the six nodes is fully functional). As a result, three nodes directly connected to X gain at least one edge and the GC grows, making SCF = 0.67. Then, node Y (green) is selected for recovery in step (vi). Recovery of node Y to its full functionality result in restoration of the SCF of the network to 1 as shown in (vi).

Fig 1