Network robustness-Graph theory

mendelian

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Dec 4, 2018
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I have 10 nodes in my network. I calculated the size of the largest component in my network, using the below formula:

Size of the largest component (when node 1 is deleted) = Number of nodes in the largest component, after node 1 is deleted/ Number of nodes in the largest component

Size of largest component, node 1 is deleted = 0.53
Size of largest component, node 2 is deleted = 0.85
Size of largest component, node 3 is deleted = 0.88
Size of largest component, node 4 is deleted = 0.94
Size of largest component, node 5 is deleted = 0.94
Size of largest component, node 6 is deleted = 0.94
Size of largest component, node 7 is deleted = 0.94

When I want to calculate robustness, do I have to average of all the above values?

Formula given to calculate robustness: Unique Robustness Measure(?-index) , defined as? =1 /? ∑? (?) (limit Q=1 to N)

where ? is the number of nodes in the network and ?(?)is the fraction of nodes in the largest connected componentafter removing ? = ?? nodes using a given strategy. Thevariable ? is a current fraction of deleted nodes against thetotal initial number ? of network nodes. The ?-index thusencompasses the whole attack process, not just one momentof damage at a current fraction q

Please let me know, if I am calculating robustness in the right way


Thank you
 
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