I am trying to determine the robustness of a regular square network of NxN nodes. I am doing this by means of the average node connectivity, which is the average of local node connectivity over all pairs of nodes.
I am doing this in Python, and I am using the function described in the attached link.
The problem: if N is relatively small, the calculation is pretty fast, but as N grows it becomes computationally demanding.
My question: is there a faster way of measuring the robustness of a network, other than using the average node connectivity?
This is what it takes me to compute the average node connectivity of regular networks of varying size:
- N=10 (100 nodes) -> 6.81 seconds per iteration;
- N=20 (400 nodes) -> 486 seconds per iteration (circa 8 min).
https://networkx.github.io/documentation/latest/reference/generated/networkx.algorithms.connectivity.connectivity.average_node_connectivity.html
What is the meaning of computationally safe? I think it is either computationally expensive or not. If you mean robustness as a connectivity, it depends whether your network is random network or a complex network. For certain complex networks, like scale free and small world, average node connectivity etc, is not a robust measure.
Hi Francesco,
You may want to consider spectral decomposition (the leading eigenvalue may give you what you're looking for...) - but the answer to your question really lies in your application.
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