My problem: what is the solution to combine different centrality metrics of a network to rank networks according to their overall importance ?.

Consider the gene network I have where I tabled several centrality measures. This is part of a 181-node network with thousands of edges. Each centrality measure would certainly have its own shortcomings, limitations and assumptions. This is because different networks would have different ways to information flow reflected by any of the centrality metrics. Hence, ranking nodes by one centrality measure would miss out capturing the particular complexity of the system. Take the case of biological networks (PPI networks depict different information to gene-signalling or neuro network). In PPI degree centrality would be more accurate to find important proteins but betweenness could be more relevant to gene-signalling.

I found several approaches with this one ranking nodes by taking the median of the max-min of centrality metrics applied to any one node then ranking nodes by the median. Although the median-taking approach is simple I am not sure if it is conceptually sound.

name degree_std closeness_std betweenness_std eigenvector eigen_centrality page_rank transitivity
CCL3 0.08571429 0.0003174603 0.01380952 0 0.3288843 0.02043274 0
IL-1 0.05714286 0.0003072197 0.00000000 0 0.3424941 0.02370958 1
EMT 0.05714286 0.0002506266 0.00000000 0 0.1849462 0.02559053 1

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