An improvement upon the previous experiment. This time, a variant of eigenvector centrality that takes into account the weights of the links is computed, yielding a very different diagram.
In order to do that, the network’s adjacency matrix is populated with weights in place of binary (connected / not connected) information. Computing the centrality measure using this matrix is sufficient to obtain a result that takes topology and weights into account, as discussed in Newman 2004 (alongwith other analysis methods for weighted networks).