[pixcavator]

Thanks for the explanation! My only concern now is the validity of the meaning of the principal eigenvalue: "λ determines how much influence people share with each other through their connections. If λ is small then the CEO has a lot of influence, if it is large then he has little." It seems to depend on λ>1 or λ<1. Also, has this method been applied in practice, if you know?

[brent]

I don't understand the interpretation of the principal eigenvalue either. Perhaps there is a more suitable interpretation in the directed case, but I'm not sure of that either.

I think this method is generally known as eigenvector centrality, that is to say, the entries in the vector x are generally known as eigenvector centralities. I think this method is quite popular, but I do not know who uses it or how often.