Calculating the eigenvector centrality of a portfolio described by a minimum spanning tree

I am working with the eigenvector centrality of a minimum spanning tree, which can be calculated as:

v(i) = lambda^-1 * sum[Omega(i,j)*v(j)]

where:

• v(i) is the eigenvector centrality of the node i-th
• Omega is an adjacency matrix (square)
• lambda is the biggest eigenvalue of the Omega matrix
• v(j) is the eigenvector centrality of each j-th neighbor node

Let's assume that I want to calculate the eigenvector centrality of a portfolio, i.e. I want to weight each i-th eigenvector centrality v(i) by means of a weighting vector w. How can I calculate the weighted centrality of n nodes?

• Do they not show how to make w a function of v(i)? Why then is their title portfolio selection – develarist Jan 20 at 13:04