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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?

Thank you for your help.

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  • $\begingroup$ which article gives the formula that you wrote $\endgroup$ – develarist Jan 19 at 21:14
  • $\begingroup$ A network approach to portfolio selection; Gustavo Peralta, Abalfazl Zareei (Nov 2014). The formula can be expressed in other ways, if you have another in mind I am flexible. $\endgroup$ – Vitomir Jan 20 at 8:40
  • $\begingroup$ Do they not show how to make w a function of v(i)? Why then is their title portfolio selection $\endgroup$ – develarist Jan 20 at 13:04
  • $\begingroup$ In their asset allocation they do not solve any optimization problem, they indirectly use eigenvector centrality to build portfolios. Nevertheless, I am not trying to replicate this work, rather build something new, i.e. I want to calculate the eigenvalue centrality of a portfolio and then use it in the optimization. $\endgroup$ – Vitomir Jan 20 at 15:08

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