Whether it's morally right or wrong to give you a hint depends on whether this is an assignment that you get credits for or not. I think you should work a bit harder before you ask. The name of your university also hints at the verdict that you should know it already. :-)

What do you mean by solving? It is an eigenvector centrality measure, which is a common descriptive metric used in social network analysis. It's calculated from an adjacency matrix of a network. In this case the edge weights are calculated from cross-country trade data on a bipartite graph.

Here is the original paper: http://www.pnas.org/content/pnas/106/26/10570.full.pdf

By the way, I do have some reservations about the practical ability of ECI to measure the knowledge capital in an economy, because countries with only a short slice of the value-chain localized, but with a high diversification, can get overestimated by the index. Using value-added terms could be more useful.