Eigenvector centrality ($Av={\lambda }_{\max }v$)

Eigenvector centrality assigns nonnegative vertex scores proportional to the sum of neighbouring scores: $v_i={\lambda }_{\max }^{-1}{\sum }_j{A}_{ij}{v}_j$. It uses a nonnegative eigenvector of the adjacency matrix for its largest positive eigenvalue. State the normalization, such as Euclidean norm one. For a three-leaf star graph, hub and leaf scores have ratio $\sqrt{3}$.