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Assuming that the spectrum of A satisfies | λ | > | λ$_{2}$ | ≥ . . . ≥ | λ$_{n}$ | , one can adopt the power method [14–16] to solve for the dominant eigenvalue λ and its corresponding left and right eigenvectors u and v . The starting point of this method is a normalized vector v $^{(0)}$, that in this case can be taken as 

Then, for t = 1 , 2 , . . . , until convergence, the following is iterated: 

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The convergence of both the eigenvalue and eigenvector is geometric, with rate O ( | λ$_{2}$/λ | $^{t}$) [39]. This algorithm can be straightforwardly adjusted for the computation of 

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the left eigenvector u , and the same convergence rates apply. Although other iterative schemes for the compu- tation of the dominant eigenvalue and the corresponding eigenvector are available, the power method is used here since its iterations directly highlight the local information of a graph. 

Indeed, the first iteration of the power method gives the degree, the number of connections that each node has, up to a normalization constant. The k th component of u (1) is proportional to the in-degree of node k , d in k = ∑ n i =1 a$_{ik}$ , while the k th component of v (1) scales with the out-degree of the same node, d out k = ∑ n i =1 a$_{ki}$ . If the graph is undirected and unweighted, the k th component of both u (1) and v (1) are proportional to the number of direct neighbors that node k has (counting itself, if a self-loop is in place). 

