We consider the multilinear pagerank problem studied in [Gleich, Lim and Yu,
Multilinear Pagerank, 2015], which is a system of quadratic equations with
stochasticity and nonnegativity constraints. We use the theory of quadratic
vector equations to prove several properties of its solutions and suggest new
numerical algorithms. In particular, we prove the existence of a certain
minimal solution, which does not always coincide with the stochastic one that
is required by the problem. We use an interpretation of the solution as a
Perron eigenvector to devise new fixed-point algorithms for its computation,
and pair them with a homotopy continuation strategy. The resulting numerical
method is more reliable than the existing alternatives, being able to solve a
larger number of problems
