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We give a complete combinatorial characterization of homogeneous quadraticrelations of "universal character" valid for minors of quantum matrices (moreprecisely, for minors in the quantized coordinate ring $O_q(M_{m,n}(K))$ of$m\times n$ matrices over a field $K$, where $q\in K^\ast$). This is obtainedas a consequence of a study of quantized minors of matrices generated by pathsin certain planar graphs, called SE-graphs, generalizing the ones associatedwith Cauchon diagrams. Our efficient method of verifying universal quadraticidentities for minors of quantum matrices is illustrated with many appealingexamples.

On universal quadratic identities for minors of quantum matrices