Based on a recently proposed $q$-dependent detrended cross-correlation coefficient $\rho_q$ (J.~Kwapie\'n, P.~O\'swi\k{e}cimka, S.~Dro\.zd\.z, Phys. Rev.~E 92, 052815 (2015)), we introduce a family of $q$-dependent minimum spanning trees ($q$MST) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data. They inherit this ability directly from the coefficients $\rho_q$ that are processed here to construct a distance matrix being the input to the MST-constructing Kruskal's algorithm. In order to illustrate their performance, we apply the $q$MSTs to sample empirical data from the American stock market and discuss the results. We show that the $q$MST graphs can complement $\rho_q$ in detection of "hidden" correlations that cannot be observed by the MST graphs based on $\rho_{\rm DCCA}$ and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest (e.g., in portfolio analysis).
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