  For certain families of finite quantum graphs, we study the question of how
eigenfunctions are distributed over the graph. To characterize properties of
the distribution, generalized entropies of the R\'{e}nyi and Tsallis types are
considered. The presented approach is similar to entropic uncertainty relations
of the Maassen-Uffink type. Using the Riesz theorem, we derive lower bounds on
symmetrized generalized entropies of eigenfunctions. A quality of such
estimates will depend on boundary conditions used at vertices of the given
graph. R\'{e}nyi and Tsallis entropies of eigenfunctions of star graphs are
separately examined. Relations between generalized entropies and variances of
eigenfunctions are considered as well. When such relations remain valid on
average, they may be used in studies of quantum ergodicity.
