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A connected $k$-uniform hypergraph with $n$ vertices and $m$ edges is called$r$-cyclic if $n=m(k-1)-r+1$. For $r=1$ or $2$, the hypergraph is simply calledunicyclic or bicyclic. In this paper we investigate hypergraphs that attainlarger spectral radii among all simple connected $k$-uniform unicyclic andbicyclic hypergraphs. Specifically, by using some edge operations, the formulaon power hypergraph eigenvalues, the weighted incidence matrix and a result onlinear unicyclic hypergraphs, we determined the first five hypergraphs withlarger spectral radius among all unicyclic hypergraphs and the first three overall bicyclic hypergraphs.

The first few unicyclic and bicyclic hypergraphs with larger spectral radii