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In 1970 Smith classified all connected graphs with the spectral radius atmost $2$. Here the spectral radius of a graph is the largest eigenvalue of itsadjacency matrix. Recently, the definition of spectral radius has been extendedto $r$-uniform hypergraphs. In this paper, we generalize the Smith's theorem to$r$-uniform hypergraphs. We show that the smallest limit point of the spectralradii of connected $r$-uniform hypergraphs is $\rho_r=(r-1)!\sqrt[r]{4}$. Wediscovered a novel method for computing the spectral radius of hypergraphs, andclassified all connected $r$-uniform hypergraphs with spectral radius at most$\rho_r$.

Connected Hypergraphs with Small Spectral Radius