Connected hypergraphs with small spectral radius

In 1970 Smith classified all connected graphs with spectral radius at most 2. Here the spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Recently, the definition of spectral radius has been extended to r-uniform hypergraphs. In this paper, we generalize Smith's theorem to r-uniform hypergraphs. We show that the smallest limit point of the spectral radii of connected r-uniform hypergraphs is ρr=4r. We discovered a novel method for computing the spectral radius of hypergraphs, and classified all connected r-uniform hypergraphs with spectral radius at most ρr.