  A hypergraph $H=(V,E)$, where $V=\{x_1,...,x_n\}$ and $E\subseteq 2^V$
defines a hypergraph algebra $R_H=k[x_1,...,x_n]/(x_{i_1}... x_{i_k};
\{i_1,...,i_k\}\in E)$. All our hypergraphs are $d$-uniform, i.e., $|e_i|=d$
for all $e_i\in E$. We determine the Poincar\'e series
$P_{R_H}(t)=\sum_{i=1}^\infty\dim_k{\rm Tor}_i^{R_H}(k,k)t^i$ for some
hypergraphs generalizing lines, cycles, and stars. We finish by calculating the
graded Betti numbers and the Poincar\'e series of the graph algebra of the
wheel graph.
