\leq j \leq n, a_{i \, j} \neq 0\}$
  Bipartite [@Hendrickson2000]    $\{r_1, \ldots, r_m, c_1, \ldots, c_n\}$                            $\{ \{r_i, c_j\} {\ |\ }1 \leq i \leq m, 1 \leq j \leq n, a_{i \, j} \neq 0\}$
  Column-net [@Catalyurek1999]             $\{r_1, \ldots, r_m\}$                                     $\{ \{r_i {\ |\ }1 \leq i \leq m, a_{i \, j} \neq 0\} {\ |\ }1 \leq j \leq n\}$
  Row-net [@Catalyurek1999]                $\{c_1, \ldots, c_n\}$                                     $\{ \{c_j {\ |\ }1 \leq j \leq n, a_{i \, j} \neq 0\} {\ |\ }1 \leq i \leq m\}$
  Finegrain [@Catalyurek2001]     $\{v_{i \, j} {\ |\ }a_{i \, j} \neq 0\}$    $\underbrace{\{ \{v_{i \, j} \vert 1 \leq i \leq m, a_{i \, j} \neq 0\} {\ |\ }1 \leq j \leq n\}}_{\text{column hyperedges}}$
                                                                              $\cup \underbrace{\{ \{v_{i \, j} \vert 1 \leq j \leq n, a_{i \, j} \neq 0\} {\ |\ }1 \leq i \leq m\}}_{\text{row hyperedges}}$

  : Several common representations of an $m \times n$-matrix $A = \left( a_{i \, j} \right)$ by a hypergraph $G = (V, E)$.[]{data-label="tab:hypergraphmatrix"}

One direct application of hypergraphs is to use them to represent sparse matrices, see . We can make a number of observations about these representations.

1.  The symmetric representation 