is only sensible if the matrix is structurally symmetric, because only then we can recover the nonzero pattern of the original matrix from its representation.

2.  The bipartite representation is a bipartite graph with the two parts consisting of the rows ($r_1, \ldots, r_m$) and the columns ($c_1, \ldots, c_n$) of the matrix.

3.  The symmetric and bipartite representations are both undirected graphs instead of hypergraphs and the size of the symmetric representation is about half that of the bipartite representation.

4.  The column-net and row-net representations are each other’s dual.

5.  The finegrain and bipartite representations are each other’s dual. This is also reflected in the fact that the hyperedges of the finegrain representation can be partitioned into two disjoint sets (the row and column hyperedges).

We will make use of these observations in .

Visual representations
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As stated in , we would like to exploit the underlying geometry of a hypergraph, usually representing a sparse matrix.

\[def:visualrepresentation\] Let $G = (V, E)$ be a given hypergraph. Then a *visual representation* of $G$ in $d \in {\mathbf{N}}$ dimensions is a mapping $$V \rightarrow {\mathbf{R}}^d$$ that reflects the structure of the underlying hypergraph.

This definition is not very precise 