With a sparse system, you might run into dependency chains that effectively make it dense. Like in an adjacency matrix for a graph, you may have a lot of spars

With a sparse system, you might run into dependency chains that effectively make it dense. Like in an adjacency matrix for a graph, you may have a lot of sparsity, but if you're forced to consider neighbors of neighbors, the adjacency matrix you need is A^2. This can be dense even if A is quite sparse.