The fraction of zeroes in a matrix If A is m by n, and A(i, j) not= 0 for k of its elements, its sparsity is k/mn Large linear programs tend to be very sparse, increasing as the dimensions get large For example, consider the standard transportation problem with s sources and d destinations This has m = (s+d) constraints and n = sd variables Each column, however, has exactly 2 nonzeroes since A is the incidence matrix of the network, so its sparsity is 2n/mn, or simply 2/m, which decreases as the number of sources and/or destinations grows large The sparsity of a simple graph (or network) is the sparsity of its adjacency matrix More generally, the sparsity of a multigraph refers to the average degree of its nodes