represented if zero is a meaningful value? In this case, either a masked or sparse representation must be used to eliminate the ambiguity:: >>> import numpy as np >>> G2_data = np.array([[np.inf, 2, 0 ], ... [2, np.inf, np.inf], ... [0, np.inf, np.inf]]) >>> G2_masked = np.ma.masked_invalid(G2_data) >>> from scipy.sparse.csgraph import csgraph_from_dense >>> # G2_sparse = csr_array(G2_data) would give the wrong result >>> G2_sparse = csgraph_from_dense(G2_data, null_value=np.inf) >>> G2_sparse.data array([ 2., 0., 2., 0.]) Here we have used a utility routine from the csgraph submodule in order to convert the dense representation to a sparse representation which can be understood by the algorithms in submodule. By viewing the data array, we can see that the zero values are explicitly encoded in the graph. Directed vs. undirected ^^^^^^^^^^^^^^^^^^^^^^^ Matrices may represent either directed or undirected graphs. This is specified throughout the csgraph module by a boolean keyword. Graphs are assumed to be directed by default. In a directed graph, traversal from node i to node j can be accomplished over the edge G[i, j], but not the edge G[j, i]. Consider the following dense graph:: >>> import numpy as np >>> G_dense = np.array([[0, 1, 0], ... [2, 0, 3], ... [0, 4, 0]]) When ``directed=True`` we get the graph:: ---1--> ---3--> (0) (1) (2) <--2--- <--4--- In a non-directed graph, traversal from node i to node j can be accomplished over either G[i, j] or G[j, i]. If both edges are not null, and the two have unequal weights, then the smaller of the two is used. So for the same graph, when ``directed=False`` we get the graph:: (0)--1--(1)--3--(2) Note that a symmetric matrix will represent an undirected graph, regardless of whether the 'directed' keyword is set to True or False. In this case, using ``directed=True`` generally leads to more efficient computation. The routines in this module accept as input either scipy.sparse representations (csr, csc, or lil format), masked representations, or dense representations with non-edges indicated by zeros, infinities, and NaN entries. z