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This approach obviously fails when the edge weights can include the value 0. In this second case, we store the graph as a pair of matrices: a value matrix A and a structure matrix S. This setup yields and A=[Aij] S=[Sij] ⎧ ⎪w(e) e=(i,j)∈E Aij =⎨ ⎪⎩0 otherwise ⎧ ⎪1 (i,j)∈E Sij =⎨ ⎪⎩0 otherwise. (6.3) (6.4) By encoding the graph structure in S and leaving the values in A, we can dis- tinguish where edges occur and their values. A similar encoding for structural and weight matrices is described in Latora and Marchiori [2001]. In the remainder of the chapter, the type of the adjacency matrix—whether it is binary, weighted, or paired—is determined by the type of graph. To summarize, when G is unweighted, A is a binary adjacency matrix; G has edge weights in R − {0}, A is a weighted adjacency matrix; and G has edge weights in R, (A, S) is weighted adjacency matrix pair. We do not consider multi-graphs. With the setup of looking at graphs as adjacency matrices, we next discuss why these adjacency matrices are the natural graph data structures in the Matlab environment and briefly review what can be done with graphs in Matlab with only small snippets of code (section 6.2). 6.1 ⋅ adjacency matrices 131PDF Image | Instagram Cheat Sheet
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