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    <p>You're right to point out that the adjacencies for a vertex are most accurately modelled by a set (or in the case of a multigraph, a multiset). So why do data structures books write about arrays and linked lists instead? I can think of three reasons:</p> <ol> <li><p>The idea that programming languages should include sets as a primitive data type is fairly recent. Older writers wouldn't have considered using it, and modern writers tend to follow the traditions of the field.</p></li> <li><p>One of the purposes of a data structures course is to enable you to think about the representation of data at a low (concrete) level as well as at a high (abstract) level. A set is an abstract datatype that (unlike linked lists and arrays) doesn't have an obvious low-level implementation: some sets are best represented as linked lists, some as hash tables, some as arrays, and so on. So it is natural for a data structures course to skip over the high level representation of sets to their low-level implementation, which you have to know about anyway in order to analyse the behaviour of algorithms that use them.</p></li> <li><p>It's important not to be dogmatic about how to represent datatypes, because algorithms can be most efficiently expressed using particular representations. Example 1. To count the paths of length <em>n</em> between each pair of vertices in a graph, represent the graph by its adjacency matrix and raise the matrix to the power <em>n</em>. If you insist on representing the adjacencies of a vertex as a set of edges, then you'll miss this algorithm (which can be parallelized using standard techniques). Example 2. Knuth's "<a href="http://lanl.arxiv.org/pdf/cs/0011047" rel="noreferrer">Dancing Links</a>" algorithm for the exact cover problem represents sets of columns using doubly linked lists, so that the links from deleted items can be reused for efficient backtracking.</p></li> </ol>
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    1. USGareth Rees
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    1. COThanks man, that's a great answer. I dindn't think about it in that way. It's true that Sets are a high level data structure.
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