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References: Foundations of Graph Structures

  1. Graph Theory - Wikipedia - Surveys the mathematical study of nodes and edges, including adjacency, paths, and the G=(V,E) notation this chapter uses to formalize Maria Chen's four-node healthcare example.

  2. Graph Database - Wikipedia - Explains how graph databases store nodes, edges, and properties natively and enable index-free adjacency, the storage-level mechanism behind this chapter's claim that traversal outperforms relational joins.

  3. Directed Acyclic Graph - Wikipedia - Covers the topological-ordering and reachability properties of DAGs, the structural guarantee this chapter relies on to explain why BFS and DFS traversals of a referral network always terminate.

  4. Algorithms (4th Edition) - Robert Sedgewick and Kevin Wayne - Addison-Wesley - Credited for the companion visualizations at algs4.cs.princeton.edu that popularized animated, step-by-step depictions of breadth-first and depth-first traversal, the same level-by-level versus branch-by-branch contrast this chapter traces by hand.

  5. Introduction to Graph Theory (2nd Edition) - Douglas B. West - Prentice Hall - A standard university reference credited for its rigorous, notation-precise treatment of digraphs, acyclicity, and reachability that underlies this chapter's formal definition of a directed acyclic graph.

  6. Graph Database Concepts - Neo4j Documentation - Defines nodes, labels, relationships, and properties in the labeled property graph model, directly matching the Patient/Provider/Facility vocabulary this chapter introduces.

  7. Breadth First Search or BFS for a Graph - GeeksforGeeks - Walks through the level-by-level BFS traversal algorithm with code and complexity analysis, reinforcing the ripple-spreading strategy this chapter demonstrates on a five-provider referral network.

  8. Depth First Search or DFS for a Graph - GeeksforGeeks - Details the recursive, branch-by-branch DFS traversal strategy, complementing this chapter's hallway analogy and hand-traced example over the same referral network.

  9. Lecture 9: Breadth-First Search - MIT OpenCourseWare - Free university lecture notes covering graph representations, adjacency, and BFS, giving a more formal algorithmic grounding for the traversal vocabulary this chapter introduces informally.

  10. What is a Graph Database? - Amazon Web Services - Explains how graph databases model entities as nodes and relationships as edges to avoid costly joins, reinforcing this chapter's central comparison between graph traversal and relational multi-table joins.