Many problems in machine learning involve understanding relationships between entities. Whether it's users and products in a recommendation system, molecules in a chemical database, or social connections in a network, graphs provide a natural and powerful way to represent this relational data.

This chapter focuses on graph data structures and fundamental graph algorithms relevant to machine learning tasks. We will cover:

• Graph Representation: Storing graphs efficiently using adjacency lists and adjacency matrices, considering their respective trade-offs.
• Traversal Algorithms: Implementing and understanding Breadth-First Search (BFS) and Depth-First Search (DFS) for systematically visiting nodes in a graph.
• Shortest Paths: Introducing algorithms like Dijkstra's for finding minimum cost paths, a common sub-problem in network analysis and optimization.
• Graph Embeddings: The concept of representing graph nodes as vectors for use in downstream machine learning models.
• Applications: Seeing how these structures and algorithms are applied in areas like recommendation systems and analyzing network data.

We will examine the implementation details and performance characteristics of these techniques, preparing you to apply graph-based approaches to relevant machine learning challenges.