Chapter 9. Graph Fundamentals

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.1 Graph Models

You need to turn a real problem into a graph before choosing an algorithm.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

You need a graph representation that supports efficient traversal, scales to large datasets, and works naturally with algorithms such as depth-first search, breadth-first search, topological sorting,...

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.3 Adjacency Matrices

You need a graph representation that can answer edge-existence queries quickly.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.4 Edge Lists

You need a graph representation that is simple to construct, compact to store, and efficient for algorithms that process edges directly.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.5 Directed Graphs

You need to model relationships that have direction.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.6 Undirected Graphs

You need to model relationships that are naturally symmetric.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.7 Weighted Graphs

You need to model relationships where connections have different costs.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.8 Degree and Connectivity

You need basic measurements that describe the local and global structure of a graph.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.9 Depth-First Search (DFS)

You need to explore a graph systematically.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.10 Breadth-First Search (BFS)

You need to explore a graph in order of increasing distance from a starting vertex.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.11 Connected Components

You need to identify independent regions within a graph.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.12 Topological Sort

You need to arrange tasks in an order that respects dependencies.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.13 Cycle Detection

You need to determine whether a graph contains a cycle.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.14 Bipartite Graphs

You need to divide vertices into two groups such that every edge connects vertices from different groups.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.15 Strongly Connected Components

You need to identify groups of vertices that are mutually reachable.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.16 Articulation Points

You need to find vertices whose removal disconnects an undirected graph.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.17 Bridges

You need to find edges whose removal disconnects a graph.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.18 Euler Paths

You need to traverse every edge in a graph exactly once.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.19 Hamiltonian Paths

You need to visit every vertex exactly once.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.20 Graph Coloring Basics

You need to assign labels, colors, or resources to vertices so that adjacent vertices do not conflict.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.21 Minimum Spanning Trees

You need to connect all vertices in a graph while minimizing total cost.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.22 Graph Representation Tradeoffs

You need to choose the right in-memory representation for a graph.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.23 Shortest Path Fundamentals

You need to find the cheapest route between vertices.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.24 Testing Graph Code

You need confidence that a graph algorithm handles real inputs, edge cases, and malformed assumptions correctly.

Programming › Algorithm Cookbook › Chapter 9. Graph Fundamentals ›

9.25 Graph Algorithm Patterns and Interview Strategies

You are given a graph problem and need to quickly identify the correct algorithmic approach.

Chapter 9. Graph Fundamentals

Chapter 9. Graph Fundamentals

9.1 Graph Models

9.2 Adjacency Lists

9.3 Adjacency Matrices

9.4 Edge Lists

9.5 Directed Graphs

9.6 Undirected Graphs

9.7 Weighted Graphs

9.8 Degree and Connectivity

9.9 Depth-First Search (DFS)

9.10 Breadth-First Search (BFS)

9.11 Connected Components

9.12 Topological Sort

9.13 Cycle Detection

9.14 Bipartite Graphs

9.15 Strongly Connected Components

9.16 Articulation Points

9.17 Bridges

9.18 Euler Paths

9.19 Hamiltonian Paths

9.20 Graph Coloring Basics

9.21 Minimum Spanning Trees

9.22 Graph Representation Tradeoffs

9.23 Shortest Path Fundamentals

9.24 Testing Graph Code

9.25 Graph Algorithm Patterns and Interview Strategies