Keywords for Graph Algorithms

Core Graph Concepts

• Graph Theory
• Vertices (Nodes)
• Edges (Arcs)
• Directed Graph (Digraph)
• Undirected Graph
• Weighted Graph
• Unweighted Graph
• Cyclic Graph
• Acyclic Graph
• Simple Graph
• Multigraph
• Self-Loop
• Parallel Edges
• Graph Density
• Graph Connectivity
• Graph Isomorphism
• Subgraph
• Spanning Subgraph

Graph Representations

• Adjacency Matrix
• Adjacency List
• Edge List
• Incidence Matrix
• Compressed Sparse Row (CSR)
• Forward Star Structure
• Nested Dissection
• Graph Visualization
• NetworkX
• igraph
• Graph Database
• Edge Properties
• Vertex Properties

Graph Traversal

• Breadth-First Search (BFS)
• Depth-First Search (DFS)
• Iterative Deepening DFS
• Bidirectional Search
• Level Order Traversal
• Preorder Traversal
• Postorder Traversal
• Inorder Traversal
• Tree Traversal
• Graph Cycle Detection
• Connected Components
• Strongly Connected Components
• Bridge Detection
• Articulation Points
• Topological Order

Shortest Path Algorithms

• Dijkstra's Algorithm
• Bellman-Ford Algorithm
• A* Search Algorithm
• Floyd-Warshall Algorithm
• Johnson's Algorithm
• Single-Source Shortest Path
• All-Pairs Shortest Path
• Shortest Path Tree
• Path Reconstruction
• Negative Weight Edges
• Negative Cycles
• Heuristic Function
• Priority Queue Optimization
• Potential Function
• Reduced Costs

Minimum Spanning Tree (MST)

• Kruskal's Algorithm
• Prim's Algorithm
• Borůvka's Algorithm
• Reverse-Delete Algorithm
• Spanning Tree
• Minimum Spanning Forest
• Cut Property
• Cycle Property
• Edge Weight
• Union-Find Data Structure
• Disjoint Set Union (DSU)
• Kruskal's Sorting
• Prim's Priority Queue
• MST Verification

Network Flow Algorithms

• Maximum Flow
• Ford-Fulkerson Method
• Edmonds-Karp Algorithm
• Dinic's Algorithm
• Push-Relabel Algorithm
• Goldberg-Tarjan Algorithm
• Residual Graph
• Residual Capacity
• Augmenting Path
• Cut Capacity
• Min-Cut Max-Flow Theorem
• Flow Network
• Source and Sink
• Capacity Constraints
• Flow Conservation
• Blocking Flow
• Level Graph

Python Implementation

• Python Algorithms
• collections.deque (BFS Queue)
• recursion (DFS)
• heapq (Priority Queue)
• itertools
• functools.lru_cache
• NetworkX Library
• adjacency_list creation
• adjacency_matrix creation
• Graph Class Implementation
• Vertex Class
• Edge Class
• Graph Iteration
• Neighborhood Iteration
• Degree Calculation

Applications

• Social Network Analysis
• Web Page Ranking
• Route Planning
• Network Routing
• Circuit Design
• Compiler Design (Control Flow)
• Database Query Optimization
• Recommendation Systems
• Fraud Detection
• Biology (Protein Interactions)
• Transportation Networks
• Communication Networks
• Resource Allocation
• Game Theory (Game Graphs)
• Puzzle Solving (Sliding Puzzles)
• Maze Solving
• Image Segmentation