Finding Paths Examples

Graph Theory · Axiom Academy

EXAMPLE Finding Paths Examples Learn to identify and find different types of paths in graphs Excellent work! You've learned essential path-finding concepts: Simple Paths: A path is simple if no vertex is repeated. This ensures we don't visit the same location twice. Path Types: Walks allow repeated vertices and edges, trails allow repeated vertices but not edges, and paths have no repetition. Breadth-First Search (BFS): BFS explores vertices level by level, guaranteeing the shortest path in unweighted graphs. Graph Connectivity: A graph is connected if there exists a path between every pair of vertices. BFS can determine this by checking if all vertices are reachable from a starting vertex. Systematic Enumeration: Finding all paths requires exploring all possible routes while avoiding cycles in simple paths. These path-finding techniques are fundamental to graph theory and have applications in networking, routing, and many real-world problems!

This is the written version of the interactive lesson above. See the full Graph Theory course.