Graph Paths Explained: Node vs Edge Based, Simple Paths, Cycles and DAGs

Hey there, let's talk about paths inside of a graph. We draw a directed weighted graph and compare node-based paths to edge-based paths. Node lists alone cannot tell which edge you took when parallel edges have different costs. Edge-based paths use tuples of start, destination and weight so every route is clear.

We also cover simple paths with no repeated edges or vertices, cyclic paths that start and end on the same node, and how a cycle proves the graph is cyclic. Then we explain DAGs, directed acyclic graphs, with examples that stay acyclic and ones that gain cycles.

This sets up algorithms for later videos. Leave a comment with topics you want next. Thanks for watching and please subscribe.

00:00 Introduction to Graph Paths
00:28 Drawing a Sample Graph
02:25 What is a Path
02:42 Node-Based Paths
03:27 Adding Weights and Parallel Edges
04:34 Example Paths with Different Costs
07:19 Edge-Based Paths
07:35 Representing Paths with Tuples
11:35 Order Matters in Directed Graphs
12:52 Simple Paths
15:34 Cyclic Paths
18:22 Directed Acyclic Graphs DAGs
19:08 Building a DAG Example
21:41 Adding a Cycle to Break the DAG
23:15 Conclusion and Future Videos

graph paths, paths in graphs, node based path, edge based path, simple path graph, cyclic path, directed acyclic graph, DAG, graph theory, graph edges, weighted graphs, graph cycles, edge list, graph algorithms basics

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