Mathematics for Data Science 1 - W10_L7: Applications of BFS & DFS | part 2

Welcome to Week 10 Lecture 7 of the course "Mathematics for Data Science I" by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview This lecture extends the applications of graph traversal to directed graphs. We introduce the concept of edges in DFS traversal—tree edges, forward edges, back edges, and cross edges—and explain their significance. Using DFS pre and post numbers, we show how to detect back edges, which are key indicators of cycles in directed graphs. The lecture also explores the idea of strongly connected components (SCCs) and highlights their deep connection to DFS. Finally, we demonstrate how DFS is applied to cycle detection in directed graphs, forming the basis for advanced algorithms in graph theory and computer science. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #DirectedGraphs #GraphTheory #Cycles #DirectedCycles #DFS #DepthFirstSearch #PrePostNumbers #BackEdges #ForwardEdges #CrossEdges #StronglyConnectedComponents #SCC #GraphAlgorithms #Algorithms #DataStructures #ArticulationPoints #Bridges #CutVertex #CutEdges #Connectivity #DirectedAcyclicGraphs #DAG