Lecture Data structures & algorithms: Graphs - Đào Trung Kiên

Graphs constitute a foundational concept within the realm of computer science and discrete mathematics, serving as an indispensable tool for modeling and analyzing complex relationships across myriad domains. This academic overview, part of the ET210x Data Structures & Algorithms course, introduces the essential principles of graph theory. Understanding graphs is paramount for students and practitioners, as these versatile data structures underpin critical aspects of modern computing, from designing efficient algorithms for network routing to representing intricate social connections. This module aims to establish a solid conceptual framework for defining, implementing, and navigating graphs, paving the way for advanced topics such as traversal, search, and determining shortest paths.

Students and professionals in computer science, software engineering, and related technical fields who are studying data structures and algorithms, or need to understand graph theory for network analysis, optimization, and system modeling.

This module offers a comprehensive introduction to graph theory, a cornerstone of data structures and algorithms. It systematically unpacks the fundamental definitions, beginning with a graph as a pair (V, E) comprising vertices (or nodes) and edges (or connections). The discussion elaborates on various graph characteristics, including the distinction between undirected graphs and directed graphs, the concepts of self-edges and multi-edges, and the definition of a simple graph. Key topological properties such as neighborhood, degree (in-degree and out-degree), paths, and connectivity are meticulously explained, providing the necessary groundwork for understanding how data points relate within a complex system. Furthermore, the document introduces simple paths and cycles, which are crucial for analyzing flow and cycles within networks. The practical significance of graphs is underscored through diverse real-world applications, spanning traffic networks, communication networks, social networks, electrical circuits, and chemical molecular structures. By detailing these core concepts, the module prepares learners to delve into the implementation of graphs and to apply specialized algorithms for traversal, search, and solving optimization problems like finding the shortest path between nodes, thus equipping them with essential tools for modeling and solving complex computational challenges.