--- title: Graphs and Digraphs description: This topic covers the fundamental structures of undirected and directed graphs. Learners will understand how to model pairwise relationships, analyze network connectivity, and apply basic graph algorithms to solve routing and structural problems. category: mathematics subcategory: graph-theory difficulty: beginner, intermediate, advanced url: /subject/graphs-and-digraphs --- # Graphs and Digraphs This topic covers the fundamental structures of undirected and directed graphs. Learners will understand how to model pairwise relationships, analyze network connectivity, and apply basic graph algorithms to solve routing and structural problems. ## Available Resources 3 Books • 3 Courses • 2 Websites ## Websites ### 1. Diestel Graph Theory Official site for Reinhard Diestel's Springer graduate text, where the main text is readable free online and paid eBook editions add the full apparatus. It covers matching, connectivity, planarity, colouring, flows, extremal theory, and minors. **Difficulty:** Beginner | **Price:** Free **Link:** https://diestel-graph-theory.com/ **Tags:** graph-theory, textbook, discrete-mathematics, combinatorics, free-online ### 2. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ## Courses ### 1. Mathematics for Computer Science (MIT 6.042J) **Author:** Tom Leighton, Marten van Dijk Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/ **Tags:** discrete-mathematics, mathematical-proofs, induction, graph-theory, combinatorics, discrete-probability ### 2. Basic Graph Theory Lectures (28-lecture course) **Author:** Reinhard Diestel Reinhard Diestel's own 28-lecture university course, recorded 2024, following his GTM 173 text: invariants, trees, matching, connectivity, planarity, colouring, flows, extremal theory and minors, with proofs worked at the board. A rigorous but accessible full course covering the undirected/directed fundamentals, taught by the author of the canonical text, free, with a complete proof-based treatment rather than a tutorial skim. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PL_qO0UBYKVJ1myNZdh3j27fniqRtHYifm **Tags:** graph-theory, extremal-graph-theory, graph-minors, proof-technique, lecture-series ### 3. Introduction to Graph Theory We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them. In this online course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible! By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students. **Difficulty:** Beginner | **Language:** English | **Duration:** 5 weeks, 3-5 hours/week | **Price:** Free **Link:** https://www.coursera.org/learn/graphs **Tags:** courses, mathematics-statistics, combinatorics ## Youtubes ### 1. Graph Theory by Sarada Herke **Author:** Dr. Sarada Herke Sixty-two short lectures building from definitions and isomorphism through trees, Eulerian and Hamiltonian graphs, planarity, colouring and matching, each proof worked step by step. A first pass before committing to a formal textbook. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PLoJC20gNfC2gmT_5WgwYwGMvgCjYVsIQg **Tags:** graph-theory, trees, planarity, graph-colouring, matching, lecture-series ## Books ### 1. Digraphs: Theory, Algorithms and Applications (free first edition) **Author:** Jørgen Bang-Jensen and Gregory Gutin The reference monograph on directed graphs: connectivity, tournaments, paths and cycles, flows in networks, orientations and hardness results, with algorithms throughout. Springer permits the corrected first edition to be downloaded free from Gutin's Royal Holloway page. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://www.cs.rhul.ac.uk/books/dbook/ **Tags:** directed-graphs, graph-algorithms, tournaments, network-flows, connectivity ### 2. Introduction to Graph Theory, 2nd Edition **Author:** Douglas B. West Proof-centred undergraduate text with 1296 exercises spanning trees and distance, matchings and factors, connectivity and paths, colouring, edges and cycles, planarity, and directed graphs. Emphasises constructing and verifying graph proofs over algorithmic complexity. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0130144002?tag=edmonddante07-20 **Tags:** graph-theory, matchings, connectivity, graph-colouring, planarity, textbook ### 3. Graph Theory (Graduate Texts in Mathematics 173), 6th Edition **Author:** Reinhard Diestel The standard modern reference, sixth edition 2025. Matching, connectivity, planarity, colouring, flows, extremal theory, Ramsey theory, random graphs and the minors theorem, with complete proofs. The author's site hosts a free online preview of the full main text. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/3662701065?tag=edmonddante07-20 **Tags:** graph-theory, extremal-graph-theory, ramsey-theory, random-graphs, graph-minors, textbook --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/graphs-and-digraphs