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Best resources to learnConnectivity

Study sheet

Connectivity measures the resilience of a graph when vertices or edges are removed. Learners will understand paths, cycles, cut-sets, and Menger's theorem, enabling them to analyze the reliability and flow of network infrastructures like communication and transportation systems.

Where to start

If graphs are new to you, start with Introduction to Graph Theory on Coursera, a free beginner course needing only basic maths and some Python. If you only use one resource, make it Reinhard Diestel's Graph Theory, Chapter 3: Connectivity, released free by the author and covering Menger's theorem, 2- and 3-connected graphs and exercises. To compute connectivity with network flows, continue with Jeff Erickson's Applications of Flows and Cuts.

8 resources · · How we curate

📺YouTube(1)

youtube

Graph Theory Lecture 9: Connectivity II — Menger's Theorem and Network Flows

Ninety-nine-minute lecture recorded live at Hamburg University in 2023/24, following the sixth edition of Diestel's book: proofs of the vertex and edge forms of Menger's theorem, global versions, and the max-flow min-cut theorem.

advanced🇬🇧

🎓Courses(1)

course

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.

beginner🇬🇧

🌐Websites(6)

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website

Wikipedia: Connectivity (graph theory)

Encyclopedia article defining vertex and edge connectivity, cut vertices, bridges, and k-connected graphs, stating Menger's theorem and bounds relating connectivity to minimum degree. Useful as a terminology reference with citations into the graph theory literature.

beginner🇬🇧
website

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.

beginner🇬🇧
website

Applications of Flows and Cuts (Algorithms, chapter 11)

Answers the how-do-you-actually-compute-connectivity half of the topic note. Chapter from Erickson's free Illinois algorithms textbook whose opening sections reduce edge-disjoint and vertex-disjoint path counting to maximum flow, giving the constructive algorithmic side of Menger's theorem; later sections extend the machinery to matching.

intermediate🇬🇧
website

Menger's Theorems and the Ear Lemma (Charles University, Lecture 8)

Lecture handout from Charles University's NDMI011 course containing a complete induction proof of the vertex form of Menger's theorem, its edge and global variants, and the ear lemma characterising 2-connected graphs.

intermediate🇬🇧
website

Graph Theory, Chapter 3: Connectivity (Diestel, 6th edition)

The complete Connectivity chapter of the sixth edition, released free by the author: 2-connected graphs and blocks, the structure of 3-connected graphs, Menger's theorem, Mader's theorem, edge-disjoint spanning trees, linking pairs of vertices, plus exercises.

advanced🇬🇧
website

Wolfram MathWorld

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.

intermediate🇬🇧
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Frequently Asked Questions

Where should I start learning Connectivity?

If graphs are new to you, start with Introduction to Graph Theory on Coursera, a free beginner course needing only basic maths and some Python. If you only use one resource, make it Reinhard Diestel's Graph Theory, Chapter 3: Connectivity, released free by the author and covering Menger's theorem, 2- and 3-connected graphs and exercises. To compute connectivity with network flows, continue with Jeff Erickson's Applications of Flows and Cuts.

What are the best free resources to learn Connectivity?

Dantes has curated 8 resources for Connectivity, including 1 YouTube videos, 1 courses, 6 websites. All resources are hand-picked for quality — no algorithmic filler. Browse the full list above to find the format that works best for you.

Is Connectivity hard to learn?

Connectivity is approachable at the beginner level — there are resources here specifically for those starting from scratch. As you progress, intermediate and advanced material is also available to take your skills further.

What types of Connectivity learning resources are available on Dantes?

For Connectivity, Dantes has curated 1 YouTube videos, 1 courses, 6 websites. Each resource type serves a different learning style: videos and YouTube for visual learners, books for depth, courses for structured progression, and websites for quick reference.

How does Dantes select Connectivity resources?

Dantes is an algorithm-free learning directory. Resources are hand-curated based on quality, accuracy, and usefulness — not engagement metrics or paid placements. The goal is to surface the best learning material for Connectivity, whether it's a free YouTube series, a classic textbook, or an open courseware from a top university.

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