Beginner Topic 11 of 51 Theory & Discrete Math
Graph Theory Basics
Vertices, edges, degrees and paths.
How it works
A graph G=(V,E); degree is the number of incident edges, handshake lemma: sum of degrees = 2|E|. Paths, cycles, connectivity and subgraphs are core concepts.
Where it is used
Networks and dependencies.
Common pitfall
Distinguishing walks, trails and paths.
Where it fits in the course
Graph Theory Basics is topic 11 of 51 in Theory & Discrete Math, rated Beginner. It follows Recurrence Relations. The next topic is Trees in Graph Theory.
Practice and explore
- Open the interactive lesson, with a mini quiz.
- Take the Theory & Discrete Math quiz.
- Explore the Graph Traversal visualizer: BFS, DFS and Dijkstra on a weighted graph.
How to study this topic
- Read the explanation above and restate the definition in your own words.
- Open the interactive lesson and answer its mini quiz.
- Read the common pitfall, then write a short example that avoids it.
- Check your understanding in the Theory & Discrete Math quiz, and revisit the topic if you miss a question.
Frequently asked questions
What is Graph Theory Basics?
Vertices, edges, degrees and paths. It belongs to Theory & Discrete Math and is a beginner-level topic.
Where do people use Graph Theory Basics?
Networks and dependencies.
What is the most common mistake with Graph Theory Basics?
Distinguishing walks, trails and paths.
What should I learn before this topic?
Start with Recurrence Relations, the topic just before it in Theory & Discrete Math.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Theory & Discrete Math quiz. You can also explore Graph Traversal in the Visual Lab.
Is Graph Theory Basics hard to learn?
It is a Beginner topic, so it works as an entry point. If the terms are new, read the explanation twice and try the visualizer before the quiz.
How long does it take to learn Graph Theory Basics?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Graph Theory Basics?
Recurrence Relations, Trees in Graph Theory, Pigeonhole Principle are closely connected. The full list is in the related topics section of this page.
What should I study after Graph Theory Basics?
Continue with Trees in Graph Theory, the next topic in Theory & Discrete Math.
Related topics
- Recurrence Relations (Theory & Discrete Math)
- Trees in Graph Theory (Theory & Discrete Math)
- Pigeonhole Principle (Theory & Discrete Math)
- Euler and Hamilton Paths (Theory & Discrete Math)
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- Command Line Basics (DevOps & Tooling)
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