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Intermediate ⛓ Discrete Math & Number Theory Topic 49 of 103

Graphs: Basics

Vertices connected by edges.

Key idea

Vertices connected by edges.

In depth

A graph is a set of vertices connected by edges, modelling networks such as roads and friendships. Only connections matter, not the positions or lengths in the drawing. Edges may be directed or weighted.

Worked example

A graph with vertices A, B, C and edges AB, BC represents a path.

Formula

G = (V, E)

Real-world uses

Common mistake

Treating a drawing’s geometry as meaningful.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Graphs: Basics?

Vertices connected by edges. It is a topic at the intermediate level in Discrete Math & Number Theory.

What is the formula for Graphs: Basics?

The key formula is G = (V, E).

Where is Graphs: Basics used in real life?

Real-world examples: Modelling road networks, social networks and the links between web pages.

What should I learn before Graphs: Basics?

Make sure you are comfortable with Divide-and-Conquer Recurrences, the previous topic in Discrete Math & Number Theory.

What is a common mistake with Graphs: Basics?

Treating a drawing’s geometry as meaningful.

How can I practise Graphs: Basics?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Graphs: Basics?

Move on to Degree and Handshake Lemma next.

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