Graph Theory Basics
📋 What it is
A GRAPH is dots (vertices) joined by lines (edges); it models any network of connections.
🗣️ Coach says
A graph is not a bar chart here — it is a map of connections. Vertices are the things (people, cities), edges are the links (friendships, roads). A PATH walks along edges; a CYCLE returns to where it started. Social networks, the internet, and delivery routes are all graphs, so this is some of the most useful math there is.
🧠 Memory hook
Dots = vertices (things), lines = edges (links). A path walks; a cycle loops back.
😂 Giggle
What did one set say to the other?
"We should unite — we'd be a great union!"
😲 Whoa!
The whole field began in 1736 when Euler proved you could NOT cross all seven bridges of Königsberg exactly once.
✅ Quick check: In a graph, what do we call the dots and the lines connecting them?
Say your answer out loud first — then reveal.
Dots are vertices; lines are edges.
A graph is defined as a set of vertices joined by edges.
🧪 Try it! (2 minutes)
Draw yourself and 3 friends as dots; draw an edge for each real friendship. Count the edges.