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math / Discrete Mathematics / free

Graph Theory

Turn connections into a structure you can trace, color, and optimize.

Follow the mechanism1 / 3

Objects become nodes and relationships become edges. A graph strips away irrelevant detail and preserves the connections that determine what can reach what.

network structureA → G · 3 hops
Focus the idea
A network graph with a highlighted shortest pathNodes A through G are connected by edges. The highlighted path from A to G takes 3 hops.connections, not coordinatesAdegree 2Bdegree 2Cdegree 3Ddegree 3Edegree 3Fdegree 3Gdegree 2A → C → E → G
starttargetshortest path
shortest path3 hops
start degree2
target degree2
reachable nodes7 / 7
Start node
Target node

A reaches G in 3 hops: A → C → E → G. The path is defined by connections, not by a straight-line measurement.

A graph records relationships: nodes are the objects, and edges are the connections between them. Once the structure is explicit, you can search paths, detect clusters, measure degree, and ask which links are critical.