Network in Graph Theory, terms

Master vertex and edge first, a network is simply a set of points (vertices) joined by lines (edges), and everything else describes them. Once that clicks, degree of a vertex, weighted edge, tree and subgraph are just extra layers of detail on the same basic picture.

A tree and a subgraph are easily mixed up: a tree is a connected network with no closed loops, while a subgraph is simply any part of a larger network, which may or may not be a tree. Students also forget that degree counts edges meeting at a vertex, not the number of vertices nearby.

Expect instructions like "state the degree of vertex X", "identify a tree in the network" or "find the total weight along a route", using a diagram of dots and connecting lines. Some questions also ask you to draw or name a subgraph that satisfies a given condition.