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SPM Mathematics: How to Master Networks (Graph Theory)
Networks are a newer, diagram-heavy chapter about vertices, edges and degrees. Precise vocabulary and neat drawing carry most of the marks.
Get the vocabulary exact
A network is built from vertices (points) and edges (connections), and each vertex has a degree, the number of edges meeting it. Directed and weighted edges add direction and a value such as distance or cost.
Because the chapter is newer, examiners lean on definitions, so learn vertex, edge, degree, directed and weighted precisely.
Draw it, then read it
Many questions give a table or a description and ask you to draw the network, or the reverse. The sum of all degrees equals twice the number of edges, a quick check that your drawing is right.
Redraw messy graphs neatly before answering, because an unclear diagram loses marks you have actually earned.
Deciding whether a network is connected
A network is connected when there is some path, however long, between every pair of vertices, and disconnected when at least one vertex sits in its own separate piece with no edge linking it to the rest. Some questions ask you to state whether a given network is connected and to justify the answer, which just means tracing outward from one vertex and checking that every other vertex can eventually be reached.
If a single vertex can't be reached that way, naming that vertex is enough to justify 'disconnected.'
Reading a network from a table, and back again
SPM questions often give a network as an adjacency table rather than a drawn diagram, listing which vertices connect to which, and expect you to sketch the network from it, or vice versa. The safest method is to place the vertices first, spaced out on the page, then add one connection at a time straight from the table, ticking each row off as you draw it.
Trying to hold the whole table in your head while drawing invites a missed or duplicated edge; working row by row does not.
The kinds of paths this topic asks you to find
Beyond describing a network, this chapter asks you to identify specific paths through it, a path that uses every edge exactly once, or a route between two particular vertices, and to justify why such a path does or doesn't exist. This connects back to vertex degree: a network where more than two vertices have an odd degree cannot have a path that traverses every edge exactly once starting and ending at different points, and recognising that pattern quickly is often the shortcut a question is testing for.
Frequently asked questions
What exactly counts as the degree of a vertex?
It's the number of edges touching that vertex, a loop at a vertex typically counts twice, so it's worth checking your textbook's exact convention for loops.
Is this the same 'graph' as a graph of a function?
No, despite the shared word, a network graph here is about vertices and edges, not about plotting coordinates or curves, and the two topics don't overlap in method.
How new is this topic in the KSSM syllabus?
Networks (graph theory) is one of the more recently introduced KSSM topics, so fewer past-year questions exist for it compared with long-standing chapters, making the textbook examples especially worth mastering.