Network in Graph Theory · Form 4
Network in Graph Theory: Key Terms
The key Network in Graph Theory terms you need for SPM Mathematics, defined plainly in English, Malay and Chinese.
- Vertex A point in a network, joined to others by edges.
- Edge A line joining two vertices in a network.
- Degree of a vertex The number of edges that meet at a vertex.
- Weighted edge An edge that carries a value such as a distance, time or cost.
- Degree of a vertex The number of edges meeting at a vertex.
- Tree A connected network with no cycles.
- Subgraph A network formed from some of the vertices and edges of a larger network.
Term pairs students mix up
- Vertex vs Edge, a vertex is a point (a town, a junction); an edge is a line joining two vertices (a road). You count points for vertices and lines for edges.
- Degree vs Weight, degree is a count of edges meeting at a vertex; weight is a number written on an edge, such as a distance or cost. One sits at a point, the other along a line.
- Directed vs Undirected edge, a directed edge has an arrow and can be travelled one way only; an undirected edge has no arrow and works both ways.
- In-degree vs Out-degree, in a directed network, in-degree counts arrows pointing into a vertex, out-degree counts arrows pointing out; their sum is the total degree.
- Tree vs Subgraph, a subgraph is any part of a network; a tree is a special connected subgraph with no cycle and exactly (vertices − 1) edges.
- Loop vs Parallel edges, a loop joins a vertex to itself and adds 2 to its degree; parallel edges are two or more separate edges joining the same pair of vertices.
How these terms show up in real SPM questions
- 'Find the degree of vertex X' means count the edges meeting X, and remember a loop counts as 2.
- 'Draw a network to represent the information in the table' asks you to turn each listed link into an edge and each item into a vertex.
- 'The number on each edge represents the distance / cost' signals a weighted network, totals come from adding edge weights, not vertices.
- 'Complete the network' expects you to add the missing edges, arrows or weights so the diagram matches the description.
- 'State whether the network is a tree' means check three things: it is connected, has no cycle, and has exactly (vertices − 1) edges.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Is 'degree' the same as 'weight'?
No, and the exam relies on you knowing this. Degree is a whole-number count of the edges meeting at a vertex, a property of a point.
Weight is a value carried by an edge, such as a distance in km, a property of a line. A vertex has a degree; an edge has a weight.
Is every network in the chapter a tree?
No. Most networks are not trees.
A tree is a special case: it must be connected, contain no cycle, and have exactly one fewer edge than it has vertices. Any network with a cycle, or with more than (vertices − 1) edges, is not a tree even if every vertex is connected.
When a question says 'network', does it mean the same as 'graph'?
Yes. In this chapter the words network and graph mean the same thing, a set of vertices joined by edges.
'Network' is the everyday word the syllabus prefers, and 'graph' is the mathematical term. Do not confuse this graph with the graph of a function like y = x², which is a different idea entirely.