Community resourceWorksheet

OCR H446 1.4.2 Graphs: concepts and representations

Part 7 of 14 · H446 1.4.2 · Data structures

Graph questions in H446 1.4.2 reward precise vocabulary, so this worksheet separates direction from weight and node from edge before any representation is chosen. A collaboration network of people, venues and routes gives students a graph to read accurately, then store as an adjacency list or an adjacency matrix.

Students will:

  • distinguish directed from undirected and weighted from unweighted graphs
  • use node, edge, path, cycle and connectedness precisely rather than loosely
  • read the outgoing neighbours and weights of a node from a drawn graph
  • compare adjacency lists with adjacency matrices for a network with few connections per node
  • design a one-way weighted route system and justify direction, weight meaning and representation

Inside: 7 explanation cells, 2 multiple-choice questions, 2 fill-in-the-blanks cells and 3 written answers. 25 marks, about 50 to 60 minutes.

Series: H446 1.4.2 · Data structures, part 7 of 14.

Shared by Coding PathwayVerified teacher

  • 14 cells
  • About 60 minutes
  • CC BY-SA 4.0
  • Shared 31 Aug 2026
  • Updated 1 Oct 2026

Preview

The whole resource, exactly as a class sees it. Answers and marking are held back.

Graphs: concepts and representations

A graph represents connections. The circles or labelled points are nodes (also called vertices), and the direct connections between them are edges (also called arcs). Routes, social links and computer networks can all be modelled as graphs, but their direction and weights may differ.

By the end, you will be able to

  • distinguish directed and undirected graphs, and weighted and unweighted graphs;
  • use node, edge, path, cycle and connectedness accurately;
  • read adjacency lists and adjacency matrices;
  • recommend a representation for a scenario.

Separate the graph properties

Directed weighted graph vocabularyABCD42531

Arrows make the graph directed. Numbers make edges weighted. A cycle follows edges and returns to its start; in a directed graph, the arrows must be followed in their permitted direction. Connectedness asks whether nodes are reachable; it is not the same as weight or direction.

Worked representations

For directed edges A→B and A→C:

Adjacency list: A:[B,C], B:[], C:[].

Adjacency matrix row A has entries under B and C. In a directed graph, matrix[A][B] need not equal matrix[B][A]. For a sparse graph, adjacency lists avoid storing many absent edges; a matrix gives direct edge lookup.

Multiple choice1 mark

Which statement is accurate?

  • AWeighted means every pair of nodes is connected
  • BA tree must contain a cycle
  • CUndirected means unconnected
  • DDirected edges have an orientation
Multiple choice1 mark

Which statement uses graph vocabulary precisely?

  • AA weight is attached to an edge, and a path is a sequence of connected edges
  • BA path is any single node with a number
  • CAn edge is always a complete route through the graph
  • DEvery node owns the weights of all possible paths

Guided reading

For each drawn edge, record start, end and weight. Then build one adjacency-list row. Check direction by asking whether the reverse edge was actually drawn.

Written answer4 marks

From the diagram, list all outgoing neighbours of A with weights and state whether a directed route A→B→C exists.

Follow arrowheads and keep each edge weight attached to that edge.

Students type their answer here.

Fill in the blanks4 marks
A directed graph contains A→B, B→C and C→A. Complete the adjacency matrix with 1 for a directed edge and 0 for no edge.
from \ toABC
A0entry 10
B00entry 2
Centry 30entry 4
Written answer4 marks

Compare adjacency lists and adjacency matrices for a social graph with many users but relatively few connections.

Use space and edge-lookup/traversal.

Students type their answer here.

Independent transfer

Design a graph for a one-way accessible route system between five venues. Specify nodes, directed edges, one weight meaning and a suitable representation.

Written answer7 marks

Give the graph design and justify direction, weight and representation.

Do not draw colour-only distinctions.

Students type their answer here.

Closed-book checkpoint

Complete each sentence from memory. There is no answer bank and correctness is held for teacher review.

Fill in the blanks4 marks
A graph contains vertices joined by completion 1. An edge with one permitted direction is completion 2. A numeric edge label is a completion 3 or cost. An adjacency completion 4 uses rows and columns; an adjacency list stores neighbours.

Review your work

Check that direction, weight, cycles and connectivity are described as separate graph properties.