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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, 1 fill-in-the-blanks cell and 3 written answers. 21 marks, about 45 to 55 minutes.
Series: H446 1.4.2 · Data structures, part 7 of 14.
Shared by Coding PathwayVerified teacher
- 13 cells
- About 45 minutes
- CC BY-SA 4.0
- Shared 31 Aug 2026
- Updated 15 Sept 2026
Preview
The whole resource, exactly as a class sees it. Answers and marking are held back.
Graphs: concepts and representations
A creative collaboration network connects people, venues and routes. Graph properties describe relationships precisely.
By the end, you will be able to
- distinguish directed/undirected and weighted/unweighted graphs;
- use node, edge, cycle and connectedness accurately;
- read adjacency lists and matrices;
- recommend a representation for a scenario.
Reactivate: a relationship connects two entities.
Separate the graph properties
Arrows make the graph directed. Numbers make edges weighted. A cycle is a route returning to its start. 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.
Which statement is accurate?
- AWeighted means every pair of nodes is connected
- BA tree must contain a cycle
- CDirected edges have an orientation
- DUndirected means unconnected
Which statement uses graph vocabulary precisely?
- AA path is any single node with a number
- BAn edge is always a complete route through the graph
- CEvery node owns the weights of all possible paths
- DA weight is attached to an edge, and a path is a sequence of connected edges
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.
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.
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.
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.
Review your work
Check that direction, weight, cycles and connectivity are described as separate graph properties.