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A network diagram represents the connections between six major train stations in Melbourne: Flinders Street, Southern Cross, Richmond, Dandenong, Box Hill, and Clayton. Each station is a node, and direct rail links between stations are edges.
The network has the following connections: Flinders Street is connected to Southern Cross, Richmond, and Dandenong; Southern Cross is connected to Flinders Street, Dandenong, and Box Hill; Richmond is connected to Flinders Street and Dandenong; Dandenong is connected to Flinders Street, Southern Cross, Richmond, and Box Hill; Box Hill is connected to Southern Cross, Dandenong, and Clayton; and Clayton is connected only to Box Hill. How many edges are in this network diagram?
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Worked solution
- The network diagram consists of six nodes (train stations) and edges representing direct rail links between them.
- List all given connections (edges) from the description: Flinders Street connects to Southern Cross, Richmond, and Dandenong.
- Southern Cross connects to Flinders Street, Dandenong, and Box Hill.
- Richmond connects to Flinders Street and Dandenong.
- Dandenong connects to Flinders Street, Southern Cross, Richmond, and Box Hill.
- Box Hill connects to Southern Cross, Dandenong, and Clayton.
- Clayton connects only to Box Hill.
- List all unique edges from the connections. Avoid double-counting: each edge is undirected (e.g., Flinders Street–Southern Cross is the same as Southern Cross–Flinders Street).
- Compile the full list of edges: Flinders Street–Southern Cross, Flinders Street–Richmond, Flinders Street–Dandenong, Southern Cross–Dandenong, Southern Cross–Box Hill, Richmond–Dandenong, Dandenong–Box Hill, Box Hill–Clayton.
- Count the edges: there are 8 distinct edges.
- Verify by summing degrees of all nodes and dividing by 2 (since each edge contributes 2 to the sum of degrees).
- Sum of degrees: Flinders Street (3), Southern Cross (3), Richmond (2), Dandenong (4), Box Hill (3), Clayton (1). Total = 3+3+2+4+3+1 = 16. Number of edges = 16 / 2 = 8. Confirmed.
Reference answer: 8
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