MTR Network Transfer Analysis

The Claim

"Has anyone noticed that any two MTR stations can be reached with at most 2 transfers? Excluding Disneyland."

Results Summary

Excluding Disneyland (97 stations)

Transfers	Station Pairs	Percentage
0	928	19.9%
1	2,620	56.3%
2	1,108	23.8%

Maximum transfers: 2 — CLAIM IS TRUE

Including Disneyland (98 stations)

Transfers	Station Pairs	Percentage
0	929	19.5%
1	2,627	55.3%
2	1,165	24.5%
3	32	0.7%

Maximum transfers: 3 — CLAIM IS FALSE

32 Stations Requiring 3 Transfers from Disneyland

Disneyland only connects to the network via Sunny Bay (Tung Chung Line), making these stations 3 transfers away:

• Kwun Tong Line (non-interchange): Choi Hung, Kowloon Bay, Kwun Tong, Lam Tin, Lok Fu, Ngau Tau Kok, Shek Kip Mei, Wong Tai Sin, Yau Tong, Whampoa
• East Rail Line (non-interchange): Exhibition Centre, Fanling, Fo Tan, Kowloon Tong, Lo Wu, Lok Ma Chau, Mong Kok East, Racecourse, Sha Tin, Sheung Shui, Tai Po Market, Tai Wo, University
• Tseung Kwan O Line (non-interchange): Hang Hau, LOHAS Park, Po Lam, Tiu Keng Leng, Tseung Kwan O
• South Island Line (non-interchange): Lei Tung, Ocean Park, South Horizons, Wong Chuk Hang

Algorithm

Graph Model

The MTR network is modeled as a weighted graph:

• Nodes: (station, line) tuples — each station appears once per line serving it

  • e.g., Admiralty has 4 nodes: (Admiralty, Island), (Admiralty, Tsuen Wan), (Admiralty, South Island), (Admiralty, East Rail)

• Edges:

Edge Type	Weight	Description
Same-line	0	Adjacent stations on the same line
Transfer	1	Same station, different lines
Walkway	1	Connected via walkway (Central↔Hong Kong, TST↔East TST)
Branch	0	Branch termini on same line (Lo Wu/Lok Ma Chau, Po Lam/LOHAS Park)

Shortest Path (Dijkstra)

For each station pair (A, B):

1. Find all nodes for station A: [(A, line1), (A, line2), ...]
2. Find all nodes for station B: [(B, line1), (B, line2), ...]
3. Run Dijkstra's algorithm to find minimum weight path
4. Return minimum weight = minimum number of transfers

Network Statistics

Total stations: 97 (excluding Disneyland)
Total station-line nodes: 121
Total edges: 142
Station pairs analyzed: 4,656

Files

• mtr_transfer_test.py — Main analysis script
• mtr_overlay_viz.py — Visualization overlay on MTR map
• routemap.png — Official MTR system map