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Graph of UK train stations
This document analyzes a graph network of UK train stations created using ticket prices as edge weights. It explores the graph in Gephi, finding statistics like average degree and diameter. Filters are applied based on degree, weight, and ego networks. Shortest path and heatmap analyses find the cheapest routes, like Edinburgh to Cardiff for £72.50 through London and Bristol Parkway. While the small dataset limits real-world meaning, graph theory principles were explored.
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Graph of UK train stations
- 1. UK Train Fares DaniyarMukhanov, Hein Min Htike
- 2. Ideas Silk road Flights fromMyanmar to Kazakhstan Family tree tradition of Kazakhstan Twitter analytics of hashtag #StormImogen Connection of Marvel heroes
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- 5. Family tree Tree isalso graph, but...
- 6. Storm Imogen Problem withretrieving data
- 7. Tools - NodeXL forMicrosoft Excel - Scraper Wiki - Next Analytics
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- 12. Aim ● Create anetwork of train stations in UK cities using ticket price as attribute for the edges. ● Analyse the graph; find cheapest way to travel ● To explore Gephi and apply graph theory
- 13. Gephi bugs - ImportingCSV tables - Finding shortest path - other minor bugs
- 14. Dataset ● Created manually ○3pm, 9th Feb ● Nodes are stations ● Edges - connections between stations ○ Weight - ticket fares
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- 16. Layout ● Fruchterman Reingold ○Node size ∝ Degree ○ Edge size ∝ Weight
- 17. Statistics of theGraph ● Nodes - 26 ● Edges - 68 ● Undirected Graph (same fare in both direction) ● Average degree - 5.231 (Avg. num of connected stations) ● Network diameter - 3 (maximum connections to reach from one station to another in the graph)
- 18. Filter - DegreeRange Degree range: 10 - 13 Stations with at least 10 neigbours.
- 19. Filter - EdgeWeight Edge weight range: £5.5 - £15 Train fares less than £15
- 20. Filter - EgoNetwork Ego Network of Cardiff (Depth 1) Shows directedly connected stations. (Depth 2) Connection with one intermediate station inbetween.
- 21. Analysis - ShortestPath ● Main aim of this graph analysis. ● Gephi provides a button to obtain shortest path between two nodes. (Using Dijkstra’s algorithm) ● Eg: Cheapest ticket between Edinburgh and Cardiff ○ Edinburgh > London > Bristol Parkway > Cardiff ■ £72.5 ○ Edinburgh > London > Cardiff ■ £100 ○ Edinburgh > Cardiff ■ £87
- 22. Analysis - Heatmap ●Visualise the cost of travel from Edinburgh to all other stations. ○ Lighter color -> More expensive. ● Gephi provides a button called heatmap to obtain this data. ● This function also gives Max distance = 167.1 ○ max possible cost to travel to any station on the network is £167.1
- 23. Conclusion ● What WeDid ○ Created our own graph ○ Analysed it in Gephi ○ Explored functionalites provided by Gephi & Graph Theory ● What to improve ○ small dataset (time limitation) ○ a lot of principles from graph theory do not have real-world meaning in our graph due to the size of its dataset and underlying simplicity.