graph of uk train stations
TRANSCRIPT
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UK Train FaresDaniyar Mukhanov, Hein Min Htike
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Ideas
Silk road
Flights from Myanmar to Kazakhstan
Family tree tradition of Kazakhstan
Twitter analytics of hashtag #StormImogen
Connection of Marvel heroes
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Silk Road
Lack of data
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Flights
Too simple graph
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Family tree
Tree is also graph, but...
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Storm Imogen
Problem with retrieving data
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Tools
- NodeXL for Microsoft Excel
- Scraper Wiki
- Next Analytics
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Marvel
Too complicated
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Quick look
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Train fares among UK
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Ticket splitting
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Aim
●Create a network 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
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Gephi bugs
- Importing CSV tables
- Finding shortest path
- other minor bugs
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Dataset
●Created manually○ 3pm, 9th Feb
●Nodes are stations
●Edges - connections between stations○ Weight - ticket fares
![Page 15: Graph of UK train stations](https://reader031.vdocument.in/reader031/viewer/2022021919/588499fb1a28ab26058b60a3/html5/thumbnails/15.jpg)
Dataset
Excerpts from data lab
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Layout
●Fruchterman Reingold○ Node size ∝ Degree
○ Edge size ∝ Weight
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Statistics of the Graph
●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)
![Page 18: Graph of UK train stations](https://reader031.vdocument.in/reader031/viewer/2022021919/588499fb1a28ab26058b60a3/html5/thumbnails/18.jpg)
Filter - Degree Range
Degree range: 10 - 13
Stations with at least 10 neigbours.
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Filter - Edge Weight
Edge weight range: £5.5 - £15
Train fares less than £15
![Page 20: Graph of UK train stations](https://reader031.vdocument.in/reader031/viewer/2022021919/588499fb1a28ab26058b60a3/html5/thumbnails/20.jpg)
Filter - Ego NetworkEgo Network of Cardiff
(Depth 1)Shows directedly connected stations.
(Depth 2)Connection with one intermediate station inbetween.
![Page 21: Graph of UK train stations](https://reader031.vdocument.in/reader031/viewer/2022021919/588499fb1a28ab26058b60a3/html5/thumbnails/21.jpg)
Analysis - Shortest Path● 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 Edinburghand Cardiff
○ Edinburgh > London > Bristol Parkway > Cardiff
■ £72.5○ Edinburgh > London > Cardiff
■ £100○ Edinburgh > Cardiff
■ £87
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Analysis - Heatmap
●Visualise the cost of travel fromEdinburgh to all other stations.
○ Lighter color -> More expensive.
●Gephi provides a button called heatmap to obtain this data.
●This function also givesMax distance = 167.1
○ max possible cost to travel to anystation on the network is £167.1
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Conclusion
●What We Did○ 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.
○ explore other tools (Gephi is extremely buggy).