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Exploring the London Underground

In this tutorial, you'll learn the basics of grph by exploring a graph of the London Underground network. By the end, you'll be able to load graphs, explore their structure, find paths between stations, and identify the busiest interchanges.

Level: Beginner Time: 15 minutes Prerequisites: grph installed, example files available

What You'll Learn​

  • Loading and inspecting a GEXF graph file
  • Listing nodes (stations) and their attributes
  • Filtering nodes by attributes
  • Finding the shortest path between stations
  • Identifying important nodes using centrality

The Dataset​

The london-underground.gexf file contains a subset of Central London's Tube network:

  • 22 stations including major interchanges like Oxford Circus, King's Cross, and Bank
  • 36 connections between stations
  • Attributes include zone, lines served, and whether a station is an interchange
  • Edge weights represent travel time in minutes

Step 1: Get an Overview​

First, let's see what we're working with. The info command gives you a quick summary:

grph info examples/london-underground.gexf

You should see output like:

                     Graph Summary
┏━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Property          ┃ Value                            ┃
┡━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩
│ File              │ examples/london-underground.gexf │
│ Version           │ 1.3                              │
│ Mode              │ static                           │
│ Default Edge Type │ undirected                       │
│ Node Count        │ 22                               │
│ Edge Count        │ 36                               │
└───────────────────┴──────────────────────────────────┘

Node Attributes: interchange, lines, zone
Edge Attributes: id, line, time_minutes

Key observations:

  • The graph is undirected - you can travel in both directions on the Tube
  • There are 22 stations connected by 36 track sections
  • Nodes have attributes like zone, lines, and interchange
  • Edges have time_minutes - the travel time between stations

Step 2: List All Stations​

Let's see all the stations in our network:

grph nodes examples/london-underground.gexf

This displays a table of all nodes with their IDs, labels, and attributes:

                                   Nodes (22)
┏━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ID                    ┃ Label                     ┃ Attributes                ┃
┡━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━┩
│ oxford-circus         │ Oxford Circus             │ zone=1,                   │
│                       │                           │ lines=Central,Victoria,B… │
│                       │                           │ interchange=True          │
│ tottenham-court-road  │ Tottenham Court Road      │ zone=1,                   │
│                       │                           │ lines=Central,Northern,E… │
│                       │                           │ interchange=True          │
...

Notice each station has:

  • zone: Which fare zone it's in (all Zone 1 in this dataset)
  • lines: Which Tube lines serve this station
  • interchange: Whether you can change lines here

Step 3: Find Interchange Stations​

Let's filter to show only interchange stations - places where you can change lines:

grph nodes examples/london-underground.gexf --attr interchange=True

This filters the list to show only stations where interchange is True. You'll see major stations like Oxford Circus, King's Cross, and Bank.

Try finding stations that are NOT interchanges:

grph nodes examples/london-underground.gexf --attr interchange=False

You should see stations like Chancery Lane, Covent Garden, and Russell Square - single-line stations.

Step 4: Find a Route​

Now for the fun part - finding routes between stations! Let's plan a journey from King's Cross to Bank:

grph path examples/london-underground.gexf kings-cross bank

Output:

Path from kings-cross to bank
Length: 4 edges

Path: kings-cross → russell-square → holborn → chancery-lane → bank

grph found the shortest path: 4 stops via the Piccadilly and Central lines.

Try Different Routes​

Find a path from Oxford Circus to Waterloo:

grph path examples/london-underground.gexf oxford-circus waterloo

What about from Baker Street to London Bridge?

grph path examples/london-underground.gexf baker-street london-bridge

Step 5: Explore Connections​

What stations are directly connected to Oxford Circus? Use the neighbors command:

grph neighbors examples/london-underground.gexf oxford-circus

This shows all stations one stop away from Oxford Circus. You should see stations like Tottenham Court Road, Bond Street, Warren Street, Green Park, and Piccadilly Circus.

Go Deeper​

To see stations within 2 stops, use the --depth option:

grph neighbors examples/london-underground.gexf oxford-circus --depth 2

This expands the search to include stations two stops away.

Step 6: Find the Busiest Interchanges​

Which stations have the most connections? We can use centrality analysis to find out:

grph centrality examples/london-underground.gexf --type degree --top 5

Output:

     Degree Centrality (Top 5)
┏━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┓
┃ Rank ┃ Node          ┃ Score    ┃
┡━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━┩
│ 1    │ oxford-circus │ 0.285714 │
│ 2    │ green-park    │ 0.238095 │
│ 3    │ embankment    │ 0.238095 │
│ 4    │ holborn       │ 0.190476 │
│ 5    │ euston        │ 0.190476 │
└──────┴───────────────┴──────────┘

Oxford Circus is the most connected station - no surprise to anyone who's been crushed in the crowds there!

Understanding Centrality​

Degree centrality measures how many direct connections a node has. Higher scores mean more connections. In a transport network, high-degree stations are natural interchange points.

Try betweenness centrality to find stations that are critical for routing:

grph centrality examples/london-underground.gexf --type betweenness --top 5

Betweenness measures how often a station appears on the shortest path between other stations. High betweenness stations are critical - if they closed, many journeys would be disrupted.

Step 7: Get Network Statistics​

Finally, let's get an overall view of the network structure:

grph stats examples/london-underground.gexf

This shows statistics like:

  • Density: How interconnected the network is (1.0 = every station connected to every other)
  • Average degree: Average number of connections per station
  • Connected: Whether you can get from any station to any other

What You've Learned​

Congratulations! You've learned how to:

  • Load a graph with grph info to see its structure
  • List nodes with grph nodes and filter by attributes
  • Find paths with grph path for journey planning
  • Explore neighborhoods with grph neighbors
  • Analyze importance with grph centrality
  • Get statistics with grph stats

Next Steps​

Exercises​

  1. Find the path from Westminster to Liverpool Street. How many stops is it?

  2. Which stations are reachable from Piccadilly Circus within 3 stops?

    grph neighbors examples/london-underground.gexf piccadilly-circus --depth 3

  3. Export the network to JSON for visualization in a tool like D3.js:

    grph export examples/london-underground.gexf --format json

  4. Find all simple paths between Oxford Circus and Bank (there might be more than one!):

    grph all-paths examples/london-underground.gexf oxford-circus bank --max-depth 6