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Routing EasyJet Crew Across Europe

In this tutorial, you'll help plan crew routes across EasyJet's European network. You'll work with a directed, weighted graph representing flight routes, learning how direction and weights affect path finding.

Level: Intermediate Time: 20 minutes Prerequisites: Completed the London Underground tutorial

What You'll Learn​

  • Working with directed graphs (flights go one way)
  • Using weighted edges for optimization
  • Finding routes with multiple connections
  • Analyzing hub airport connectivity
  • Finding all reachable destinations

The Scenario​

You're helping EasyJet's crew scheduling team. A crew member based in London Luton needs to get to Dubrovnik for an assignment. The challenge: there's no direct flight. You need to find a route using EasyJet's network.

The Dataset​

The easyjet-routes.gexf file contains:

  • 30 airports across the UK and Europe
  • 86 flight routes with direction (origin → destination)
  • Node attributes: city, country, hub status, IATA code
  • Edge attributes: flight time (hours), distance (km), weekly frequency

Step 1: Understand the Network​

Let's start by examining the network:

grph info examples/easyjet-routes.gexf
                   Graph Summary
┏━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Property          ┃ Value                        ┃
┡━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩
│ File              │ examples/easyjet-routes.gexf │
│ Version           │ 1.3                          │
│ Mode              │ static                       │
│ Default Edge Type │ directed                     │
│ Node Count        │ 30                           │
│ Edge Count        │ 86                           │
└───────────────────┴──────────────────────────────┘

Key difference from the Underground: This graph is directed. A flight from London to Barcelona doesn't automatically mean there's a flight back. This is realistic - some routes are seasonal or one-way only.

Step 2: Find Hub Airports​

Hub airports have the most connections. Let's identify EasyJet's hubs:

grph nodes examples/easyjet-routes.gexf --attr hub=True

You'll see 16 hub airports including London Luton (LTN), London Gatwick (LGW), Amsterdam (AMS), Barcelona (BCN), and others.

Analyze Hub Connectivity​

Which hubs have the most outgoing flights? Use degree centrality with the out direction:

grph degree examples/easyjet-routes.gexf --direction out --top 5

This shows which airports you can fly TO the most destinations from.

Now check incoming flights:

grph degree examples/easyjet-routes.gexf --direction in --top 5

This shows which airports receive the most flights - useful for crew positioning.

Step 3: Route Crew to Dubrovnik​

Now for our main task: get a crew member from London Luton (LTN) to Dubrovnik (DBV).

First, check if there's a direct flight:

grph has-path examples/easyjet-routes.gexf LTN DBV
Path exists: Yes

There's a path. Let's find it:

grph path examples/easyjet-routes.gexf LTN DBV
Path from LTN to DBV
Length: 3 edges

Path: LTN → EDI → LGW → DBV

Interesting! The route goes via Edinburgh and Gatwick. Let's find alternative routes.

Step 4: Find Alternative Routes​

Maybe there's a shorter route. Use all-paths to find alternatives:

grph all-paths examples/easyjet-routes.gexf LTN DBV --max-depth 4

This finds all simple paths with up to 4 connections. You might see routes via different hubs like Amsterdam or Barcelona.

Understanding Direction​

Let's check what destinations are directly reachable from Luton:

grph neighbors examples/easyjet-routes.gexf LTN --direction out

The --direction out flag is crucial for directed graphs. It shows where you can fly TO from Luton. Compare with:

grph neighbors examples/easyjet-routes.gexf LTN --direction in

This shows where you can fly FROM to reach Luton - useful for return journeys.

Step 5: Analyze Reachability​

Where can crew get to from Luton with one connection? Use reachable:

grph reachable examples/easyjet-routes.gexf LTN --max-depth 2

This shows all airports reachable with up to 2 flights (direct + one connection).

Check Specific Destinations​

Can we reach Athens (ATH) from Luton?

grph has-path examples/easyjet-routes.gexf LTN ATH && grph path examples/easyjet-routes.gexf LTN ATH

What about Corfu (CFU)?

grph path examples/easyjet-routes.gexf LTN CFU

Step 6: Find Strategic Connections​

Which airports are most important for connecting the network? Use betweenness centrality:

grph centrality examples/easyjet-routes.gexf --type betweenness --top 5

Airports with high betweenness are critical connection points. If one of these airports had problems, many routes would be disrupted.

PageRank for Importance​

PageRank considers both the number and quality of connections:

grph centrality examples/easyjet-routes.gexf --type pagerank --top 5

This often surfaces airports that are well-connected to OTHER well-connected airports.

Step 7: Filter by Country​

Let's see all Spanish airports in the network:

grph nodes examples/easyjet-routes.gexf --attr country=Spain

What about UK airports?

grph nodes examples/easyjet-routes.gexf --attr country=UK

Step 8: Analyze Route Details​

Let's look at the actual flight connections using edges:

grph edges examples/easyjet-routes.gexf --source LTN

This shows all flights departing from Luton, including their attributes like flight time and frequency.

Filter for longer flights:

grph edges examples/easyjet-routes.gexf --source LTN --json | head -30

The JSON output lets you pipe to tools like jq for advanced filtering.

Step 9: Network Statistics​

Get an overview of network characteristics:

grph stats examples/easyjet-routes.gexf

This shows:

  • How connected the network is
  • Whether it's strongly connected (can get anywhere from anywhere)
  • Network density and structure

What You've Learned​

You've mastered working with directed, weighted graphs:

  • Direction matters: --direction in vs --direction out for analyzing flows
  • Path finding: Finding routes when direct connections don't exist
  • Reachability: Understanding what's accessible within N steps
  • Hub analysis: Identifying critical connection points
  • Filtering: Finding nodes by country, hub status, and other attributes

Real-World Applications​

This same approach works for:

  • Logistics networks: Shipping routes, delivery networks
  • Communication networks: Data routing, network topology
  • Supply chains: Supplier → manufacturer → distributor flows
  • Any directed flow system: Water, electricity, information

Next Steps​

Exercises​

  1. Find all routes from Bristol (BRS) to Athens (ATH):

    grph all-paths examples/easyjet-routes.gexf BRS ATH --max-depth 4

  2. Which airport can reach the most destinations directly? Use degree centrality with --direction out.

  3. Find airports that are reachable from Luton but can't fly back directly to Luton: Compare grph reachable LTN --max-depth 1 with grph neighbors LTN --direction in.

  4. Create a subgraph of just UK airports:

    grph subgraph examples/easyjet-routes.gexf LTN LGW STN BRS EDI MAN BFS