Practice: Flights and Other Networks

Module 5: Complex Networks

This page continues Practice: Real Networks. Pick the USA flights network or a network of your own instead of the Enron network. Keep the same seed protocol: a fixed SEED, and SEED + r for trial r.

import networkx as nx
import numpy as np
import matplotlib.pyplot as plt

SEED = 7  # fixed seed for reproducibility

USA flights network

The USA Flights graph used here is a preprocessed snapshot built from OpenFlights airport/route data (Patokal 2017). It is commonly used to study connectivity, robustness, and hub structure.

Figure 1: USA flights: subgraph snapshot (random sample of airports).

Load and check the flights data

Use the local GraphML file if you cloned this repository:

data/openflights/openflights_usa.graphml.gz

If you are working from the rendered website and do not have the data/ folder, download the exact same file from this repository:

https://raw.githubusercontent.com/daniprec/BAM-Applied-Math-Lab/main/data/openflights/openflights_usa.graphml.gz

import networkx as nx
from pathlib import Path
import urllib.request

path = Path("data/openflights/openflights_usa.graphml.gz")
if not path.exists():
    url = "https://raw.githubusercontent.com/daniprec/BAM-Applied-Math-Lab/main/data/openflights/openflights_usa.graphml.gz"
    path.parent.mkdir(parents=True, exist_ok=True)
    urllib.request.urlretrieve(url, path)

G = nx.read_graphml(path)
G = nx.Graph(G)  # simplify to an undirected graph

print("N, E =", G.number_of_nodes(), G.number_of_edges())
print("Is connected?", nx.is_connected(G))

Optional warm-up: node attributes and itineraries

The OpenFlights data comes with node attributes (metadata) stored in the GraphML.

airport = next(iter(G.nodes))
print("Example airport:", airport)
print("Attributes:", G.nodes[airport])

You can also ask simple connectivity questions:

a, b = "IND", "FAI"  # pick two IATA codes that exist in the graph
print("Direct flight?", G.has_edge(a, b))
print("Path exists?", nx.has_path(G, a, b))

# Fewest flights itinerary (unweighted shortest path)
print("Itinerary:", nx.shortest_path(G, a, b))

Basic properties of the flights network

In addition to core connectivity/clustering metrics, report the top-10 nodes by degree centrality and one other centrality metric (betweenness, PageRank, etc.) with a brief interpretation.

Try these metrics:

num_nodes = G.number_of_nodes()
num_edges = G.number_of_edges()
avg_degree = sum(dict(G.degree()).values()) / num_nodes

print(num_nodes, num_edges, avg_degree)

Explore hubs

Exercise

Compute the degree centrality of every airport and print the 10 airports with the highest values.

import networkx as nx

centrality = nx.degree_centrality(G)
# TODO: sort and print top 10 airports

Solution

The same sorting pattern as for betweenness on the Enron network works here. The name attribute stored in the GraphML file gives the full airport name.

import networkx as nx

centrality = nx.degree_centrality(G)
top10 = sorted(centrality.items(), key=lambda item: item[1], reverse=True)[:10]
for airport, value in top10:
    print(f"{airport}: {value:.3f}  {G.nodes[airport].get('name', '')}")

On the local file the top three are Atlanta (ATL), Chicago O’Hare (ORD) and Denver (DEN), each with a direct connection to more than a quarter of all airports.

Questions to explore

Which airports act as hubs? Your answer will matter for the epidemic simulations later.
How does the network change if you remove the top hub?
Is the graph connected, or are there isolated components?

Your own network

If you prefer, you can choose any real network instead of Enron or USA Flights.

Source the data

Your data must come from a trusted source. In your report, include:

source URL,
source organization (who publishes/maintains it),
date accessed,
file format and any preprocessing you performed.

Accepted source types include university/government open-data portals, curated research repositories, or peer-reviewed supplementary datasets.

Characterize the structure

Report the same core metrics as for the Enron and flights networks:

$N$, $E$, average degree, density,
connected components + largest component size,
clustering,
top-10 by degree centrality + one additional centrality metric.

Choose a propagation process

You may choose one of these:

Default: SIS and SIR.
Alternative: another process such as fake-news diffusion, independent cascade, threshold adoption, or rumor spreading.

For the alternative, clearly define your node states and transition rules.

The next step is the same for every network: Practice: Propagation.

References

Patokal, Jani. 2017. “OpenFlights Data Repository (Airport, Airline, and Route Snapshots).” GitHub repository snapshot. https://github.com/jpatokal/openflights/tree/5d623a6969a1adee7961cf1c9a8a212c4a784713/data.

--- title: "Practice: Flights and Other Networks" subtitle: "Module 5: Complex Networks" format: html --- This page continues [Practice: Real Networks](practice-real-networks.qmd). Pick the USA flights network or a network of your own instead of the Enron network. Keep the same seed protocol: a fixed `SEED`, and `SEED + r` for trial `r`. ```{python} #| message: false #| warning: false import networkx as nx import numpy as np import matplotlib.pyplot as plt SEED = 7 # fixed seed for reproducibility ``` ## USA flights network The USA Flights graph used here is a preprocessed snapshot built from OpenFlights airport/route data [@openflightsdataset]. It is commonly used to study connectivity, robustness, and hub structure. ```{python} #| label: fig-usa-flights #| fig-cap: 'USA flights: subgraph snapshot (random sample of airports).' #| fig-width: 7 #| fig-height: 4 #| echo: false import random path = "data/openflights/openflights_usa.graphml.gz" G = nx.read_graphml(path) G = nx.Graph(G) # Sample a manageable subgraph for visualization nodes = list(G.nodes) random.seed(SEED) sub_nodes = random.sample(nodes, k=min(250, len(nodes))) H = G.subgraph(sub_nodes).copy() pos = nx.spring_layout(H, seed=SEED) fig, ax = plt.subplots(figsize=(7, 4)) nx.draw(H, pos=pos, node_size=10, edge_color="#999", node_color="#1f77b4", ax=ax) ax.set_title("OpenFlights USA (sample)") plt.show() plt.close() ``` ### Load and check the flights data Use the local GraphML file if you cloned this repository: `data/openflights/openflights_usa.graphml.gz` If you are working from the rendered website and do not have the `data/` folder, download the exact same file from this repository: `https://raw.githubusercontent.com/daniprec/BAM-Applied-Math-Lab/main/data/openflights/openflights_usa.graphml.gz` ```python import networkx as nx from pathlib import Path import urllib.request path = Path("data/openflights/openflights_usa.graphml.gz") if not path.exists(): url = "https://raw.githubusercontent.com/daniprec/BAM-Applied-Math-Lab/main/data/openflights/openflights_usa.graphml.gz" path.parent.mkdir(parents=True, exist_ok=True) urllib.request.urlretrieve(url, path) G = nx.read_graphml(path) G = nx.Graph(G) # simplify to an undirected graph print("N, E =", G.number_of_nodes(), G.number_of_edges()) print("Is connected?", nx.is_connected(G)) ``` ::: {.callout-tip collapse="true"} ## Optional warm-up: node attributes and itineraries The OpenFlights data comes with **node attributes** (metadata) stored in the GraphML. ```python airport = next(iter(G.nodes)) print("Example airport:", airport) print("Attributes:", G.nodes[airport]) ``` You can also ask simple connectivity questions: ```python a, b = "IND", "FAI" # pick two IATA codes that exist in the graph print("Direct flight?", G.has_edge(a, b)) print("Path exists?", nx.has_path(G, a, b)) # Fewest flights itinerary (unweighted shortest path) print("Itinerary:", nx.shortest_path(G, a, b)) ``` ::: ### Basic properties of the flights network In addition to core connectivity/clustering metrics, report the top-10 nodes by degree centrality and one other centrality metric (betweenness, PageRank, etc.) with a brief interpretation. Try these metrics: ```python num_nodes = G.number_of_nodes() num_edges = G.number_of_edges() avg_degree = sum(dict(G.degree()).values()) / num_nodes print(num_nodes, num_edges, avg_degree) ``` ### Explore hubs ::: {.callout-note} ## Exercise Compute the degree centrality of every airport and print the 10 airports with the highest values. ```python import networkx as nx centrality = nx.degree_centrality(G) # TODO: sort and print top 10 airports ``` ::: ::: {.callout-tip collapse="true"} ## Solution The same sorting pattern as for betweenness on the Enron network works here. The `name` attribute stored in the GraphML file gives the full airport name. ```python import networkx as nx centrality = nx.degree_centrality(G) top10 = sorted(centrality.items(), key=lambda item: item[1], reverse=True)[:10] for airport, value in top10: print(f"{airport}: {value:.3f} {G.nodes[airport].get('name', '')}") ``` On the local file the top three are Atlanta (ATL), Chicago O'Hare (ORD) and Denver (DEN), each with a direct connection to more than a quarter of all airports. ::: ### Questions to explore - Which airports act as hubs? Your answer will matter for the epidemic simulations later. - How does the network change if you remove the top hub? - Is the graph connected, or are there isolated components? ## Your own network If you prefer, you can choose **any real network** instead of Enron or USA Flights. ### Source the data Your data must come from a **trusted source**. In your report, include: - source URL, - source organization (who publishes/maintains it), - date accessed, - file format and any preprocessing you performed. Accepted source types include university/government open-data portals, curated research repositories, or peer-reviewed supplementary datasets. ### Characterize the structure Report the same core metrics as for the [Enron](practice-real-networks.qmd) and flights networks: - $N$, $E$, average degree, density, - connected components + largest component size, - clustering, - top-10 by degree centrality + one additional centrality metric. ### Choose a propagation process You may choose one of these: - **Default**: SIS and SIR. - **Alternative**: another process such as fake-news diffusion, independent cascade, threshold adoption, or rumor spreading. For the alternative, clearly define your node states and transition rules. The next step is the same for every network: [Practice: Propagation](practice-propagation.qmd).