Knuth Miles

miles_graph() returns an undirected graph over 128 US cities. The cities each have location and population data. The edges are labeled with the distance between the two cities.

This example is described in Section 1.1 of

Donald E. Knuth, “The Stanford GraphBase: A Platform for Combinatorial Computing”, ACM Press, New York, 1993. http://www-cs-faculty.stanford.edu/~knuth/sgb.html

The data file can be found at:

plot knuth miles

Out:

Loaded miles_dat.txt containing 128 cities.
Graph with 128 nodes and 8128 edges

import gzip
import re

# Ignore any warnings related to downloading shpfiles with cartopy
import warnings

warnings.simplefilter("ignore")

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


def miles_graph():
    """Return the cites example graph in miles_dat.txt
    from the Stanford GraphBase.
    """
    # open file miles_dat.txt.gz (or miles_dat.txt)

    fh = gzip.open("knuth_miles.txt.gz", "r")

    G = nx.Graph()
    G.position = {}
    G.population = {}

    cities = []
    for line in fh.readlines():
        line = line.decode()
        if line.startswith("*"):  # skip comments
            continue

        numfind = re.compile(r"^\d+")

        if numfind.match(line):  # this line is distances
            dist = line.split()
            for d in dist:
                G.add_edge(city, cities[i], weight=int(d))
                i = i + 1
        else:  # this line is a city, position, population
            i = 1
            (city, coordpop) = line.split("[")
            cities.insert(0, city)
            (coord, pop) = coordpop.split("]")
            (y, x) = coord.split(",")

            G.add_node(city)
            # assign position - Convert string to lat/long
            G.position[city] = (-float(x) / 100, float(y) / 100)
            G.population[city] = float(pop) / 1000.0
    return G


G = miles_graph()

print("Loaded miles_dat.txt containing 128 cities.")
print(G)

# make new graph of cites, edge if less then 300 miles between them
H = nx.Graph()
for v in G:
    H.add_node(v)
for (u, v, d) in G.edges(data=True):
    if d["weight"] < 300:
        H.add_edge(u, v)

# draw with matplotlib/pylab
fig = plt.figure(figsize=(8, 6))

# nodes colored by degree sized by population
node_color = [float(H.degree(v)) for v in H]

# Use cartopy to provide a backdrop for the visualization
try:
    import cartopy.crs as ccrs
    import cartopy.io.shapereader as shpreader

    ax = fig.add_axes([0, 0, 1, 1], projection=ccrs.LambertConformal(), frameon=False)
    ax.set_extent([-125, -66.5, 20, 50], ccrs.Geodetic())
    # Add map of countries & US states as a backdrop
    for shapename in ("admin_1_states_provinces_lakes_shp", "admin_0_countries"):
        shp = shpreader.natural_earth(
            resolution="110m", category="cultural", name=shapename
        )
        ax.add_geometries(
            shpreader.Reader(shp).geometries(),
            ccrs.PlateCarree(),
            facecolor="none",
            edgecolor="k",
        )
    # NOTE: When using cartopy, use matplotlib directly rather than nx.draw
    # to take advantage of the cartopy transforms
    ax.scatter(
        *np.array([v for v in G.position.values()]).T,
        s=[G.population[v] for v in H],
        c=node_color,
        transform=ccrs.PlateCarree(),
        zorder=100  # Ensure nodes lie on top of edges/state lines
    )
    # Plot edges between the cities
    for edge in H.edges():
        edge_coords = np.array([G.position[v] for v in edge])
        ax.plot(
            edge_coords[:, 0],
            edge_coords[:, 1],
            transform=ccrs.PlateCarree(),
            linewidth=0.75,
            color="k",
        )

except ImportError:
    # If cartopy is unavailable, the backdrop for the plot will be blank;
    # though you should still be able to discern the general shape of the US
    # from graph nodes and edges!
    nx.draw(
        H,
        G.position,
        node_size=[G.population[v] for v in H],
        node_color=node_color,
        with_labels=False,
    )

plt.show()

Total running time of the script: ( 0 minutes 0.141 seconds)

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