Knuth Miles

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

This example is described in Section 1.1 in Knuth’s book (see [1] and [2]).

References.

[1]Donald E. Knuth, “The Stanford GraphBase: A Platform for Combinatorial Computing”, ACM Press, New York, 1993.
[2]http://www-cs-faculty.stanford.edu/~knuth/sgb.html
../../_images/sphx_glr_plot_knuth_miles_001.png

Out:

Loaded miles_dat.txt containing 128 cities.
digraph has 128 nodes with 8128 edges

# Author: Aric Hagberg (hagberg@lanl.gov)

#    Copyright (C) 2004-2017 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.

import re
import sys

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)
    import gzip
    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("^\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 - flip x axis for matplotlib, shift origin
            G.position[city] = (-int(x) + 7500, int(y) - 3000)
            G.population[city] = float(pop) / 1000.0
    return G


if __name__ == '__main__':

    G = miles_graph()

    print("Loaded miles_dat.txt containing 128 cities.")
    print("digraph has %d nodes with %d edges"
          % (nx.number_of_nodes(G), nx.number_of_edges(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
    plt.figure(figsize=(8, 8))
    # with nodes colored by degree sized by population
    node_color = [float(H.degree(v)) for v in H]
    nx.draw(H, G.position,
            node_size=[G.population[v] for v in H],
            node_color=node_color,
            with_labels=False)

    # scale the axes equally
    plt.xlim(-5000, 500)
    plt.ylim(-2000, 3500)

    plt.show()

Total running time of the script: ( 0 minutes 0.117 seconds)

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