add uniform generator of random proper interval graphs

[dcoudert]

This PR implements the random proper interval graph generator proposed in

• Toshiki Saitoh, Katsuhisa Yamanaka, Masashi Kiyomi, Ryuhei Uehara: Random Generation and Enumeration of Proper Interval Graphs. IEICE Trans. Inf. Syst. 93-D(7): 1816-1823 (2010)

The time complexity of the generator is in $O(n^3)$.

To check that the generator is uniform, we can use:

def test(n, steps=1000):
    from collections import Counter
    C = Counter()
    for _ in range(steps):
        G = graphs.RandomProperIntervalGraph(n)
        C[G.canonical_label().copy(immutable=True)] += 1
    L = list(C.values())
    import numpy
    print(f"different graphs = {len(L)}, avg number = {numpy.mean(L)}, standard deviation = {numpy.std(L)}")

and we get

sage: test(10, 100000)
different graphs = 2542, avg number = 39.33910306845004, standard deviation = 7.640982640860865
sage: test(15, 100000)
different graphs = 96384, avg number = 1.0375166002656042, standard deviation = 0.19487594733725658
sage: test(100, 100000)
different graphs = 100000, avg number = 1.0, standard deviation = 0.0

It seems that the generator is asymptotically uniform.

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies

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[dcoudert]

@cyrilbouvier this generator can be useful for your tests.

[fchapoton]

nice addition, thanks

[dcoudert]

Thanks for the review.