A simple way to calculate how many leaves the synset has and what its level in the hypernym/hyponym tree

pwn_synset_cardinality.py

import wn
import csv

from collections import Counter, defaultdict
from tqdm.notebook import tqdm


wn.download("pwn:3.1")
pwn = wn.Wordnet("pwn:3.1")


def count_cardinality_and_levels(pos):
    synset_cardinality = Counter()
    synset_level = defaultdict(lambda: 1000000)

    for synset in wn.taxonomy.leaves(pwn, pos=pos):
        for path in synset.hypernym_paths():
            path.reverse()

            synset_cardinality.update([p.id for p in path])

            for level, p in enumerate(path):
                synset_level[p.id] = min(synset_level[p.id], level)

            synset_level[synset.id] = min(synset_level[synset.id], len(path))

    return synset_cardinality, synset_level


synset_cardinality, synset_level = count_cardinality_and_levels("n")


with open("pwn_synset_levels_and_cardinality.csv", "w") as fp_out:
    w = csv.DictWriter(fp_out, fieldnames=["id", "lemmas", "gloss", "cardinality", "level"])
    w.writeheader()
    for synset_id, cardinality in tqdm(synset_cardinality.most_common()):
        synset = wn.synset(synset_id)

        w.writerow(
            {
                "id": synset_id,
                "lemmas": "; ".join(synset.lemmas()),
                "gloss": synset.definition(),
                "cardinality": cardinality,
                "level": synset_level[synset_id],
            }
        )