I suspect you don’t just want the most common phrases, but rather you want the most interesting collocations. Otherwise, you could end up with an overrepresentation of phrases made up of common words and fewer interesting and informative phrases.
To do this, you’ll essentially want to extract n-grams from your data and then find the ones that have the highest point wise mutual information (PMI). That is, you want to find the words that co-occur together much more than you would expect them to by chance.
The NLTK collocations how-to covers how to do this in a about 7 lines of code, e.g.:
import nltk
from nltk.collocations import *
bigram_measures = nltk.collocations.BigramAssocMeasures()
trigram_measures = nltk.collocations.TrigramAssocMeasures()
# change this to read in your data
finder = BigramCollocationFinder.from_words(
nltk.corpus.genesis.words('english-web.txt'))
# only bigrams that appear 3+ times
finder.apply_freq_filter(3)
# return the 10 n-grams with the highest PMI
finder.nbest(bigram_measures.pmi, 10)