{'fraction_non_alphanumeric': 0.012219959266802444, 'fraction_numerical': 0.0, 'mean_word_length': 4.655172413793103, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Cayley Graphs and the Discrete Fourier Transform

Given a group G, we can construct a graph relating the elements of G to each other, called the Cayley graph. Using Fourier analysis on a group allows us to apply our knowledge of the group to gain insight into problems about various properties of the graph. Ideas from representation theory are powerful tools for analysis of groups and their Cayley graphs, but we start with some simpler theory to motivate the use of group representations.