{'fraction_non_alphanumeric': 0.016203703703703703, 'fraction_numerical': 0.0, 'mean_word_length': 5.765625, '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}}
Application of Tree-like Structure of Graph to Matrix Analysis

Formulas for matrix determinants, algebraic adjunctions, characteristic polynomial coefficients, components of eigenvectors are obtained in the form of signless sums of matrix elements products taking by special graphs. Signless formulas are very important for singular and stochastic problems. They are also useful for spectral analysis of large very sparse matrices.