{'fraction_non_alphanumeric': 0.047685834502103785, 'fraction_numerical': 0.011220196353436185, 'mean_word_length': 4.578125, '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}}
Scale-Free Network in Stock Markets

We study the cross-correlations in stock price changes among the S&P 500 companies by introducing a weighted random graph, where all vertices (companies) are fully connected via weighted edges. The weight of each edge is distributed in the range of [−1, 1] and is given by the normalized covariance of the two modified returns connected, where the modified return means the return minus the mean over all companies. We define an influence-strength at each vertex as the sum of the weights on the edges incident upon that vertex. Then we find that the influence-strength distribution in its absolute magnitude |q| follows a power-law, P (|q|) ∼ |q|−δ, with exponent δ ≈ 1.8(1).