Multifractal cross-correlation effects in two-variable time series of complex network vertex observables

Exploring Word-Adjacency Networks with Multifractal Time Series Analysis Techniques

A novel method of exploring linguistic networks is introduced by mapping word-adjacency networks to time series and applying multifractal analysis techniques. This approach captures the complex structural patterns of language by encoding network properties-such as clustering coefficients and node degrees-into temporal sequences. Using Alice's Adventures in Wonderland by Lewis Carroll as a case study, both traditional word-adjacency networks and extended versions that incorporate punctuation are examined. The results indicate that the time series derived from clustering coefficients, when following the natural reading order, exhibits multifractal characteristics, revealing inherent complexity in textual organization. Statistical validation confirms that observed multifractal properties arise from genuine correlations rather than from spurious effects. Extending this analysis by taking into account punctuation equally with words, however, changes the nature of the global scaling to a more convolved form that is not describable by a uniform multifractal. An analogous analysis based on the node degrees does not show such rich behaviors, however. These findings reveal a new perspective for quantitative linguistics and network science, providing a deeper understanding of the interplay between text structure and complex systems.

Topological properties of the limited penetrable horizontal visibility graph family

The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. In this work, we extend this algorithm to create a directed-limited penetrable horizontal visibility graph and an image-limited penetrable horizontal visibility graph. We define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real-value series. We perform several numerical simulations to check the accuracy of our theoretical results. Finally, we present an application of the directed-limited penetrable horizontal visibility graph to measure real-value time series irreversibility and an application of the image-limited penetrable horizontal visibility graph that discriminates noise from chaos. We also propose a method to measure the systematic risk using the image-limited penetrable horizontal visibility graph, and the empirical results show the effectiveness of our proposed algorithms.