Right-side-stretched multifractal spectra indicate small-worldness in networks

Abstract

Complex network formalism allows to explain the behavior of systems composed by interacting units. Several prototypical network models have been proposed thus far. The small-world model has been introduced to mimic two important features observed in real-world systems: i) local clustering and ii) the possibility to move across a network by means of long-range links that significantly reduce the characteristic path length. A natural question would be whether there exist several "types" of small-world architectures, giving rise to a continuum of models with properties (partially) shared with other models belonging to different network families. Here, we take advantage of the interplay between network theory and time series analysis and propose to investigate small-world signatures in complex networks by analyzing mul- * Corresponding Author tifractal characteristics of time series generated from such networks. In particular, we suggest that the degree of right-sided asymmetry of multifractal spectra is linked with the degree of small-worldness present in networks. This claim is supported by numerical simulations performed on several parametric models, including prototypical small-world networks, scale-free, fractal and also real-world networks describing protein molecules. Our results also indicate that right-sided asymmetry emerges with the presence of the following topological properties: low edge density, low average shortest path, and high clustering coefficient.

Multifractal analysis of financial markets: a review

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Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses

“…Multifractal detrended fluctuation analysis (MFDFA) [32] is a method for detecting and quantifying the scaling properties of time-series which is widely applied across diverse areas of experimental and computational science [39][40][41][42][43][44]. It comprises multiple steps, which may be summarized as follows.…”

Multifractal analysis of financial markets

“…Multifractal cross-correlation analysis (MF-CCA) of the time series of degree, clustering coefficient, and closeness centrality can distinguish between Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks [1031]. Also, the degree of right-sided asymmetry of multifractal spectra of the time series of these local node variables is linked with the degree of small-worldness present in networks [1032]. This method can be applied to financial networks.…”