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

## TL;DR

This paper links the right-sided asymmetry of multifractal spectra derived from network-generated time series to the small-world properties of networks, providing a new method to identify small-worldness in complex systems.

## Contribution

It introduces a novel approach using multifractal analysis of time series to detect small-world features in various network models and real-world networks.

## Key findings

- Right-sided asymmetry correlates with small-world properties.
- Low edge density and high clustering are associated with asymmetry.
- Method successfully distinguishes small-world networks from others.

## 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 multifractal 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.