  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.
