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During the past decade, bridging the gap between time series and complex networks, which aims to investigate the usage of network features to depict geometry of different type of timeseries becomes a hot topic. In this brief paper, the internal relationship between a typical static scale-free networks and its associated nonlinear timeseries (under the viewpoint of duality analysis of networks and time series) was investigated. A ubiquitous process to discuss such a problem are introduced. It is found that, the scale-free degree exponent has linear relationship with its associated timeseries’ hurst exponent. Research in this direction will provide new methods and powerful tools for analysis of the causal relationships between complex structures and temporal behaviors of a complex dynamical system. Also, it is useful for further investigation on structure and function analysis of complex networks via classical timeseries analysis methods.

journal of physics. conference series

Relationship between the degree exponent and its associated timeseries’ hurst exponent of a static scale-free network — Under the viewpoint of mutual representation between timeseries and network graph