Abstract
Complex systems have attracted considerable interest because of their wide range of applications, and are often studied via a “classic” approach: study a specific system, find a complex network behind it, and analyze the corresponding properties. This simple methodology has produced a great deal of interesting results, but relies on an often implicit underlying assumption: the level of detail on which the system is observed. However, in many situations, physical or abstract, the level of detail can be one out of many, and might also depend on intrinsic limitations in viewing the data with a different level of abstraction or precision. So, a fundamental question arises: do properties of a network depend on its level of observability, or are they invariant? If there is a dependence, then an apparently correct network modeling could in fact just be a bad approximation of the true behavior of a complex system. In order to answer this question, we propose a novel micro-macro analysis of complex systems that quantitatively describes how the structure of complex networks varies as a function of the detail level. To this extent, we have developed a new telescopic algorithm that abstracts from the local properties of a system and reconstructs the original structure according to a fuzziness level. This way we can study what happens when passing from a fine level of detail (“micro”) to a different scale level (“macro”), and analyze the corresponding behavior in this transition, obtaining a deeper spectrum analysis. The obtained results show that many important properties are not universally invariant with respect to the level of detail, but instead strongly depend on the specific level on which a network is observed. Therefore, caution should be taken in every situation where a complex network is considered, if its context allows for different levels of observability.
Highlights
Real world dynamical complex networks are non linear systems
Being a structure embedded in space makes such network a physical object, that is the subject of observation
The aim of this section is (i) to describe our new micro-macro analysis, using the telescopic algorithm, that is capable of abstracting networks at various granularities and (ii) to assess whether the statistical properties usually employed in complex networks analysis are affected by the multidimensional network analysis itself
Summary
Real world dynamical complex networks are non linear systems. This means that the full set of elements that interact pairwise (even in a trivial way) will result in a behavior that is often unpredictable. For a wide variety of such complex systems, the spatial informative component is crucial: for example, protein-to-protein networks, brain networks [1], transportation networks [2] [3], social networks [4], power grids [5], the Internet, companies networks [6], etc are all embedded in Euclidean space, and most interestingly, the space variable itself constraints their natural evolution. Being a structure embedded in space makes such network a physical object, that is the subject of observation. As a physical object, every such network can be observed.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
