From the Difference of Structures to the Structure of the Difference

Massimiliano Zanin,Xiaoqian Sun,Sebastian Wandelt,Ernestina Menasalvas

doi:10.1155/2018/4326097

Abstract

When dealing with evolving or multidimensional complex systems, network theory provides us with elegant ways of describing their constituting components, through, respectively, time-varying and multilayer complex networks. Nevertheless, the analysis of how these components are related is still an open problem. We here propose a general framework for analysing the evolution of a (complex) system, by describing the structure created by the difference between multiple networks by means of the Information Content metric. Differently from other approaches, which focus on assessing the magnitude of the change, the proposed one allows understanding if the observed changes are due to random noise or to structural (targeted) modifications; in other words, it allows describing the nature of the force driving the changes and discriminating between stochastic fluctuations and intentional modifications. We validate the framework by means of sets of synthetic networks, as well as networks representing real technological, social, and biological evolving systems. We further propose a way of reconstructing network correlograms, which allow converting the system’s evolution to the frequency domain.

Highlights

Complex networks theory [1, 2] was initially used to describe the structure underpinning individual complex systems, in recent years there has been an explosion in the number of situations in which sets of networks have to be studied in a comparative way
The availability of multiple related networks may be the natural result of analysing different, yet compatible systems, for instance, functional brain networks obtained from a large set of healthy people, with the aim of identifying common connectivity patterns [3], or from control subjects and patients suffering from a given condition [4], to detect differences between them
We further demonstrate the usefulness of the proposed solution by analysing three real systems, respectively, technical, social, and biological

Summary

Introduction

Complex networks theory [1, 2] was initially used to describe the structure underpinning individual complex systems, in recent years there has been an explosion in the number of situations in which (potentially large) sets of networks have to be studied in a comparative way. The availability of multiple related networks may be the natural result of analysing different, yet compatible systems, for instance, functional brain networks obtained from a large set of healthy people, with the aim of identifying common connectivity patterns [3], or from control subjects and patients suffering from a given condition [4], to detect differences between them. This can stem from the analysis of a single system across its parameters’ and temporal dimensions. In the specific case of brain functional networks, the presence of an unstructured difference between control subjects and patients may be ascribed to a global loss of brain connectivity, while structured changes may suggest a focused reorganisation of the information flow

Methods

Results

Conclusion