Complex systems: Features, similarity and connectivity

Cesar H.Comin, Thomas Peron, Filipi N.Silva, Diego R.Amancio, Francisco A.Rodrigues, Luciano da F.Costa

Physics Reports
Volume 861, 25 May 2020, Pages 1-41


The increasing interest in complex networks research has been motivated by intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of concepts and methods deriving from many areas, from statistical physics to sociology, which are often used in an independent way. Yet, for this same reason, it would be desirable to integrate these various aspects into a more coherent and organic framework, which would imply in several benefits normally allowed by the systematization in science, including the identification of new types of problems and the cross-fertilization between fields. More specifically, the identification of the main areas to which the concepts frequently used in complex networks can be applied paves the way to adopting and applying a larger set of concepts and methods deriving from those respective areas. Among the several areas that have been used in complex networks research, pattern recognition, optimization, linear algebra, and time series analysis seem to play a particularly basic and recurrent role. In the present manuscript, we propose a systematic way to integrate the concepts from these diverse areas regarding complex networks research. In order to do so, we start by grouping the multidisciplinary concepts into three main groups of representations, namely features, similarity, and network connectivity. Then we show that several of the analysis and modeling approaches to complex networks can be thought as a composition of maps between these three groups, with emphasis on nine main types of mappings, which are presented and illustrated. For instance, we argue that many models used to generate networks can be understood as a mapping from features to similarity, and then to network connectivity concepts. Such a systematization of principles and approaches also provides an opportunity to review some of the most closely related works in the literature, which is also developed in this article.