The increasing interest in complex networks research has been a consequence of several 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 more 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, 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. 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.

中文翻译：

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复杂系统：特征、相似性和连通性

对复杂网络研究的兴趣日益增加是该领域几个内在特征的结果，例如表示和建模几乎任何离散系统的方法的普遍性，以及结合来自许多领域的概念和方法，来自统计物理学社会学，它们通常以独立的方式使用。然而，出于同样的原因，将这些不同的方面整合到一个更加连贯和有机的框架中是可取的，这将意味着科学系统化通常允许的几个好处，包括识别新类型的问题和交叉田间施肥。进一步来说，确定复杂网络中经常使用的概念可以应用的主要领域，为采用和应用源自这些各自领域的更多概念和方法铺平了道路。在复杂网络研究中已经使用的几个领域中，模式识别、优化、线性代数和时间序列分析似乎扮演着更基本和经常性的角色。在本手稿中，我们提出了一种系统的方法来整合来自这些不同领域的复杂网络研究的概念。为此，我们首先将多学科概念分为三个主要组，即特征、相似性和网络连接。然后我们展示了对复杂网络的几种分析和建模方法可以被认为是这三组之间映射的组合，重点是九种主要类型的映射，这些映射被呈现和说明。这种原则和方法的系统化也提供了一个机会来回顾文献中一些最密切相关的作品，这些作品也在本文中展开。