Multiplex Structures: Patterns of Complexity in Real-World Networks

Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it represents a natural route to understand the dynamics, as well as to synthesize or optimize the functions, of networks. A broad spectrum of network structural patterns have been respectively reported in the past decade, such as communities, multipartites, hubs, authorities, outliers, bow ties, and others. Here, we show that most individual real-world networks demonstrate multiplex structures. That is, a multitude of known or even unknown (hidden) patterns can simultaneously situate in the same network, and moreover they may be overlapped and nested with each other to collaboratively form a heterogeneous, nested or hierarchical organization, in which different connective phenomena can be observed at different granular levels. In addition, we show that the multiplex structures hidden in exploratory networks can be well defined as well as effectively recognized within an unified framework consisting of a set of proposed concepts, models, and algorithms. Our findings provide a strong evidence that most real-world complex systems are driven by a combination of heterogeneous mechanisms that may collaboratively shape their ubiquitous multiplex structures as we observe currently. This work also contributes a mathematical tool for analyzing different sources of networks from a new perspective of unveiling multiplex structures, which will be beneficial to multiple disciplines including sociology, economics and computer science.