  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.
