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The study of complex systems whose behavior and responses are determined by exhcanges and interactions between subsystems across a well-defined (possible dynamics) set of pathways,  The central point is that the behavior of a network is determined both by the pathways (structure) and by the exchanges and interactions (dynamics).  Moreover the structure itself may be (and usually is) dynamics.  This is a flexible definition that allows flexible interpretation in the various applications domains.  (Network Science, National Research Council of the National Academies)

Network analysis is based on the intuitive notion that these patterns are important features of the lives of the individuals who display them. Network analysts believe that how an individual lives depends in large part on how that individual is tied into the larger web of social connections. Many believe, moreover, that the success or failure of societies and organizations often depends on the patterning of their internal structure.

Research Challenges in Network Science
Network Science in Three Important Ways 
History of Network Science

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