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Over the last decade or so, the study of complex networks has attracted a surge of interest in varied branches of science and industry, from engineering to economics, from neurobiology to statistical physics. Network theory emerging as a blooming science has been recognized as a network-based paradigm that is taking science by storm. Much progress has been achieved, but even more questions are being posed. At the dawn of the millennium, S.H.Strogatz [1] enumerated some possible complications facing network theory: (1) structural complexity; (2) network evolution; (3) connection diversity; (4) dynamical complexity; (5) node diversity; and (6) meta-complication. These challenges have resisted complete solutions so far. A special issue on complex systems and networks composed by leading scientists in the field was honored by Science in 2009, which highlights important sweeping advances as well as up-to-date insightful perspectives [2]. Albeit young, network theory was preceded by an old and profound subject, graph theory, in mathematics that governs the discrete universe.

Can Network Theory be the Gold Standard for Mathematicians?