Can Network Theory be the Gold Standard for Mathematicians?

[摘要] 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 beingposed. At the dawn of the millennium, S.H.Strogatz [1] enumeratedsome possible complications facing network theory: (1) structural complexity; (2) network evolution; (3) connection diversity; (4) dynamicalcomplexity; (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 fieldwas honored by Science in 2009, which highlights important sweepingadvances as well as up-to-date insightful perspectives [2]. Albeit young,network theory was preceded by an old and profound subject, graphtheory, in mathematics that governs the discrete universe.