Abstract：This paper starts from the seven bridges problem solved by Euler, and extends the principles of topology and graph theory. Then we give a review of the network sciences development from regular networks to random networks and then to complex networks, expounding the connotation of network sciences and discussing the cross with other disciplines. Finally, we point out four aspects of mathematical challenges including the new topological representation theory of complexity, computing technology of million level of sparse networks, dynamic behavior of large scale network structure, and aggregation mechanism of different levels hybrid networks.
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