Abstract
In this paper, we first create a network model using a complex number-weighted node, where the real number-weighted network model is its special case. According to the send a and receive b of node measures, the complex number weight can be determined as a +i b . Then, we build a complex vector space on the complex plane, and the real network can be mapped into the field of this space, where the importance (I) and classification of the node may be determined (Importance on Left, Minimum, Importance on Right). Finally, we present four theorems that trigger the evolutionary dynamics of network systems when the node measure or topological structure is changed, so that the conjunction principle and entangled effect between the topological structure and kinetic characteristics are revealed. As a result, a new path is discovered to explain some real phenomena in nature or human society, such as the mechanism of the stronger the strong and win-win cooperation. The method may be applied to the analysis of various network models including regular networks, stochastic networks, and small-world networks, which may exhibit special explanatory capabilities.
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