# Evolution of the Complex Supply Chain Network Based on Deviation from the Power-Law Distribution
## 2 Evolutionary Characteristics and Model Analysis of Complex SCNs
### Complex SCN Evolution and Degree Distribution Model  
The first two sections briefly analyze the evolution mechanism and topology structure of the SCN with small-world and scale-free characteristics. Through an analysis of the previous material, it can be concluded that the complex SCN is a scale-free network that conforms to the characteristics of the \"small-world\" and follows the nonuniform dynamic evolution mechanism, such as difference, preference, growth, maintenance, and emergence. From a macro perspective, the SCN is a network of business operation models derived from node enterprises to adapt to the dynamic economic market environment. It is also a product of competition and cooperation between node enterprises on the network under different time and space conditions. The formation process of the SCN is a dynamic self-organization evolution process. This process is based on the competition and cooperation mechanism of the enterprises in the market, and carries out the growth of the enterprise itself, the dynamic competition, and cooperation between the enterprises in the international market environment. It optimizes with the survival of the fittest in this process, i.e., the joining and exiting of network nodes. With the continuous transformation of the value chain in the contemporary social economy, the continuous increase in the scale of the enterprise's operational planning, the in-depth refinement of the division of labor in the production process, and the continuous transformation of the production and sales model, the complexity and dynamics of SCN have increased, while the evolution mechanism of the network in time can be explored from multiple dimensions. First, from a microlevel analysis, the evolution of complex SCNs is manifested by the node joining and elimination by node companies to adapt to the market environment and the pursuit of maximizing benefits, as well as the disconnection and reconnection of node companies. Behavior mode is also a product of competition and cooperation between enterprises. Second, from a macro perspective, the evolution of the SCN is reflected in the dynamic change in the overall topology, the time-varying network robust performance, and the scale of the network. Continuous expansion occurs, and the network distributed structure gradually tends to the ideal state. In general, the evolution mechanism of complex SCNs is based on internal and external environments and interactions, and the evolutionary dynamics of \"node enterprises-single supply chain-SCN\" gradually change from the underlying individual behavior changes to overall network structure changes. Subtle changes in any link may cause huge changes in the SCN system. These changes are closely related to the topology and macro nature of the SCN itself. The SCN has gradually evolved from a very small initial stage to a network system with complex characteristics. At this time, the degree distribution of the SCN follows the power-law characteristic and satisfies the following formula:  
\[P(k)\propto k^{-\gamma}, \tag{4}\]  
where \(k\) is the node degree value of the network and \(\gamma\) is the exponent of the power-law distribution. The power index \(\gamma\) will be different in different SCNs and evolution periods. It can be seen from Formula (4) that the probability of network size distribution is inversely proportional to the power index \(\gamma\). When \(\gamma\) becomes larger, it indicates that the number of node enterprises with a larger degree value in the network is reduced, and the scale of the node enterprises tends to be homogeneous. When \(\gamma\) decreases, it indicates that the number of node enterprises with a larger degree in the network increases, and the development scale of node enterprises is more heterogeneous.