# Evolution of the Complex Supply Chain Network Based on Deviation from the Power-Law Distribution
## 4 Simulation of SCN Evolution
### Simulation Analysis of Network Evolution Based on Deviation of Single Power Law Distribution  
To further analyze the deviation of the power law distribution of SCN evolution, this section selects a state-owned energy technology company with a special evolution mechanism as the research object and uses the relevant theoretical knowledge and model methods of complex networks to simulate the growth evolution of the network. The phenomenon of distribution deviation was studied. In addition, the business networks of energy production companies conform to the structural characteristics of complex SCNs, and the network node degree values follow a single power law distribution. Energy production enterprises, such as coal and petroleum-based state-controlled energy enterprises, can divide their internal organizations into procurement departments, assembly and distribution departments, production departments, and management departments according to business content. Each department can be regarded as an SCN node. The energy company has three large-scale production centers nationwide, 11 first-level sales centers, 58 second-level sales offices, and 28 raw material suppliers. Eventually, the energy supply company's business SCN can be extracted as a scale-free SCN with 100 nodes. Due to the steady development strategy of state-controlled enterprises, this SCN will have fewer new energy companies to join in a certain period of time, which can be approximately regarded as \(p_{1}=0\). The evolution process and mechanism of the network on the time scale. In the numerical simulation, to more clearly show the evolution characteristics of the energy supply enterprise's business SCN, the number of network nodes is expanded tenfold, i.e., the total network node number \(m=1\times 10^{3}\) is set, and different evolution time steps \(t_{i}\) are set. The time step corresponding to the square is \(t_{1}=5\times 10^{3}\), the time step corresponding to the triangle is \(t_{2}=7\times 10^{3}\), and the time step corresponding to the circle is \(t_{3}=1.0\times 10^{4}\). Figure 7 below shows the transformation process of the degree distribution \(P(k)\) of the SCN from the original single power law distribution to a more complicated distribution form under different logarithmic coordinates. As seen from the above figure, in the initial state at \(t_{1}\), the degree distribution of the energy supply network of the energy enterprise is fitted with a straight line, which is represented by a single power law distribution with a power index of 3. As the evolution time \(t_{1}\) increases, a small deviation at \(t_{i}\) begins to appear in the distribution area of the smaller node value, the probability value corresponding to this type of node gradually decreases, and the probability value corresponding to the node with a larger degree gradually increases. When the evolution time reaches \(t_{3}\), the \"head\" deviation phenomenon is very obvious, but the degree distribution form and Gaussian distribution are very different at this time. Figure 6: Network node degree distribution of the numerical experiment and model simulation under different parameters. During the evolution of the entire SCN, it can be predicted that the degree distribution of the network will have a tendency to change to the \(\delta\) distribution when the time step is large enough, and the form of the single power law distribution has not changed. This further validated the effectiveness of the model in this paper. At this time, the energy enterprise SCN can guarantee the connection of goods and information between any two enterprises, but the robustness of the network and the ability to resist risks are poor. Once some node companies have some problems, it will cause more problems. The division of the entire relationship network is broken, blocking the normal flow of information and products between enterprises.