A survey on the network models applied in the industrial network optimization

Network architecture design is critical for optimizing industrial networks. Network architectures can be classified into small-scale networks and large-scale networks based on scale. Graph theory is an efficient mathematical tool for network topology modeling. For small-scale networks, their structure often has regular topology. For large-scale ones, the current body of work mainly focuses on random characteristics of network nodes and edges. Recently, widely used models include random networks, small-world networks, and scale-free networks. In this study, starting from the scale of the network, network modeling methods based on graph theory as well as their industrial applications, are summarized and analyzed. Moreover, a novel network performance metric, called system entropy, is proposed. From the perspective of mathematical properties, an analysis of its non-negativity and concavity is performed. The advantage of system entropy is that it can cover the existing regular networks, random networks, small-world networks, and scale-free networks, and has strong generality. The simulation results reveal that this proposed metric can achieve the comparison of various industrial networks under different models.