## Minimum Spanning Tree
### How to Build the Connected Graph \"G\"
#### 2.2.2 Improved Method, ESLP  
To overcome the defects in PTP, an Energy Station-to-Load Points model is developed. The model does not connect all the adjacent points randomly, and conforms to the following rules:  
* Select Energy Station and Load Points according to their own characteristics
* Only the path that starts from the Energy Station and ends at a Load Point is calculated. The reverse path that satisfies Equation (2) is not calculated, to simplify the calculation. \[\cos V_{tp}V_{sp}L\leq 0,\] (2) where \(V_{tp}\) represents the end point of the line segment, \(V_{sp}\) represents the starting point of the line segment, and \(L\) represents the target Load Point.
* Repeat the above steps until all Load Points have been connected.
* For easy solution, more constraints are added to the ESLP model as follows:
* Load points (dots) can only be connected to adjacent load-road nodes (triangles).
* Any two adjacent points can be connected, but pipe that does not end at load points (dots) must be located on the road.
* Load points (dots) can only be set as the end point of a line segment  
Figure 7 shows the ESLP diagram. This configuration guarantees that all line segments are connected to load points in one direction, thus ensuring that each load point is the last terminal of the final network topology. Compared with the traditional PTP model, the ESLP model has two benefits. First, it guarantees that all the pipelines are distributed along the road. Second, the load points are designated as the terminal of the network topology, allowing for easy solution in the subsequent optimization process.  
The modeling procedure of ESLP mainly consists of the generation of a grid connected graph, the construction of the digital adjacency matrix, and the optimization of topology using the minimum spanning tree algorithm. The subsequent optimization of pipe diameter selection is based on the ESLP model.  
ESLP is a different type of pipe network connected graph construction model. It divides nodes (which include load nodes, road-load nodes, load points, and energy stations) according to their own characteristics, avoiding the problems caused by unconstrained pipeline connections. Instead of connecting any two adjacent points, ESLP first selects energy stations and load points, and connects energy stations to all load points, respectively and independently.  
Figure 7: A schematic of connection graph G by Energy Station-to-Load Points model.  
After classifying the four categories of nodes, new results are obtained according to the principles mentioned above, as shown in Figure 8, when constructing a new network connected graph. The new pipe network design scheme is shown in Figure 9.  
Obviously, ESPL ensures that pipes are laid along the road. However, previous studies have been conducted on the basis of the relative position relationship between nodes. The resulting network topology scheme also targets the optimal path, that is, the shortest pipe length, which is inconsistent with the cost optimization goal of network design in DES. The economic cost is related to the pipe diameter and pipe length, which will be discussed in Section 3.2.