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##### 2.2 Graph of a Power System Network

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A *graph* represents the geometrical structure of a power system network. In other words, it describes how various power system components are interconnected to form a network. In the graph, components are represented as line segments. Consider the following example to understand the significance of the graph theory. Three network segments extracted from three different networks and their structure is represented by a graph, as shown in Figure 2.1.

It may be seen from Figure 2.1 that the same network equation *I*_{3} = *I*_{2} + *I*_{1} can be obtained by applying KCL to the junction node in the three segments shown in Figure 2.1 (*i* – *iii*), as well as in the graph (Figure 2.1(*iv*)). This means that network equations developed based on either KCL or KVL do not depend on the type of elements (such as R, L, C) but rather on the structure of the network. Since the structure of the three segments is similar to that in Figure 2.1(*iv*), the same network equation is obtained. This process simplifies working with complicated networks since we merely use the network structure to formulate network equations. Topological and graphical techniques form the basis of using the computer in network analysis.