# Terminology

In order to discuss the more involved methods of circuit analysis, we must define a few basic terms necessary for a clear, concise description of important circuit features.â€‹

**Circuit illustrating terminologies**

A node is a point in a circuit where two or more circuit elements join.*Node***Example***a*,*b*,*c*,*d*,*e*,*f*and*g*A node that joins three or more elements.*Essential Node***Example***b*,*c*,*e*and*g*A branch is a path that connects two nodes.*Branch***Example***v*,_{1}*R*_{1},*R*_{2},*R*_{3},*v*,_{2}*R*_{4},*R*_{5},*R*_{6},*R*_{7}and*I*Those paths that connect essential nodes without passing through an essential node.*Essential branch***Example**câ€“aâ€“b, câ€“dâ€“e, câ€“fâ€“g, bâ€“e, eâ€“g, bâ€“g (through*R*_{7}), and bâ€“g (through*I*)A loop is a complete path, i.e., it starts at a selected node, traces a set of connected basic circuit elements and returns to the original starting node without passing through any intermediate node more than once.*Loop***Example***a**b**e**d**c**a*,*a**b**e**g**f**c**a*,*c**d**e**b**g**f**c*, etc.A mesh is a special type of loop, i.e., it does not contain any other loops within it.*Mesh***Example***a**b**e**d**c**a*,*c**d**e**g**f**c*,*g**e**b**g*(through*R*_{7}) and*g**e**b**g*(through*I*)A graph whose branches are oriented is called a directed or oriented graph.*Oriented Graph*The rank of a graph is (*Rank of Graph**n*â€“1) where*n*is the number of nodes or vertices of the graph.A graph is planar if it can be drawn in a plane such that no two branches intersect at a point which is not a node.*Planar and Non-planar Graph*

**(a)**

*Planar graph*

**(b)***Non-planar graph*A subgraph is a subset of the branches and nodes of a graph. The subgraph is said to be proper if it consists of strictly less than all the branches and nodes of the graph.*Subgraph*A path is a particular sub graph where only two branches are incident at every node except the internal nodes (i.e., starting and finishing nodes). At the internal nodes, only one branch is incident.*Path*