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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.

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Circuit illustrating terminologies
  1. Node A node is a point in a circuit where two or more circuit elements join.
    Example abcdef and g
  2. Essential Node A node that joins three or more elements.
    Example bce and g
  3. Branch A branch is a path that connects two nodes.
    Example v1R1R2R3v2R4R5R6R7 and I
  4. Essential branch Those paths that connect essential nodes without passing through an essential node.
    Example c–a–b, c–d–e, c–f–g, b–e, e–g, b–g (through R7), and b–g (through I )
  5. Loop 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.
    Example a b e d c aa b e g f c ac d e b g f c, etc.
  6. Mesh A mesh is a special type of loop, i.e., it does not contain any other loops within it.
    Example a b e d c ac d e g f cg e b g (through R7) and g e b g (through I )
  7. Oriented Graph A graph whose branches are oriented is called a directed or oriented graph.
  8. Rank of Graph The rank of a graph is (n–1) where n is the number of nodes or vertices of the graph.
  9. Planar and Non-planar 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.
(a) Planar graph
(b) Non-planar graph
  1. Subgraph 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.
  2. Path 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.

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