ee-304 electrical network theory [class notes1] - 2013
DESCRIPTION
Electrical Network Topology, Electrical Network Graph Theory, Node, Branch, Twig, Link, Tree, CotreeTRANSCRIPT
Network Topology and Graph TheoryEE-304 ENT credits: 4 L3 P0 T1
Lairenlakpam Joyprakash Singh, PhD
Department of ECE,North-Eastern Hill University (NEHU),
Shillong – 793 [email protected]
August 8, 2013
1 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
TreeTwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
TreeTwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
TreeTwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
TreeTwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
TreeTwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
TreeTwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology
- Graph and its types
TreeTwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology- Graph and its types
TreeTwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology- Graph and its types
Tree
TwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology- Graph and its types
TreeTwigs
Co-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology- Graph and its types
TreeTwigsCo-tree
Links or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Introduction to Electrical Network Topology
Terms and Definitions
Circuit elements
Node
Branch
Path
Closed path or Circuit or Loop or Mesh
Topology, rather Electrical network topology- Graph and its types
TreeTwigsCo-treeLinks or Chords
2 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:
- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:
- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.
Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,
- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:
- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.
Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,
- Can not be subdivided into other two-terminal devices.Node:
- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:
- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.
Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:
- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.
Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:
- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:
- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.
Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:
- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.
Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:
- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.
Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:
- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.
Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - I
Circuit elements:- The mathematical models of a two terminal electrical devices,- Completely characterized by its voltage-current relationship,- Can not be subdivided into other two-terminal devices.
Node:- A point at which two or more circuit elements have a commonconnection,
- The number of branches incident to a node is known as thedegree of that node.
Branch:- A single path, containing one circuit element, which connnectsone node to any other node,
- Represented by a line in the graph.Path:
- A set of elements that may be traversed in order without passingthrough the same node twice.
3 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:
- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:
- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,
- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:
- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:
- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.
Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:
- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:
- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,
- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:
- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:
- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:
- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:- The interconnection of two or more circuit elements forms anelectical network.
Circuit:
- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:- The interconnection of two or more circuit elements forms anelectical network.
Circuit:- Network that contains at least one closed path,
- Every circuit is a network, but not all networks are circuits.Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:- The interconnection of two or more circuit elements forms anelectical network.
Circuit:- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:- The interconnection of two or more circuit elements forms anelectical network.
Circuit:- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:
- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - II
Loop:- A close path or a closed contour selected in a network/circuit,- A path that may be started from a prticular node to other nodesthrough branches and comes to the original/starting node,
- Also known as closed path or circuit.Mesh1 [2]:
- A loop that does not contain any other loops within it,- Any mesh is a circuit/loop but any loop/circuit may not be amesh.
Network:- The interconnection of two or more circuit elements forms anelectical network.
Circuit:- Network that contains at least one closed path,- Every circuit is a network, but not all networks are circuits.
Planar circuit:- A circuit that may drawn on a plane surface in such a way thatno branch passes over or under any other branch.
1Engineering Circuit Analysis, 8e4 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - III
Topology:
- Deals with properties of networks which are unaffected when thenetwork is stretched, twisted, or otherwise distorted the size andthe shape,
- Not concerned with the particular types of elements appearing inthe circuit, but only with the way in which branches and nodesare arranged.
Graph:
- A graph corresponding to a given network is obtained byreplacing all circuit elements with lines.
- Connected graph: A graph in which at least one path existsbetween any two nodes of the graph. If the network has atransformer as one of the element, then the resulted graph isunconnected
- Directed or Oriented graph: A graph that has all the nodesand branches numbered and also directions are given to thebranches.
- Subgraph: The subset of a graph. If the number of nodes andbranches of a subgraph is less than that of the graph, thesubgraph is said to be proper.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - III
Topology:- Deals with properties of networks which are unaffected when thenetwork is stretched, twisted, or otherwise distorted the size andthe shape,
- Not concerned with the particular types of elements appearing inthe circuit, but only with the way in which branches and nodesare arranged.
Graph:
- A graph corresponding to a given network is obtained byreplacing all circuit elements with lines.
- Connected graph: A graph in which at least one path existsbetween any two nodes of the graph. If the network has atransformer as one of the element, then the resulted graph isunconnected
- Directed or Oriented graph: A graph that has all the nodesand branches numbered and also directions are given to thebranches.
- Subgraph: The subset of a graph. If the number of nodes andbranches of a subgraph is less than that of the graph, thesubgraph is said to be proper.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - III
Topology:- Deals with properties of networks which are unaffected when thenetwork is stretched, twisted, or otherwise distorted the size andthe shape,
- Not concerned with the particular types of elements appearing inthe circuit, but only with the way in which branches and nodesare arranged.
Graph:
- A graph corresponding to a given network is obtained byreplacing all circuit elements with lines.
- Connected graph: A graph in which at least one path existsbetween any two nodes of the graph. If the network has atransformer as one of the element, then the resulted graph isunconnected
- Directed or Oriented graph: A graph that has all the nodesand branches numbered and also directions are given to thebranches.
- Subgraph: The subset of a graph. If the number of nodes andbranches of a subgraph is less than that of the graph, thesubgraph is said to be proper.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - III
Topology:- Deals with properties of networks which are unaffected when thenetwork is stretched, twisted, or otherwise distorted the size andthe shape,
- Not concerned with the particular types of elements appearing inthe circuit, but only with the way in which branches and nodesare arranged.
Graph:
- A graph corresponding to a given network is obtained byreplacing all circuit elements with lines.
- Connected graph: A graph in which at least one path existsbetween any two nodes of the graph. If the network has atransformer as one of the element, then the resulted graph isunconnected
- Directed or Oriented graph: A graph that has all the nodesand branches numbered and also directions are given to thebranches.
- Subgraph: The subset of a graph. If the number of nodes andbranches of a subgraph is less than that of the graph, thesubgraph is said to be proper.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - III
Topology:- Deals with properties of networks which are unaffected when thenetwork is stretched, twisted, or otherwise distorted the size andthe shape,
- Not concerned with the particular types of elements appearing inthe circuit, but only with the way in which branches and nodesare arranged.
Graph:- A graph corresponding to a given network is obtained byreplacing all circuit elements with lines.
- Connected graph: A graph in which at least one path existsbetween any two nodes of the graph. If the network has atransformer as one of the element, then the resulted graph isunconnected
- Directed or Oriented graph: A graph that has all the nodesand branches numbered and also directions are given to thebranches.
- Subgraph: The subset of a graph. If the number of nodes andbranches of a subgraph is less than that of the graph, thesubgraph is said to be proper.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - III
Topology:- Deals with properties of networks which are unaffected when thenetwork is stretched, twisted, or otherwise distorted the size andthe shape,
- Not concerned with the particular types of elements appearing inthe circuit, but only with the way in which branches and nodesare arranged.
Graph:- A graph corresponding to a given network is obtained byreplacing all circuit elements with lines.
- Connected graph: A graph in which at least one path existsbetween any two nodes of the graph. If the network has atransformer as one of the element, then the resulted graph isunconnected
- Directed or Oriented graph: A graph that has all the nodesand branches numbered and also directions are given to thebranches.
- Subgraph: The subset of a graph. If the number of nodes andbranches of a subgraph is less than that of the graph, thesubgraph is said to be proper.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - III
Topology:- Deals with properties of networks which are unaffected when thenetwork is stretched, twisted, or otherwise distorted the size andthe shape,
- Not concerned with the particular types of elements appearing inthe circuit, but only with the way in which branches and nodesare arranged.
Graph:- A graph corresponding to a given network is obtained byreplacing all circuit elements with lines.
- Connected graph: A graph in which at least one path existsbetween any two nodes of the graph. If the network has atransformer as one of the element, then the resulted graph isunconnected
- Directed or Oriented graph: A graph that has all the nodesand branches numbered and also directions are given to thebranches.
- Subgraph: The subset of a graph. If the number of nodes andbranches of a subgraph is less than that of the graph, thesubgraph is said to be proper.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - III
Topology:- Deals with properties of networks which are unaffected when thenetwork is stretched, twisted, or otherwise distorted the size andthe shape,
- Not concerned with the particular types of elements appearing inthe circuit, but only with the way in which branches and nodesare arranged.
Graph:- A graph corresponding to a given network is obtained byreplacing all circuit elements with lines.
- Connected graph: A graph in which at least one path existsbetween any two nodes of the graph. If the network has atransformer as one of the element, then the resulted graph isunconnected
- Directed or Oriented graph: A graph that has all the nodesand branches numbered and also directions are given to thebranches.
- Subgraph: The subset of a graph. If the number of nodes andbranches of a subgraph is less than that of the graph, thesubgraph is said to be proper.
5 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Network Circuits & Their Graphs
Network Topology: An example
A circuit with topologically equivalent graphs:
12
3
4
+−Vs
Is
R1IR1
R2IR2
R3
IR3
C
IC
LIL
12
3
4
12
3
4
i) A Circuit ii) its graph iii) directed graph
1
2
3
4
1
2
3
4
1
2
3
4
Three topologically equivalent graphs of figure ii).
6 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - I
1 2 3
4
5 A
R1 R2
R4CR3
(a)
12
3
4
a b
c
d e f
(b)
Figure 1 : (a) A circuit and (b) its graph.
Note:
The maximum number of branches possible, in a circuit, will be equalto the number of nodes or vertices.
There are at least two branches in a circuit.
7 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - II
1 2 3
4
5 A
R1IR1
R2IR2
R4
IR4
C
IC
R3
IR3
(a)
12
3
4
a b
c
d e f
(b)
Figure 2 : (a) A circuit and (b) its directed graph.
Note:
Each of the lines of the graph is indicated a reference direction by anarrow, and the resulted graph is called oriented/directed graph.
8 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - III
12
3
4
5
+−Vs
Is
R
R1I1
R2I2
R3
I3
C
IC
LIL
(a)
12
3
4
5
a
b c
fe
d
g
(b)
12
3
4, 5
a
b c
fed
(c)
Figure 3 : (a) A circuit, (b) its directed graph and (c) simplified directedgraph of (b).
Note:
The active element branch is replaced by its internal resistance tosimplify analysis and computation.
9 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - IV
12
3
4
+−Vs
Ivs
R
R1I1
R2I2
IIsC
IC
LIL
(a)
12
3
4
a
b c
ed
(b)
1
2
3
4
a
b c
e
d
(c)
Figure 4 : (a) A circuit, and (b),(c) its directed graphs.
Note:
The active elements are excluded from the graph to simplify analysisand computation.
10 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Network Circuits & Their Graphs
An Electrical Network & its Graph - V
1A
1 Ω
1 Ω
1 Ω
1 Ω
1 Ω
+−1V
(a) (b) (c)
Figure 5 : (a) A circuit, and its- (b) simplified graph and (c) directedgraph.
Note:
When voltage source is not in series with any passive element in thegiven network, it is kept in the graph as a branch.
11 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:
- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,
Links or Chords:
- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.
Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:
- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,
Links or Chords:
- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.
Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,
Links or Chords:
- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.
Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:
- The branches of a tree are known as twigs,Links or Chords:
- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.
Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:- The branches of a tree are known as twigs,
Links or Chords:
- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.
Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:- The branches of a tree are known as twigs,
Links or Chords:
- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:- The branches of a tree are known as twigs,
Links or Chords:- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:- The branches of a tree are known as twigs,
Links or Chords:- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.
Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:- The branches of a tree are known as twigs,
Links or Chords:- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Network Topology: Terms and Definitions - IV
Tree:- A connected subgraph having all the nodes of a graph withoutany loop.
- Thus, a tree is a subgraph that has the following properties:- It must consist of all nodes of a complete graph.- For a graph having n number of nodes, the tree of the given graph
will have n− 1 branches.- There exists one and only one path between any pair of nodes.- A tree should not have any closed path.- The rank of a tree is (n− 1). This is also the rank of the graph to
which the tree belongs.
Twigs:- The branches of a tree are known as twigs,
Links or Chords:- The branches that are removed from the graph while forming atree are termed as links or chords,
- Links are complement of twigs.Co-tree:
- The graph constituted with links is known as co-tree.
12 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Tree and Cotree
Given a Graph:1 2 3
4
a b
c d ef
Tree Twigs of tree Links of cotree
12 3
4
a b
c d ef
a,b,d c,e,f
12 3
4
a b
c d ef
a,d,f c,b,e
13 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Summary and a Question:
Q. Does the following graph with branches a and e form a tree?
12
3
4
a
b c
fed
+ The number of nodes in this subgraph isequal to that of the given graph.
+ But it has unconnected subgraphs andmoreover total number branches6= n− 1(= 3). Therefore, it is not a tree.
14 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Summary and a Question:
Q. Does the following graph with branches a and e form a tree?
12
3
4
a
b c
fed
+ The number of nodes in this subgraph isequal to that of the given graph.
+ But it has unconnected subgraphs andmoreover total number branches6= n− 1(= 3). Therefore, it is not a tree.
14 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Terms & Definitions
Summary and a Question:
Q. Does the following graph with branches a and e form a tree?
12
3
4
a
b c
fed
+ The number of nodes in this subgraph isequal to that of the given graph.
+ But it has unconnected subgraphs andmoreover total number branches6= n− 1(= 3). Therefore, it is not a tree.
14 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy References
Text Books & References
M. E. Van ValkenburgNetwork Analysis, 3/e.PHI, 2005.
W.H. Hayt, J.E. Kemmerly, S.M. DurbinEngineering Circuit Analysis, 8/e.MH, 2012.
M. Nahvi, J.A. EdministerSchuamâĂŹs Outline Electric Circuits, 4/e.TMH, SIE, 2007.
A. Sudhakar, S.S. PalliCircuits and Networks: Analysis and Synthesis, 2/e.TMH, 2002.
15 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy References
Text Books & References
M. E. Van ValkenburgNetwork Analysis, 3/e.PHI, 2005.
W.H. Hayt, J.E. Kemmerly, S.M. DurbinEngineering Circuit Analysis, 8/e.MH, 2012.
M. Nahvi, J.A. EdministerSchuamâĂŹs Outline Electric Circuits, 4/e.TMH, SIE, 2007.
A. Sudhakar, S.S. PalliCircuits and Networks: Analysis and Synthesis, 2/e.TMH, 2002.
15 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Network Toplogy Khublei Shibun!
Thank You!Any Question?
16 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Home Assignment Graph and Incidence Matrix
Problems for Practice: Graph and Incidence Matrix
1. Classify whether each of the following graphs as planar ornonplanar.2. Find the number of possible trees for each graph and draw allpossible trees.
1
2
3
4
(a)
ab c
d
(b)
1 2
3
4
5
(c)
17 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Home Assignment Graph and Incidence Matrix
Problems for Practice - II
Note: While replacing all elements of the network with lines to form agraph, we replace active elements by their internal resistancesto simplify analysis and computation.For example - 1:
1
23 4
5
+−Vs
R1
Is
R2I1
R3I2
R4
I3
C
IC
LIL
Is
(a)
23
4
1, 5
(b)
18 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Home Assignment Graph and Incidence Matrix
Problems for Practice - II
Note: While replacing all elements of the network with lines to form agraph, we replace active elements by their internal resistancesto simplify analysis and computation.For example - 1:
1
23 4
5
+−Vs
R1
Is
R2I1
R3I2
R4
I3
C
IC
LIL
Is
(a)
23
4
1, 5
(b)
18 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Home Assignment Graph and Incidence Matrix
Problems for Practice - II
Note: Transformer gives a unconnected graph!For example - 2:
12 3 4
56
+−Vs
R1
I1
R2I2
K
CIC
R3
I3
I
(a)
12
6
34
5
(b)
19 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Home Assignment Graph and Incidence Matrix
Problems for Practice - II
Note: Transformer gives a unconnected graph!For example - 2:
12 3 4
56
+−Vs
R1
I1
R2I2
K
CIC
R3
I3
I
(a)
12
6
34
5
(b)
19 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph
Home Assignment Graph and Incidence Matrix
Few non-planar Graphs
1
2
3
4
(a)
1 2
3
45
6
(b)
20 / 20 L. Joyprakash Singh (ECE, NEHU) EE-304 ENT :: Network topology and graph