Examples on Graph Theory in Network Theory explained with following Timestamps:
0:00 - Examples on Graph Theory - Network Theory
0:26 - 1 Example on Graph Theory (Example of Cut Set Matrix)
6:35 - 2 Example on Graph Theory (Example of Cut Set Matrix)
11:32 - 3 Example on Graph Theory (Example of Tie Set Matrix)
15:37 - Summery
Examples on Graph Theory in Network Theory explained with following outlines:
0. Network Theory
1. Graph Theory
2. Examples on Graph Theory
3. Cut Set Matrix
3. Example of Cut Set Matrix
4. Tie Set Matrix
5. Example of Tie Set Matrix
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Details of Graph Theory Terminologies:
Graph Theory Terminologies (Node, Branch, Degree of Node, Tree, Co Tree, Twig & Link)
Here are some of the common terminologies used in graph theory:
Node/Vertex: A node, also known as a vertex, is a fundamental unit of a graph. It is a point or a location in a graph that represents an entity, such as a person, place, or thing.
Edge/Branch: An edge, also known as a branch, is a connection between two nodes in a graph. It represents the relationship between two entities.
Degree of Node: The degree of a node is the number of edges connected to it. In an undirected graph, the degree is the number of adjacent edges, while in a directed graph, the degree is the number of incoming and outgoing edges.
Tree: A tree is a type of graph where each node has a maximum of one parent node. It is a connected graph with no cycles. A tree can be used to represent hierarchical relationships, such as a family tree.
Co-Tree: A co-tree is the complement of a tree in a graph. It is a set of edges that are not present in the tree.
Twig: A twig is a subgraph of a tree that consists of a node and all its descendants.
Link: A link is a subgraph of a graph that connects two nodes without creating a cycle. It is a path between two nodes in a graph.
These terminologies are used to describe and analyze graphs, and they are essential for understanding the behavior of graphs in different applications.