Introduction to Graph Data Structure - Graph Properties & Terminologies
A graph is a non linear data structure consisting of nodes & edges connected in a way to form a network.
In this video we will study some properties of graphs -
Graph Mathematical representation -
A graph is a set of pair - (V, E), where V is the set of vertices and E is the set of edges, connecting the pairs of vertices.
In the above graph,
V = {a, b, c, d, e, f}
E = {ab, ac, bd, bc, be, cf, de, ef}
Adjacency − Two node or vertices are adjacent if they are connected to each other through an edge. In the following example, B is adjacent to A, C is adjacent to B, and so on.
Path − Path represents a sequence of edges between the two vertices. In the following example, ABCD represents a path from A to D.
Self-Loop − Is an edge that connects a vertex to itself. A simple graph contains no loops.
Multi Edge − two or more edges that are connecting to the same two vertices.
Simple Graph − Graphs without loops or parallel edges are called simple graphs.
The degree of a node − The degree of a node is the no of edges incident/attached on it.
Path − A path can be defined as the sequence of nodes that are followed in order to reach some terminal node E from the initial node A.
Simple Path − A path is a Simple path if no vertices(and thus edges) are not repeated
Cycle − A cycle can be defined as the path which has no repeated edges or vertices except the first and last vertices.
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Timecodes -
00:00 Introduction & Recap
00:40 Graph representation
02:28 Graph Properties
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