What is Graph ? || Graph Data Structure || What is Graph Data Structure || Graph in Data Structure || Types of Graph Data Structure || Property of Graph Data Structure
Graph Data Structure
A graph is a collection of two sets V and E where V is a finite non empty set of vertices and E is a finite non empty set of Edges.
Vertices are nothing but the nodes in the graph.
Two adjacent vertices are joined by Edges.
A graph is denoted as G(V, E) .
Types of Graph
basically graph are two types
Directed Graph:- in the directed graph the direction are shown on the edges.
Now directed graph is divided into two category is unidirectional and bidirectional.
Undirected Graph :- when edges has no Direction this is called undirected graph
Note:- Undirected graph actually working as a bidirectional graph.
Property of Graph
Complete Graph :- a graph is a called complete. if every vertex in G is connected to every other vertex in G thus a complete graph must be a connected. the complete graph with n vertices is denoted by Kn.
Sub Graph :- let G=(V, E) be a graph. A graph G' = (V', E') is said to be a subgraph of G, E' is a subset of E and V' is a subset of V, such that the ages in E' are incident only with the vertices in V'.
Connected Graph :- a path can be found between every pair of distinct vertices, we can call that the graph is a connected graph.
Disconnected Graph :- A graph is disconnected if at least two vertices of the graph are not connected directly by a path or edges.
Weighted Graph :- A weighted graph is a graph in which each graph is given a numerical weight on edge.
Path :- an open walk in which no vertex appears more than once is called a path it connected intersect itself and a self loop cannot be a part of the path.
Walk :- Walk in a graph G is a finite alternatively sequence of vertices and edges, beginning and ending with same or different vertices such that no ages can appear as more than once however a vertex may be. walk can also be referred as edges chain.
Cycle :- a cycle is a closed path in which all vertices are distinct except v0=vn a cycle of length K is called a k cycle in a graph any cycle must have length 3 or more.
Loop :- A loop is an edge that connects a vertex to itself.
Degree of Graph :- A degree of path is a sequence of nodes in which each node is connected by an edge to the next.
Circuit :- a close walk in which no vertex appears more than once is called a circuit.