GRAPH
A graph is a data structure that consists of a set of vertices
(also known as nodes) and a set of edges connecting these
vertices. It is used to represent relationships or connections
between objects
1.CONCEPT OF GRAPH
The concept of a graph is a fundamental data structure used
to represent relationships or connections between objects.
A graph consists of a set of vertices (also called nodes or
points) and a set of edges (also called arcs or lines) that
connect pairs of vertices. Here are some key points to
understand about graphs:
1. Vertices: Vertices represent entities or objects in a graph.
For example, in a social network graph, vertices can
represent users, and in a road network graph, vertices can
represent cities or intersections.
2. Edges: Edges represent the connections or relationships
between vertices. They can be directed (pointing from one
vertex to another) or undirected (bi-directional). In a social
network graph, edges can represent friendships, and in a
transportation network graph, edges can represent roads or
connections between cities.
3. Types of Graphs:
- Undirected Graph: A graph in which edges have no
specific direction.
- Directed Graph (Digraph): A graph in which edges have a
specific direction.
- Weighted Graph: A graph in which edges have associated
weights or costs.
- Cyclic Graph: A graph that contains cycles (a path that
starts and ends at the same vertex).
- Acyclic Graph: A graph that does not contain any cycles.
4. Adjacency: The adjacency of a vertex refers to its
neighboring vertices. In a graph, vertices can be adjacent if
there is an edge connecting them. The adjacency can be
represented using adjacency lists or adjacency matrices.
5. Graph Traversals: Traversing a graph means visiting all
its vertices and edges. Common graph traversal algorithms
include Depth-First Search (DFS) and Breadth-First Search
(BFS).
6. Applications: Graphs have numerous real-world
applications, such as social networks, computer networks,
transportation systems, recommendation systems,
genealogy, and more. They are used for modeling and
A graph is a data structure that consists of a set of vertices
(also known as nodes) and a set of edges connecting these
vertices. It is used to represent relationships or connections
between objects
1.CONCEPT OF GRAPH
The concept of a graph is a fundamental data structure used
to represent relationships or connections between objects.
A graph consists of a set of vertices (also called nodes or
points) and a set of edges (also called arcs or lines) that
connect pairs of vertices. Here are some key points to
understand about graphs:
1. Vertices: Vertices represent entities or objects in a graph.
For example, in a social network graph, vertices can
represent users, and in a road network graph, vertices can
represent cities or intersections.
2. Edges: Edges represent the connections or relationships
between vertices. They can be directed (pointing from one
vertex to another) or undirected (bi-directional). In a social
network graph, edges can represent friendships, and in a
transportation network graph, edges can represent roads or
connections between cities.
3. Types of Graphs:
- Undirected Graph: A graph in which edges have no
specific direction.
- Directed Graph (Digraph): A graph in which edges have a
specific direction.
- Weighted Graph: A graph in which edges have associated
weights or costs.
- Cyclic Graph: A graph that contains cycles (a path that
starts and ends at the same vertex).
- Acyclic Graph: A graph that does not contain any cycles.
4. Adjacency: The adjacency of a vertex refers to its
neighboring vertices. In a graph, vertices can be adjacent if
there is an edge connecting them. The adjacency can be
represented using adjacency lists or adjacency matrices.
5. Graph Traversals: Traversing a graph means visiting all
its vertices and edges. Common graph traversal algorithms
include Depth-First Search (DFS) and Breadth-First Search
(BFS).
6. Applications: Graphs have numerous real-world
applications, such as social networks, computer networks,
transportation systems, recommendation systems,
genealogy, and more. They are used for modeling and
