CLASS-6
GRAPHAS

GRAPHS -

Graphs are mathematical and data structures that consist of nodes (vertices) and edges. They are widely used to represent relationships and connections between various entities. Here are some key concepts related to graphs:

  1. Nodes (Vertices):- These are the fundamental units of a graph. Nodes represent entities, and they may contain additional information, which is referred to as "payload."
  2. Edges:- Edges connect nodes and represent relationships between them. An edge may be directed or undirected, indicating the direction of the relationship.
  3. Directed Graphs (Digraphs):- In a directed graph, edges have a direction. If there is an edge from node A to node B, it does not necessarily mean there is an edge from B to A.
  4. Undirected Graphs:- In an undirected graph, edges have no direction. If there is an edge between nodes A and B, it implies a mutual relationship.
  5. Weighted Graphs:- In some cases, edges are assigned weights to represent the cost, distance, or some other metric associated with the connection between nodes.
  6. Cyclic and Acyclic Graphs:- A graph is cyclic if it contains at least one cycle (a closed loop of edges). A graph without cycles is acyclic.
  7. Connected Graphs:- A graph is connected if there is a path between every pair of nodes. Disconnected graphs have two or more components that are not connected.
  8. Tree:- A tree is a special type of graph that is acyclic and connected. In a tree, there is a unique path between any pair of nodes.
  9. Graph Traversal:- Traversal involves visiting all the nodes and edges of a graph in a systematic way. Common algorithms for graph traversal include depth-first search (DFS) and breadth-first search (BFS).
  10. Applications:- Graphs have a wide range of applications in various fields, including computer science, social networks, transportation networks, biology, and more. Examples include social network analysis, route planning, and circuit design.

Common representations of graphs include adjacency matrix and adjacency list. In an adjacency matrix, a two-dimensional array is used to represent whether there is an edge between two nodes. In an adjacency list, each node maintains a list of its adjacent nodes.

Understanding graph theory and algorithms related to graphs is crucial in computer science and various other disciplines. Graphs provide a powerful way to model and analyse relationships between entities in complex systems.