Graph

👉BFS (Breadth-First Search) – Introduction Breadth-First Search (BFS) is a fundamental graph traversal algorithm used to visit all vertices of a graph in a breadth-wise (level-by-level) manner. Starting from a given source vertex, BFS explores all its adjacent vertices first before moving on to vertices at the next level. BFS uses a queue data structure to keep track of vertices to be visited and a visited array to avoid revisiting the same vertex. It is especially useful for finding the shortest path in an unweighted graph and for level-order traversal.   Key Characteristics of BFS: Traversal Type:  Level-by-level (or layer-by-layer). Data Structure Used:  Queue (First In, First Out — FIFO). Time Complexity:  O(V + E), where V is the number of vertices and E is the number of edges. Space Complexity:  O(V), as it stores vertices in the queue. Applicable To:  Both graphs and trees. How BFS Works BFS uses a  queue  to store nodes to be explo...

      "Representation of Graph Data Structure"😊 A graph data structure represents relationships between entities. It consists of: Vertices (Nodes) : entities Edges (Links) : connections between entities There are several common ways to represent a graph, each with trade-offs. 1. Adjacency Matrix A 2D array V × V where V is the number of vertices. Example 👉Graph with vertices A, B, C: A B C A 0 1 1 B 1 0 0 C 1 0 0 1 indicates an edge, 0 indicates no edge For weighted graphs, store weights instead of 1 Properties Space : O(V²) Edge lookup : O(1) Best for : Dense graphs 2. Adjacency List Each vertex stores a list of adjacent vertices. Example Properties Space : O(V + E) Edge lookup : O(deg(V)) Best for : Sparse graphs 3. Edge List Graph is represented as a list of edges. Example ( A , B ) ( A , C) ( B , A ) (C, A ) Properties Space : O(E) Edge lookup : O(E) Best for : Simple alg...

 Graph   👉 Introduction to Graph👇 A graph is a non-linear data structure used to represent relationships between different objects. It consists of a set of vertices (nodes) and a set of edges that connect pairs of vertices. Graphs are widely used in computer science to model real-world problems such as computer networks, social networks, transportation systems, and web page links. Formally, a graph G is defined as G = (V, E) , where: V is a finite set of vertices (nodes) E is a set of edges that connect the vertices  Definition of Graph 😀 A graph is a non-linear data structure that consists of a finite set of vertices (nodes) and a set of edges that connect pairs of vertices. Formally, a graph is defined as: