Basic Problems on Graph Data Structure

This section includes some of the basic examples and problems involving Graph Data structure.

In graph theory, a connected component refers to a subset of vertices in a graph where each vertex is connected to every other vertex in the subset, either directly or indirectly. Grouping all connected components in a graph is the process of identifying these subsets and assigning a unique identifier or label to each subset/group of vertices.

A cycle in a graph is a sequence of edges and vertices where you can start from a specific vertex, follow a continuous path, and return to the same vertex without repeating any edge. In simpler terms, a cycle occurs when you can start at a vertex, traverse a set of edges, and return to the same vertex without retracing any edge.

Finding Number of Islands is a common problem in computer science, where the task is to determine the number of distinct islands in a 2-dimensional grid. In this problem, the grid is represented as a 2D matrix, where each cell can have a value of either 0 or 1. Value of 1 represents land, and a 0 represents water. An island is defined as a group or cluster of connected land cells (represented by 1s) in the 2D matrix. These land cells are considered connected if they are adjacent to each other horizontally or vertically, but not diagonally.