A graph is a non-linear data structure consisting of nodes (also called vertices) and edges that connect pairs of nodes. Graphs are extremely versatile and are used to model relationships and interactions in various real-world scenarios. For example, social networks like Facebook or LinkedIn can be represented as graphs, where users are the nodes and their connections (friendships or professional relationships) are the edges. Another example is a roadmap, where cities are the nodes and roads are the edges connecting them. Graphs can be directed or undirected, depending on whether the edges have a direction. In a directed graph, the edges have a direction, indicating a one-way relationship between nodes, while in an undirected graph, the edges represent bidirectional relationships. Graphs can also be weighted or unweighted. In a weighted graph, each edge has a weight or cost associated with it, which can represent distance, time, or any other metric. One of the most common uses of graphs is in graph traversal algorithms like Depth-First Search (DFS) and Breadth-First Search (BFS). These algorithms are used to explore or search through all the nodes in a graph and are essential in solving problems like finding the shortest path between two nodes (Dijkstra's algorithm), detecting cycles, or finding connected components. Graphs are also used in network flow problems, where the goal is to find the maximum flow through a network, and in recommendation systems, where relationships between users and products are modeled as a graph. Graphs are highly flexible and can be represented in various ways, such as adjacency matrices, adjacency lists, or edge lists, depending on the problem and the algorithm being used. Understanding how to work with graphs and graph algorithms is crucial in many fields, including computer networking, AI, and even biology, where graphs are used to model gene interactions and protein networks.