A graph is a collection of nodes (vertices) connected by edges. It can represent relationships like networks or paths, and it’s used in algorithms like shortest path and network flow.

A graph is a data structure consisting of a set of nodes, known as vertices, and edges that connect pairs of vertices. Graphs can be used to model many real-world problems such as networks (social networks, computer networks), paths (navigation systems), and relationships (dependency graphs in programming). Graphs can be classified into two main types: directed and undirected. In a directed graph, edges have a direction, indicating the flow from one vertex to another, while in an undirected graph, edges have no direction. Graphs can also be weighted or unweighted. In a weighted graph, each edge has a weight (or cost) associated with it, which is used in algorithms like Dijkstra’s shortest path. Graphs are represented in several ways, including adjacency lists and adjacency matrices. An adjacency list represents each vertex as a list of its neighbors, while an adjacency matrix represents the graph as a 2D array, where the entry at row i and column j indicates whether there is an edge between vertex i and vertex j. Common algorithms used on graphs include depth-first search (DFS), breadth-first search (BFS), and algorithms for finding the shortest path, like Dijkstra’s or the Bellman-Ford algorithm. Understanding graphs is crucial for solving problems related to connectivity, paths, and flows.