Description: A path in a graph is a sequence of edges that connects a sequence of vertices. In more technical terms, a path is defined as a succession of vertices where each pair of consecutive vertices is connected by an edge. Paths can be classified into different types, such as simple paths, where vertices do not repeat, and closed paths, which start and end at the same vertex. The length of a path is measured by the number of edges it comprises. Paths are fundamental in graph theory as they allow for the analysis of connectivity and the structure of networks. Additionally, they are essential for solving problems related to route optimization, finding shortest paths, and exploring complex networks. In a directed graph, paths have a specific direction, meaning edges can only be traversed in a certain direction. Conversely, in an undirected graph, paths can be traversed in both directions. The existence of a path between two vertices can be an indicator of a graph’s connectivity, which has implications in various fields such as computer science, biology, and social sciences.
