In graph theory, what is defined as a sequence of consecutive edges?

In graph theory, a path is defined as a sequence of consecutive edges that connect a sequence of vertices without revisiting any vertex. A path indicates a direct connection from one node to another through edges, and it captures the idea of traveling through a graph from one point to another while adhering to the condition of not duplicating any vertices.

Paths are fundamental in graph theory as they help analyze relationships and connections within networks. They are used in various applications, such as finding the shortest route in navigation systems or analyzing the flow in networks.

A loop, on the other hand, refers to an edge that connects a vertex to itself, making it distinct from a path, which involves at least two different vertices. A node (or vertex) is a fundamental unit in a graph, representing points where edges meet, while a walk is a broader concept that allows for the revisiting of vertices and edges. Thus, while a walk can include paths, it is less strict in its definition and can traverse the same nodes and edges multiple times.