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Simple Paths Explained: Meaning, Examples and Uses
In graph theory, a simple path is a route through a graph that does not visit any vertex more than once. It connects a sequence of distinct vertices with edges, avoiding loops and repeated stops.
Suppose a graph contains vertices A, B, C, and D. The route A–B–C–D is a simple path if each consecutive pair is connected by an edge. A route such as A–B–C–B is not simple because it visits B twice.
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A general path or walk may allow repeated vertices or edges, depending on the definition being used. A simple path specifically prohibits repeated vertices. If a simple path returns to its starting vertex, it forms a simple cycle rather than an open simple path.
Simple paths help describe efficient, non-repeating routes in transportation systems, computer networks, and relationship maps. They are also used in algorithms that test whether two vertices are connected or identify possible routes without unnecessary detours.
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In a graph with edges A–B, B–C, and C–D, A–B–C–D is a path. Each step follows an edge connecting one vertex to the next.
A simple path in graph theory is a sequence of connected vertices in which no vertex appears more than once. Its length equals the number of edges traveled.
A path is a sequence of vertices connected by edges. Definitions may vary regarding whether repeated vertices or edges are permitted.
A triangle with vertices A, B, and C and edges A–B, B–C, and C–A is a simple graph. It has no loops or multiple edges between the same pair of vertices.
A path on a graph is a route from one vertex to another along connected edges. It records the order in which the vertices are reached.
A graph is simple when it has no self-loops and no duplicate edges connecting the same two vertices. Each edge therefore connects two distinct vertices only once.
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