Explain Path and Circuit of a graph.

In graph theory, a path and a circuit are two important concepts.

1. Path: A path in a graph is a sequence of vertices where each adjacent pair is connected by an edge. The length of the path is the number of edges in the path. For example, if we have a graph with vertices A, B, C, and D, and there is an edge between A and B, B and C, and C and D, then A-B-C-D is a path in the graph. A path is simple if it does not contain any repeated vertices.

2. Circuit: A circuit is a path that starts and ends at the same vertex. In other words, it's a closed path. For example, in the same graph as above, if there is also an edge between D and A, then A-B-C-D-A is a circuit. A circuit is simple if, apart from the starting and ending vertex, it does not contain any repeated vertices.

In summary, a path is a sequence of vertices with each pair connected by an edge, and a circuit is a path that starts and ends at the same vertex.