In graph theory, a graph shows a set of connections between objects. Each object is a vertex. Each connection, between two vertices, forms an

**edge**, or

**arc**.

A *directed* edge has a direction associated with it, so it is thought of as coming from one of the vertices and going to the other one. An *undirected* edge treats both vertices interchangeably. Often, a real number is associated with each edge. These numbers are called *weights*.

Curves have what is known as an "**arc-length**". This is the length the curve would have if it were straightened, such that, it became a line. The arc-length, of some curved function, *f*(*x*), between points *a* and *b*, is equal to the integral of the square root of the quantity, one plus the square derivatived (or squared slope) of *f*(*x*) multiplied by the derivative of *x* -- *s* = ∫ √ (1 + [*df/dx*(*x*)]^{2}*dx*. The arc-length formula is derived from the distance formula.