Paths
A path of length n from u to v, where n is a positive integer, in an
undirected (multi) graph is a sequence of edges e1,…,en of the graph
such that f(e1)={x0,x1}, f(e2)={x1,x2}, …, f(en)={xn-1,xn}, where x0=u
When the graph is simple, or when it is not necessary to distinguish
between multiple edges, we denote the path by its vertex sequence
The path is a circuit if it begins and ends at the same vertex, that is,
The path is said to pass through or traverse the vertices x1,…, xn-1.
A path or circuit is simple if it does not contain the same edge more
The definitions for directed (multi)graphs are the same, simply we
we talk about ordered pairs (xi,xj) instead of unordered pairs {xi,xj}.