graph theory:
    A path is a nonempty graph G = (V, E) of the form `V = {x_0, x_1, ..., x_n}`, `E = {x_0x_1, x_1x_2, ... x_(n-1)x_n}` where `n in NN`. All `x_i` (`i in NN`) are distinct.
    
    Path (n-path) is usually denoted by P or `P_n`. It can be also written as `P = x_0 x_1 ... x_n`, `x_0Px_n` (if path is well known for example from image).
    
    Path can be called "path from `x_0` to `x_n`" or "path between `x_0` and `x_n`".
    
    Vertices `x_0` and `x_n` are called ends, vertices `x_1, ..., x_(n-1)` are called inner vertices.
    
    The number of edges in path is called length of path and it is denoted by `P^n`. If G has only 1 vertex then `P^0 = K^1` (where `K^1` is complete graph on 1 vertex, or isolated vertex).
    
    If `x_0Px_n` then `x_0` is starting point of path and end `x_n` is ending point of path.
    
    A path is the combinatorial analog of a homeomorphic image of a closed line segment.
    
    Each of the paths `P_n` and `P_m` (`m, n in NN`) are homeomorphic graphs.