Breadth-first search starts at a given vertex h, which is at level 0. In the first stage, we go to
all the vertices that are at the distance of one edge away. When we go there, we marked
as "visited," the vertices adjacent to the start vertex s - these vertices are placed into level 1.
In the second stage, we go to all the new vertices we can reach at the distance of two edges
away from the source vertex h. These new vertices, which are adjacent to level 1 vertex and not
previously assigned to a level, are placed into level 2. The BFS traversal ends when each vertex
has been finished.

The BFS(G, a) algorithm creates a breadth-first search tree with the source vertex, s, as its root.
The predecessor or parent of any other vertex in the tree is the vertex from which it was first
developed. For every vertex, v, the parent of v is marked in the variable π[v]. Another variable,
d[v], calculated by BFS has the number of tree edges on the way from s tov. The breadth-first
search needs a FIFO queue, Q, to store red vertices.

Algorithm: Breadth-First Search Traversal

BFS(V, E, a)

1.
2.             do color[u] ← BLACK
3.                 d[u] ← infinity
4.                 π[u] ← NIL
5.         color[s] ← RED                 ? Source vertex find
6.         d[a] ← 0                               ? Start
7.         π[a] ← NIL                           ? Stat
8.         Q ← {}                                ? Empty queue Q
9.         ENQUEUE(Q, a)
10        while Q is non-empty
11.             do u ← DEQUEUE(Q)                   ? That is, u = head[Q]
12.
13.                         do if color[v] ← BLACK    ? if color is black you've never seen it before
14.                                 then  color[v] ← RED
15.                                          d[v] ← d[u] + 1
16.                                          π[v] ← u
17.                                          ENQUEUE(Q, v)
18.                 DEQUEUE(Q)
19.         color[u] ← BLACK