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A directed graph, or digraph G consists of a finite nonempty set of vertices V, and a finite set of edges E, where an edge is an ordered pair of vertices in V. Vertices are also commonly referred to as nodes. Edges are sometimes referred to as arcs.

BFS starts at a given vertex, which is at level 0. In the first stage, we visit all vertices at level 1. In the second stage, we visit all vertices at second level. These new vertices, which are adjacent to level 1 vertices, and so on. The BFS traversal terminates when every vertex has been visited.
BREADTH FIRST SEARCH (G, S)
Input: A graph G and a vertex.
Output: Edges labeled as discovery and cross edges in the connected component.
Create a Queue Q.
ENQUEUE (Q, S) // Insert S into Q.
While Q is not empty do
for each vertex v in Q do
for all edges e incident on v do
if edge e is unexplored then
let w be the other endpoint of e.