Breadth-First Search

// transshipment (segment)

we assume that the input graphic G(V, E) is described by adjacency table.
for each vertex u∈V, save its is-visited-flag in color[u] (white for undiscovered, gray for discovered, black for visited), save its parent vertex in π[u] (π[u] = NIL if it doesnt have parent or doesnt know who's its parent), save its distance to the start s in d[u].
a first-in-first-out queue Q is used by the algorithm to hold the set of gray vertices. head[Q] is used to describe the head of Q, Enqueue(Q,v) means to add a vertex into Q and Dequeue(Q) is a operation of removing the head of Q.
Adj[u] is the set of neighbors of u.

here's the pseudo-code:

   procedure BFS(G,S);
  begin
1.   for each vertex u∈V[G]-{s} do
    begin
2.     color[u]←White;
3.     d[u]←∞;
4.     π[u]←NIL;
    end;

5.   color[s]←Gray;
6.   d[s]←0;
7.   π[s]←NIL;
8.   Q←{s}

9.   while Q≠φ do
    begin
10.    u←head[Q];
11.    for each vertex v∈Adj[u] do
12.      if color[v]=White then
        begin
13.        color[v]←Gray;
14.        d[v]←d[v]+1;
15.        π[v]←u;
16.        Enqueue(Q,v);
        end;
17.      Dequeue(Q);
18.      color[u]←Black;
      end;
    end;