# Why DFS `discoveres` the vertex, that it should not?

i have a very simple directed graph:
V0 -> V2
V1 -> V2

i use BFS and DFS algorithms starting from V0 and get different results from
`discover_vertex` function:
for BFS it does not discover V1, that is correct - there is no path from V0
to V1
but for DFS it does discover V1

output:
directed graph
0 2 BFS visited 2 // correct
0 2 1 DFS visited 3 // wrong

undirected graph
0 2 1 BFS visited 3 // correct
0 2 1 DFS visited 3 // correct

code:

import graph_tool.all as gt

class BFSCheck(gt.BFSVisitor):
def __init__(self):
self.visited = 0

def discover_vertex(self, u):
self.visited += 1
print u,

class DFSCheck(gt.DFSVisitor):
def __init__(self):
self.visited = 0

def discover_vertex(self, u):
self.visited += 1
print u,

def Cmp(graph):

bfs_check = BFSCheck()
gt.bfs_search(graph, v0, bfs_check)
print "BFS visited %d" % bfs_check.visited

dfs_check = DFSCheck()
gt.dfs_search(graph, v0, dfs_check)
print "DFS visited %d" % dfs_check.visited

graph_u = gt.Graph(directed = False)
graph_d = gt.Graph(directed = True)

print "directed graph"
Cmp(graph_d)

print
print "undirected graph"
Cmp(graph_u)

This seems to be the default behavior of the depth_first_search()
function in boost. See:

Note that in this function _all_ vertices are eventually visited, not
only the (out-)component from the source! I don't really understand why
it was done like this, since, as you observed, it is inconsistent with
BFS. I have modified the code in graph-tool to use the function
depth_first_visit() instead, where this is avoided, and the expected
behavior is obtained. Just try the current git version.

Thanks for the very simple example.

Cheers,
Tiago