Hi all,

I’ve got a very large undirected graph (407 mil vertices, 522 mil edges, 2 vertex properties) that  consists of multiple connected components (ccs).

I noticed that when I call e.g. dfs_iterator or dfs_search on a source vertex, it takes around 1 – 2 seconds to return. The upper bound is depending on the component’s size, but the lower bound seems to be the same for all components.

I have created a test graph with only a subset of the ccs of the large graph. Iterating the same cc in the test graph takes only a couple of milliseconds instead of ≥ 1 s. This tells me, that the dfs/bfs iterators have some kind of overhead depending on the complete graph size.

I wrote a DFSVisitor that collects some timings during iteration to better see which steps consume time. Here are the results (rounded for readability):

In [30]: test_dfs(graph, graph.vertex(0))

# first time the function is entered
visitor.start_vertex_t                2.3e-05 s
visitor.first_discover_vertex_t       0.18 s
visitor.first_examine_edge_t          0.18 s
visitor.first_tree_edge_t             0.63 s
visitor.first_finish_vertex_t         0.63 s

# average time between last 2 calls of the function
visitor.discover_vertex_t             0.002 s
visitor.examine_edge_t                0.001 s
visitor.tree_edge_t                   0.001 s
visitor.finish_vertex_t               0.001 s

# last time finished() is called
visitor.finished                      1.3 s

# number of times the functions were called
visitor.discovered_vertices           565
visitor.examined_edges                1978
visitor.tree_edges                    564
visitor.finished_vertices             565

took                                  1.38 s

As you can see, start_vertex is called immediately, but then it takes a very long time until the other Visitor functions are called for the first time after which the calls are faster again, but still quite slow. On the test graph I think I can see the same trend with smaller numbers because the graph is smaller:

In [30]: test_dfs(test_graph, test_graph.vertex(0))

# first time the function is entered
visitor.start_vertex_t                2e-05 s
visitor.first_discover_vertex_t      
0.0007 s
visitor.first_examine_edge_t         
0.0007 s
visitor.first_tree_edge_t             0.0016
s
visitor.first_finish_vertex_t        
0.0015 s

# average time between last 2 calls of the function
visitor.discover_vertex_t             1.6e-05 s
visitor.examine_edge_t               
3.7e-06 s
visitor.tree_edge_t                  
1.4e-05 s
visitor.finish_vertex_t              
1.4e-05 s

# last time finished() is called
visitor.finished                      
0.01 s

# number of times the functions were called
visitor.discovered_vertices           565
visitor.examined_edges                1978
visitor.tree_edges                    564
visitor.finished_vertices             565

took                                  0.01 s

If I iterate the same cc in the large graph in python, it takes me only a couple of milliseconds:

def dfs(graph, vertex_idx):
    t = time.time()
    todo = {vertex_idx}
    visited = set()
    while len(todo) > 0:
        next_vertex = todo.pop()
        visited.add(next_vertex)
        todo |= set(graph.iter_all_neighbors(graph.vertex(next_vertex))) - visited
    print(f'dfs took {time.time() - t} s')
    return visited

In [38]: d = dfs(graph, 0)
dfs took 0.01653146743774414 s

Because of graph_tool’s slowness for small ccs I ended up writing a heuristic that always attempts a naive python dfs first, but aborts if 1 second is exceeded and only then does the graph_tool dfs. Anyone know what’s going on here?


Best

My-Tien