Quick start using graph-tool

exported as notebook from here by @eliaswalyba

The graph_tool module provides a Graph class and several algorithms that operate on it. The internals of this class, and of most algorithms, are written in C++ for performance, using the Boost Graph Library.

The module must be of course imported before it can be used. The package is subdivided into several sub-modules. To import everything from all of them, one can do:

from graph_tool.all import *

In the following, it will always be assumed that the previous line was run.

Creating and manipulating graphs

An empty graph can be created by instantiating a Graph class:

g = Graph()

By default, newly created graphs are always directed. To construct undirected graphs, one must pass a value to the directed parameter:

ug = Graph(directed=False)

A graph can always be switched on-the-fly from directed to undirected (and vice versa), with the set_directed() method. The “directedness” of the graph can be queried with the is_directed() method,

ug = Graph()
ug.set_directed(False)
print(ug.is_directed() == False)

True

A graph can also be created by providing another graph, in which case the entire graph (and its internal property maps, see Property maps) is copied:

g1 = Graph()
g2 = Graph(g1)

Above, g2 is a “deep” copy of g1, i.e. any modification of g2 will not affect g1.

Once a graph is created, it can be populated with vertices and edges. A vertex can be added with the add_vertex() method, which returns an instance of a Vertex class, also called a vertex descriptor. For instance, the following code creates two vertices, and returns vertex descriptors stored in the variables v1 and v2.

v1 = g.add_vertex()
v2 = g.add_vertex()

Edges can be added in an analogous manner, by calling the add_edge() method, which returns an edge descriptor (an instance of the Edge class):

e = g.add_edge(v1, v2)

The above code creates a directed edge from v1 to v2. We can visualize the graph we created so far with the graph_draw() function.

graph_draw(g, vertex_text=g.vertex_index, output="assets/graph.png")

<VertexPropertyMap object with value type 'vector<double>', for Graph 0x7f18ed2835e0, at 0x7f1920eaca90>

With vertex and edge descriptors, one can examine and manipulate the graph in an arbitrary manner. For instance, in order to obtain the out-degree of a vertex, we can simply call the out_degree() method:

print(v1.out_degree())

1

Analogously, we could have used the in_degree() method to query the in-degree.

Note: For undirected graphs, the “out-degree” is synonym for degree, and in this case the in-degree of a vertex is always zero.

Edge descriptors have two useful methods, source() and target(), which return the source and target vertex of an edge, respectively.

print(e.source(), e.target())

0 1

The add_vertex() method also accepts an optional parameter which specifies the number of vertices to create. If this value is greater than 1, it returns an iterator on the added vertex descriptors:

vlist = g.add_vertex(10)
print(len(list(vlist)))

10

Each vertex in a graph has an unique index, which is always between 0 and N−1, where N is the number of vertices. This index can be obtained by using the vertex_index attribute of the graph (which is a property map, see Property maps), or by converting the vertex descriptor to an int.

v = g.add_vertex()
print(g.vertex_index[v])
print(int(v))

12
12

Edges and vertices can also be removed at any time with the remove_vertex() and remove_edge() methods

g.remove_edge(e)                               # e no longer exists
g.remove_vertex(v2)                # the second vertex is also gone

Note: Removing a vertex is typically an O(N) operation. The vertices are internally stored in a STL vector, so removing an element somewhere in the middle of the list requires the shifting of the rest of the list. Thus, fast O(1) removals are only possible either if one can guarantee that only vertices in the end of the list are removed (the ones last added to the graph), or if the relative vertex ordering is invalidated. The latter behavior can be achieved by passing the option fast == True, to remove_vertex(), which causes the vertex being deleted to be ‘swapped’ with the last vertex (i.e. with the largest index), which will in turn inherit the index of the vertex being deleted.

Warning: Because of the above, removing a vertex with an index smaller than N−1 will invalidate either the last (fast = True) or all (fast = False) descriptors pointing to vertices with higher index.

As a consequence, if more than one vertex is to be removed at a given time, they should always be removed in decreasing index order:

# 'del_list' is a list of vertex descriptors
for v in reversed(sorted(del_list)):
    g.remove_vertex(v)

Alternatively (and preferably), a list (or any iterable) may be passed directly as the vertex parameter of the remove_vertex() function, and the above is performed internally (in C++).

Note that property map values (see Property maps) are unaffected by the index changes due to vertex removal, as they are modified accordingly by the library.

Note: Removing an edge is an O(ks+kt) operation, where ks is the out-degree of the source vertex, and kt is the in-degree of the target vertex. This can be made faster by setting set_fast_edge_removal() to True, in which case it becomes O(1), at the expense of additional data of size O(E). No edge descriptors are ever invalidated after edge removal, with the exception of the edge being removed.

Since vertices are uniquely identifiable by their indexes, there is no need to keep the vertex descriptor lying around to access them at a later point. If we know its index, we can obtain the descriptor of a vertex with a given index using the vertex() method,

v = g.vertex(8)

which takes an index, and returns a vertex descriptor. Edges cannot be directly obtained by its index, but if the source and target vertices of a given edge are known, it can be retrieved with the edge() method

g.add_edge(g.vertex(2), g.vertex(3))
e = g.edge(2, 3)

Another way to obtain edge or vertex descriptors is to iterate through them, as described in section Iterating over vertices and edges. This is in fact the most useful way of obtaining vertex and edge descriptors.

Like vertices, edges also have unique indexes, which are given by the edge_index property:

e = g.add_edge(g.vertex(0), g.vertex(1))
print(g.edge_index[e])

1

Differently from vertices, edge indexes do not necessarily conform to any specific range. If no edges are ever removed, the indexes will be in the range [0,E−1], where E is the number of edges, and edges added earlier have lower indexes. However if an edge is removed, its index will be “vacant”, and the remaining indexes will be left unmodified, and thus will not all lie in the range [0,E−1]. If a new edge is added, it will reuse old indexes, in an increasing order.

Iterating over vertices and edges

Algorithms must often iterate through vertices, edges, out-edges of a vertex, etc. The Graph and Vertex classes provide different types of iterators for doing so. The iterators always point to edge or vertex descriptors.

Iterating over all vertices or edges

In order to iterate through all the vertices or edges of a graph, the vertices() and edges() methods should be used:

for v in g.vertices():
    print(v)
for e in g.edges():
    print(e)

0
1
2
3
4
5
6
7
8
9
10
11
(0, 1)
(2, 3)

The code above will print the vertices and edges of the graph in the order they are found.

Iterating over the neighborhood of a vertex

The out- and in-edges of a vertex, as well as the out- and in-neighbors can be iterated through with the out_edges(), in_edges(), out_neighbors() and in_neighbors() methods, respectively.

for v in g.vertices():
   for e in v.out_edges():
       print(e)
   for w in v.out_neighbors():
       print(w)

   # the edge and neighbors order always match
   for e, w in zip(v.out_edges(), v.out_neighbors()):
       assert e.target() == w

(0, 1)
1
(2, 3)
3

The code above will print the out-edges and out-neighbors of all vertices in the graph.

Warning: You should never remove vertex or edge descriptors when iterating over them, since this invalidates the iterators. If you plan to remove vertices or edges during iteration, you must first store them somewhere (such as in a list) and remove them only after no iterator is being used. Removal during iteration will cause bad things to happen.

Fast iteration over vertices and edges

While convenient, looping over the graph as described in the previous section is not the most efficient approach. This is because the loops are performed in pure Python, and hence it undermines the main feature of the library, which is the offloading of loops from Python to C++. Following the numpy philosophy, graph_tool also provides an array-based interface that avoids loops in Python. This is done with the get_vertices(), get_edges(), get_out_edges(), get_in_edges(), get_all_edges(), get_out_neighbors(), get_in_neighbors(), get_all_neighbors(), get_out_degrees(), get_in_degrees() and get_total_degrees() methods, which return numpy.ndarray instances instead of iterators.

For example, using this interface we can get the out-degree of each node via:

print(g.get_out_degrees(g.get_vertices()))

[1 0 1 0 0 0 0 0 0 0 0 0]

or the sum of the product of the in and out-degrees of the endpoints of each edge with:

edges = g.get_edges()
in_degs = g.get_in_degrees(g.get_vertices())
out_degs = g.get_out_degrees(g.get_vertices())
print((out_degs[edges[:,0]] * in_degs[edges[:,1]]).sum())

2

Property maps

Property maps are a way of associating additional information to the vertices, edges or to the graph itself. There are thus three types of property maps: vertex, edge and graph. They are handled by the classes VertexPropertyMap, EdgePropertyMap, and GraphPropertyMap. Each created property map has an associated value type, which must be chosen from the predefined set: