.. _quickstart:
.. testsetup::
from graph_tool.all import *
Quick start guide
=================
The :mod:`graph_tool` module provides a :class:`~graph_tool.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:
.. doctest:: two-nodes
>>> from graph_tool.all import *
In the following, it will always be assumed that the previous line was run.
Creating graphs
---------------
An empty graph can be created by instantiating a :class:`~graph_tool.Graph`
class:
.. doctest:: two-nodes
>>> g = Graph()
By default, newly created graphs are always directed. To construct undirected
graphs, one must pass a value to the ``directed`` parameter:
.. doctest:: two-nodes
>>> ug = Graph(directed=False)
A graph can always be switched *on-the-fly* from directed to undirected
(and vice versa), with the :meth:`~graph_tool.Graph.set_directed`
method. The "directedness" of the graph can be queried with the
:meth:`~graph_tool.Graph.is_directed` method:
.. doctest:: two-nodes
>>> ug = Graph()
>>> ug.set_directed(False)
>>> assert ug.is_directed() == False
Once a graph is created, it can be populated with vertices and edges. A
vertex can be added with the :meth:`~graph_tool.Graph.add_vertex`
method, which returns an instance of a :class:`~graph_tool.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``.
.. doctest:: two-nodes
>>> v1 = g.add_vertex()
>>> v2 = g.add_vertex()
Edges can be added in an analogous manner, by calling the
:meth:`~graph_tool.Graph.add_edge` method, which returns an edge
descriptor (an instance of the :class:`~graph_tool.Edge` class):
.. doctest:: two-nodes
>>> e = g.add_edge(v1, v2)
The above code creates a directed edge from ``v1`` to ``v2``.
A graph can also be created by providing another graph, in which case
the entire graph (and its internal property maps, see
:ref:`sec_property_maps`) is copied:
.. doctest:: two-nodes
>>> g2 = Graph(g) # g2 is a copy of g
Above, ``g2`` is a "deep" copy of ``g``, i.e. any modification of
``g2`` will not affect ``g``.
.. note::
:class: margin
Graph visualization in ``graph-tool`` can be interactive! When the ``output``
parameter of :func:`~graph_tool.draw.graph_draw` is omitted, instead of saving
to a file, the function opens an interactive window. From there, the user can
zoom in or out, rotate the graph, select and move individual nodes or node
selections. See :func:`~graph_tool.draw.GraphWidget` for documentation on the
interactive interface.
If you are using a `Jupyter `__ notebook, the graphs
are drawn inline if ``output`` is omitted. If an interactive window is
desired instead, the option ``inline = False`` should be passed.
We can visualize the graph we created so far with the
:func:`~graph_tool.draw.graph_draw` function.
.. doctest:: two-nodes
>>> graph_draw(g, vertex_text=g.vertex_index, output="two-nodes.pdf")
<...>
.. figure:: two-nodes.png
:align: center
:width: 200px
A simple directed graph with two vertices and one edge, created by
the commands above.
We can add attributes to the nodes and edges of our graph via :ref:`property
maps`. For example, suppose we want to add an edge weight and
node color to our graph we have first to create two :class:`~graph_tool.PropertyMap`
objects as such:
.. doctest:: two-nodes
>>> eweight = g.new_ep("double") # creates an EdgePropertyMap of type double
>>> vcolor = g.new_vp("string") # creates a VertexPropertyMap of type string
And now we set their values for each vertex and edge:
.. doctest:: two-nodes
>>> eweight[e] = 25.3
>>> vcolor[v1] = "#1c71d8"
>>> vcolor[v2] = "#2ec27e"
Property maps can then be used in many ``graph-tool`` functions to set node
and edge properties, for example:
.. doctest:: two-nodes
>>> graph_draw(g, vertex_text=g.vertex_index, vertex_fill_color=vcolor,
... edge_pen_width=eweight, output="two-nodes-color.pdf")
<...>
.. testcleanup:: two-nodes
conv_png("two-nodes.pdf")
conv_png("two-nodes-color.pdf")
.. figure:: two-nodes-color.png
:align: center
:width: 200px
The same graph as before, but with edge width and node color specified by
property maps.
Property maps are discussed in more detail in the section
:ref:`sec_property_maps` below.
Adding many edges and vertices at once
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. note::
:class: margin
The vertex values passed to the constructor need to be integers per default,
but arbitrary objects can be passed as well if the option ``hashed = True``
is passed. In this case, the mapping of vertex descriptors to
vertex ids is obtained via an internal
:class:`~graph_tool.VertexPropertyMap` called ``"ids"``. E.g. in the
example above we have
.. testsetup:: margin
g = gt.Graph([('foo', 'bar'), ('gnu', 'gnat')], hashed=True)
.. doctest:: margin
>>> print(g.vp.ids[0])
foo
See :ref:`sec_property_maps` below for more details.
It is also possible to add many edges and vertices at once when the graph is
created. For example, it is possible to construct graphs directly from a list of edges, e.g.
.. doctest::
>>> g = Graph([('foo', 'bar'), ('gnu', 'gnat')], hashed=True)
which is just a convenience shortcut to creating an empty graph and calling
:meth:`~graph_tool.Graph.add_edge_list` afterward, as we will discuss below.
Edge properties can also be initialized together with the edges by using
tuples ``(source, target, property_1, property_2, ...)``, e.g.
.. doctest::
>>> g = Graph([('foo', 'bar', .5, 1), ('gnu', 'gnat', .78, 2)], hashed=True,
... eprops=[('weight', 'double'), ('time', 'int')])
The ``eprops`` parameter lists the name and value types of the properties, which
are used to create internal property maps with the value encountered (see
:ref:`sec_property_maps` below for more details).
It is possible also to pass an adjacency list to construct a graph,
which is a dictionary of out-neighbors for every vertex key:
.. doctest::
>>> g = Graph({0: [2, 3], 1: [4], 3: [4, 5], 6: []})
The above functionality also means that you can easily construct graphs
from adjacency matrices. This can be done via the :func:`numpy.nonzero`
function to extract an edge list from a matrix, e.g.:
.. doctest::
>>> m = np.array([[0, 1, 0],
... [0, 0, 1],
... [0, 1, 0]])
>>> g = Graph(np.array(np.nonzero(m)).T) # we need to transpose
If you wish to store also the non-zero values as a edge properties, you
need only to add them to the list:
.. doctest::
>>> m = np.array([[0, 1.2, 0],
... [0, 0, 10],
... [0, 7, 0]])
>>> es = np.nonzero(m)
>>> g = Graph(np.array([es[0], es[1], m[es]]).T, eprops=[("weight", "double")])
>>> print(g.ep.weight.a)
[ 1.2 10. 7. ]
For undirected graphs we need to consider only the upper (or lower) diagonal
entries, otherwise we would end up with duplicate edges. For this we can use the
:func:`numpy.triu` function:
.. doctest::
>>> m = np.triu(m)
>>> es = np.nonzero(m)
>>> g = Graph(np.array([es[0], es[1], m[es]]).T, eprops=[("weight", "double")],
... directed=False)
>>> print(g.ep.weight.a)
[ 1.2 10. ]
We can also add many edges at once `after` the graph has been created using the
:meth:`~graph_tool.Graph.add_edge_list` method. It accepts any iterable of
``(source, target)`` pairs, and automatically adds any new vertex seen:
.. doctest::
>>> g.add_edge_list([(0, 1), (2, 3)])
.. note::
:class: margin
As above, if ``hashed = True`` is passed, the function
:meth:`~graph_tool.Graph.add_edge_list` returns a
:class:`~graph_tool.VertexPropertyMap` object that maps vertex descriptors to
their id values in the list. See :ref:`sec_property_maps` below.
The vertex values passed to :meth:`~graph_tool.Graph.add_edge_list` need to be
integers per default, but arbitrary objects can be passed as well if the
option ``hashed = True`` is passed, e.g. for string values:
.. doctest::
>>> g.add_edge_list([('foo', 'bar'), ('gnu', 'gnat')], hashed=True,
... hash_type="string")
<...>
or for arbitrary (hashable) Python objects:
.. doctest::
>>> g.add_edge_list([((2, 3), 'foo'), (3, 42.3)], hashed=True,
... hash_type="object")
<...>
Manipulating graphs
-------------------
With vertex and edge descriptors at hand, 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
:meth:`~graph_tool.Vertex.out_degree` method:
.. doctest::
>>> g = Graph()
>>> v1 = g.add_vertex()
>>> v2 = g.add_vertex()
>>> e = g.add_edge(v1, v2)
>>> print(v1.out_degree())
1
.. note::
:class: margin
For undirected graphs, the "out-degree" is synonym for degree, and
in this case the in-degree of a vertex is always zero.
Analogously, we could have used the :meth:`~graph_tool.Vertex.in_degree`
method to query the in-degree.
Edge descriptors have two useful methods, :meth:`~graph_tool.Edge.source`
and :meth:`~graph_tool.Edge.target`, which return the source and target
vertex of an edge, respectively.
.. doctest::
>>> print(e.source(), e.target())
0 1
We can also directly convert an edge to a tuple of vertices, to the same effect:
.. doctest::
>>> u, v = e
>>> print(u, v)
0 1
The :meth:`~graph_tool.Graph.add_vertex` method also accepts an optional
parameter which specifies the number of additional vertices to create. If this
value is greater than 1, it returns an iterator on the added vertex descriptors:
.. doctest::
>>> vlist = g.add_vertex(10)
>>> print(len(list(vlist)))
10
Each vertex in a graph has a unique index, which is ***always*** between
:math:`0` and :math:`N-1`, where :math:`N` is the number of
vertices. This index can be obtained by using the
:attr:`~graph_tool.Graph.vertex_index` attribute of the graph (which is
a *property map*, see :ref:`sec_property_maps`), or by converting the
vertex descriptor to an ``int``.
.. doctest::
>>> v = g.add_vertex()
>>> print(g.vertex_index[v])
12
>>> print(int(v))
12
Edges and vertices can also be removed at any time with the
:meth:`~graph_tool.Graph.remove_vertex` and :meth:`~graph_tool.Graph.remove_edge` methods,
.. doctest::
>>> g.remove_edge(e) # e no longer exists
>>> g.remove_vertex(v2) # the second vertex is also gone
When removing edges, it is important to keep in mind some performance considerations:
.. warning::
:class: margin
Because of the contiguous indexing, removing a vertex with an index smaller
than :math:`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:
.. code-block::
# 'vs' is a list of
# vertex descriptors
vs = sorted(vs)
vs = reversed(vs)
for v in vs:
g.remove_vertex(v)
Alternatively (and preferably), a list (or any iterable) may be
passed directly as the ``vertex`` parameter of the
:meth:`~graph_tool.Graph.remove_vertex` function, and the above is
performed internally (in C++).
Note that property map values (see :ref:`sec_property_maps`) are
unaffected by the index changes due to vertex removal, as they are
modified accordingly by the library.
.. note::
Removing a vertex is typically an :math:`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 :math:`O(1)` removals are only
possible 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
:meth:`~graph_tool.Graph.remove_vertex`, which causes the vertex
being deleted to be 'swapped' with the last vertex (i.e. with the
largest index), which, in turn, will inherit the index of the vertex
being deleted.
Removing an edge is an :math:`O(k_{s} + k_{t})` operation, where
:math:`k_{s}` is the out-degree of the source vertex, and
:math:`k_{t}` is the in-degree of the target vertex. This can be made
faster by setting :meth:`~graph_tool.Graph.set_fast_edge_removal` to
`True`, in which case it becomes :math:`O(1)`, at the expense of
additional data of size :math:`O(E)`.
No edge descriptors are ever invalidated after edge removal, with the
exception of the edge itself that is being removed.
Since vertices are uniquely identifiable by their indices, 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 :meth:`~graph_tool.Graph.vertex`
method,
.. doctest::
>>> 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
:meth:`~graph_tool.Graph.edge` method
.. doctest::
>>> 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 :ref:`sec_iteration`. This is in fact the
most useful way of obtaining vertex and edge descriptors.
Like vertices, edges also have unique indices, which are given by the
:attr:`~graph_tool.Graph.edge_index` property:
.. doctest::
>>> e = g.add_edge(g.vertex(0), g.vertex(1))
>>> print(g.edge_index[e])
1
Differently from vertices, edge indices do not necessarily conform to
any specific range. If no edges are ever removed, the indices will be in
the range :math:`[0, E-1]`, where :math:`E` is the number of edges, and
edges added earlier have lower indices. However if an edge is removed,
its index will be "vacant", and the remaining indices will be left
unmodified, and thus will not all lie in the range :math:`[0, E-1]`. If
a new edge is added, it will reuse old indices, in an increasing order.
.. _sec_iteration:
Iterating over vertices and edges
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Algorithms must often iterate through vertices, edges, out-edges of a
vertex, etc. The :class:`~graph_tool.Graph` and
:class:`~graph_tool.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
:meth:`~graph_tool.Graph.vertices` and :meth:`~graph_tool.Graph.edges`
methods should be used:
.. testcode::
for v in g.vertices():
print(v)
for e in g.edges():
print(e)
.. testoutput::
:hide:
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
""""""""""""""""""""""""""""""""""""""""""""
.. warning::
:class: margin
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.
The out- and in-edges of a vertex, as well as the out- and in-neighbors can be
iterated through with the :meth:`~graph_tool.Vertex.out_edges`,
:meth:`~graph_tool.Vertex.in_edges`, :meth:`~graph_tool.Vertex.out_neighbors`
and :meth:`~graph_tool.Vertex.in_neighbors` methods, respectively.
.. testcode::
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
.. testoutput::
:hide:
(0, 1)
1
(2, 3)
3
The code above will print the out-edges and out-neighbors of all
vertices in the graph.
.. _facebook:
Example analysis: an online social network
------------------------------------------
Let us consider an online social network of `facebook users
`__, available from the
`Netzschleuder network repository `__. We can load it
in ``graph-tool`` via the :data:`graph_tool.collection.ns` interface:
.. testsetup:: facebook
from graph_tool.all import *
.. doctest:: facebook
>>> g = collection.ns["ego_social/facebook_combined"]
We can quickly inspect the structure of the network by visualizing it:
.. doctest:: facebook
>>> graph_draw(g, g.vp._pos, output="facebook.pdf")
<...>
.. figure:: facebook.png
:align: center
:width: 600px
Network of friendships among users on Facebook.
.. note::
:class: margin
A SBM provides a statistically principled method to cluster the nodes of a
network according to their latent mixing patterns. ``graph-tool`` provides
extensive support for this kind of analysis, as detailed in a :ref:`dedicated
HOWTO `.
This methodology overcomes some serious limitations of outdated approaches,
such as modularity maximization, which should in general `be avoided
`__.
This network seems to be composed of many communities with homophilic patterns.
We can identify them reliably by inferring a `stochastic block model` (SBM),
achieved by calling :func:`~graph_tool.inference.minimize_blockmodel_dl`:
.. doctest:: facebook
>>> state = minimize_blockmodel_dl(g)
.. testcode:: facebook
:hide:
state.multiflip_mcmc_sweep(niter=10000, beta=np.inf)
This returns a :class:`~graph_tool.inference.BlockState` object. We can
visualize the results with:
.. doctest:: facebook
>>> state.draw(pos=g.vp._pos, output="facebook-sbm.pdf")
<...>
.. figure:: facebook-sbm.png
:align: center
:width: 600px
Groups of nodes identified by fitting a SBM to the facebook frendship data.
.. note::
:class: margin
The algorithm to compute betweenness centrality has a quadratic complexity on
the number of nodes of the network, so it can become slow as it becomes large.
However in ``graph-tool`` it is implemented in parallel, affording us more
performance. For the network being considered, it finishes in under a second
with a modern laptop.
We might want to identify the nodes and edges that act as "bridges" between
these communities. We can do so by computing the `betweenness centrality
`__, obtained via
:func:`~graph_tool.centrality.betweenness`:
.. doctest:: facebook
>>> vb, eb = betweenness(g)
This returns an vertex and edge property map with the respective betweenness
values. We can visualize them with:
.. doctest:: facebook
>>> graph_draw(g, g.vp._pos, vertex_fill_color=prop_to_size(vb, 0, 1, power=.1),
... vertex_size=prop_to_size(vb, 3, 12, power=.2), vorder=vb,
... output="facebook-bt.pdf")
<...>
.. figure:: facebook-bt.png
:align: center
:width: 600px
The node betweeness values correspond to the color and size of the nodes.
.. testcleanup:: facebook
conv_png("facebook.pdf")
conv_png("facebook-sbm.pdf")
conv_png("facebook-bt.pdf")
.. _sec_property_maps:
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 :class:`~graph_tool.VertexPropertyMap`,
:class:`~graph_tool.EdgePropertyMap`, and
:class:`~graph_tool.GraphPropertyMap`. Each created property map has an
associated *value type*, which must be chosen from the predefined set:
.. tabularcolumns:: |l|l|
.. table::
======================== ======================
Type name Alias
======================== ======================
``bool`` ``uint8_t``
``int16_t`` ``short``
``int32_t`` ``int``
``int64_t`` ``long``, ``long long``
``double`` ``float``
``long double``
``string``
``vector`` ``vector``
``vector`` ``vector``
``vector`` ``vector``
``vector`` ``vector``, ``vector``
``vector`` ``vector``
``vector``
``vector``
``python::object`` ``object``
======================== ======================
New property maps can be created for a given graph by calling one of the
methods :meth:`~graph_tool.Graph.new_vertex_property` (alias
:meth:`~graph_tool.Graph.new_vp`),
:meth:`~graph_tool.Graph.new_edge_property` (alias
:meth:`~graph_tool.Graph.new_ep`), or
:meth:`~graph_tool.Graph.new_graph_property` (alias
:meth:`~graph_tool.Graph.new_gp`), for each map type. The values are
then accessed by vertex or edge descriptors, or the graph itself, as
such:
.. testcode::
from numpy.random import randint
g = Graph()
g.add_vertex(100)
# insert some random links
for s,t in zip(randint(0, 100, 100), randint(0, 100, 100)):
g.add_edge(g.vertex(s), g.vertex(t))
vprop = g.new_vertex_property("double") # Double-precision floating point
v = g.vertex(10)
vprop[v] = 3.1416
vprop2 = g.new_vertex_property("vector") # Vector of ints
v = g.vertex(40)
vprop2[v] = [1, 3, 42, 54]
eprop = g.new_edge_property("object") # Arbitrary Python object.
e = g.edges().next()
eprop[e] = {"foo": "bar", "gnu": 42} # In this case, a dict.
gprop = g.new_graph_property("bool") # Boolean
gprop[g] = True
It is possible also to access vertex property maps directly by vertex indices:
>>> print(vprop[10])
3.1416
.. warning::
:class: margin
The following lines are equivalent:
.. code-block::
eprop[(30, 40)]
eprop[g.edge(30, 40)]
Which means that indexing via (source, target) pairs is slower than via edge
descriptors, since the function :meth:`~graph_tool.Graph.edge` needs to be
called first.
And likewise we can access edge descriptors via (source, target) pairs:
>>> g.add_edge(30, 40)
<...>
>>> eprop[(30, 40)] = "gnat"
We can also iterate through the property map values directly, i.e.
>>> print(list(vprop)[:10])
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
Property maps with scalar value types can also be accessed as a
:class:`numpy.ndarray`, with the
:meth:`~graph_tool.PropertyMap.get_array` method, or the
:attr:`~graph_tool.PropertyMap.a` attribute, e.g.,
.. testcode::
from numpy.random import random
# this assigns random values to the vertex properties
vprop.get_array()[:] = random(g.num_vertices())
# or more conveniently (this is equivalent to the above)
vprop.a = random(g.num_vertices())
.. _sec_internal_props:
Internal property maps
^^^^^^^^^^^^^^^^^^^^^^
Any created property map can be made "internal" to the corresponding
graph. This means that it will be copied and saved to a file together
with the graph. Properties are internalized by including them in the
graph's dictionary-like attributes
:attr:`~graph_tool.Graph.vertex_properties`,
:attr:`~graph_tool.Graph.edge_properties` or
:attr:`~graph_tool.Graph.graph_properties` (or their aliases,
:attr:`~graph_tool.Graph.vp`, :attr:`~graph_tool.Graph.ep` or
:attr:`~graph_tool.Graph.gp`, respectively). When inserted in the graph,
the property maps must have an unique name (between those of the same
type):
.. doctest::
>>> eprop = g.new_edge_property("string")
>>> g.ep["some name"] = eprop
>>> g.list_properties()
some name (edge) (type: string)
Internal graph property maps behave slightly differently. Instead of
returning the property map object, the value itself is returned from the
dictionaries:
.. doctest::
>>> gprop = g.new_graph_property("int")
>>> g.gp["foo"] = gprop # this sets the actual property map
>>> g.gp["foo"] = 42 # this sets its value
>>> print(g.gp["foo"])
42
>>> del g.gp["foo"] # the property map entry is deleted from the dictionary
For convenience, the internal property maps can also be accessed via
attributes:
.. doctest::
>>> vprop = g.new_vertex_property("double")
>>> g.vp.foo = vprop # equivalent to g.vp["foo"] = vprop
>>> v = g.vertex(0)
>>> g.vp.foo[v] = 3.14
>>> print(g.vp.foo[v])
3.14
.. _sec_graph_io:
Graph I/O
---------
Graphs can be saved and loaded in four formats: `graphml
`_, `dot
`_, `gml
`_
and a custom binary format ``gt`` (see :ref:`sec_gt_format`).
.. warning::
The binary format ``gt`` and the text-based ``graphml`` are the
preferred formats, since they are by far the most complete. Both
these formats are equally complete, but the ``gt`` format is faster
and requires less storage.
The ``dot`` and ``gml`` formats are fully supported, but since they
contain no precise type information, all properties are read as
strings (or also as double, in the case of ``gml``), and must be
converted by hand to the desired type. Therefore you should always
use either ``gt`` or ``graphml``, since they implement an exact
bit-for-bit representation of all supported :ref:`sec_property_maps`
types, except when interfacing with other software, or existing
data, which uses ``dot`` or ``gml``.
.. note::
:class: margin
Graph classes can also be pickled with the :mod:`pickle` module.
A graph can be saved or loaded to a file with the :attr:`~graph_tool.Graph.save`
and :attr:`~graph_tool.Graph.load` methods, which take either a file name or a
file-like object. A graph can also be loaded from disc with the
:func:`~graph_tool.load_graph` function, as such:
.. testcode::
g = Graph()
# ... fill the graph ...
g.save("my_graph.gt.gz")
g2 = load_graph("my_graph.gt.gz")
# g and g2 should be identical copies of each other
.. _sec_graph_filtering:
Graph filtering
---------------
.. note::
:class: margin
It is important to emphasize that the filtering functionality does not add
any performance overhead when the graph is not being filtered. In this case,
the algorithms run just as fast as if the filtering functionality didn't
exist.
One of the unique features of ``graph-tool`` is the "on-the-fly" filtering of
edges and/or vertices. Filtering means the temporary masking of vertices/edges,
which are in fact not really removed, and can be easily recovered.
Ther are two different ways to enable graph filtering: via graph views or
inplace filtering, which are covered in the following.
.. _sec_graph_views:
Graph views
^^^^^^^^^^^
It is often desired to work with filtered and unfiltered graphs
simultaneously, or to temporarily create a filtered version of graph for
some specific task. For these purposes, ``graph-tool`` provides a
:class:`~graph_tool.GraphView` class, which represents a filtered "view"
of a graph, and behaves as an independent graph object, which shares the
underlying data with the original graph. Graph views are constructed by
instantiating a :class:`~graph_tool.GraphView` class, and passing a
graph object which is supposed to be filtered, together with the desired
filter parameters. For example, to create a directed view of an undirected graph
``g`` above, one could do:
.. doctest::
>>> ug = GraphView(g, directed=True)
>>> ug.is_directed()
True
Graph views also provide a direct and convenient approach to vertex/edge
filtering. Let us consider the facebook friendship graph we used before and the
betweeness centrality values:
.. testsetup:: gview
from graph_tool.all import *
.. doctest:: gview
>>> g = collection.ns["ego_social/facebook_combined"]
>>> vb, eb = betweenness(g)
Let us suppose we would like to see how the graph would look like if some of the
edges with higher betweeness values were removed. We can do this by a
:class:`~graph_tool.GraphView` object and passing the `efilt` paramter:
.. doctest:: gview
>>> u = GraphView(g, vfilt=eb.fa < 1e-6)
.. note::
:class: margin
:class:`~graph_tool.GraphView` objects behave *exactly* like regular
:class:`~graph_tool.Graph` objects. In fact,
:class:`~graph_tool.GraphView` is a subclass of
:class:`~graph_tool.Graph`. The only difference is that a
:class:`~graph_tool.GraphView` object shares its internal data with
its parent :class:`~graph_tool.Graph` class. Therefore, if the
original :class:`~graph_tool.Graph` object is modified, this
modification will be reflected immediately in the
:class:`~graph_tool.GraphView` object, and vice versa.
Since :class:`~graph_tool.GraphView` is a derived class from
:class:`~graph_tool.Graph`, and its instances are accepted as regular graphs
by every function of the library. Graph views are "first class citizens" in
``graph-tool``.
If we visualize the graph we can see it now has been broken up in many components:
.. doctest:: gview
>>> graph_draw(u, pos=g.vp._pos, output="facebook-filtered.pdf")
<...>
.. figure:: facebook-filtered.png
:align: center
:width: 600px
Facebook friendship network with edges with a betweeness centrality value
above :math:`10^{-6}` filtered out.
Note however that no copy of the original graph was done, and no edge has been
in fact removed. If we inspect the original graph ``g`` in the example above, it
will be intact.
In the example above, we passed a boolean array as the ``efilt``, but we could
have passed also a boolean property map, a function that takes an edge as
single parameter, and returns ``True`` if the edge should be kept and
``False`` otherwise. For instance, the above could be equivalently achieved as:
.. doctest:: gview
>>> u = GraphView(g, efilt=lambda e: eb[e] < 1e-6)
But note however that would be slower, since it would involve one function call
per edge in the graph.
Vertices can also be filtered in an entirerly analogous fashion using the
``vfilt`` paramter.
Composing graph views
"""""""""""""""""""""
Since graph views behave like regular graphs, one can just as easily create
graph views `of graph views`. This provides a convenient way of composing
filters. For instance, suppose we wanto to isolate the minimum spanning tree of all
vertices of agraph above which have a degree larger than four:
>>> g, pos = triangulation(random((500, 2)) * 4, type="delaunay")
>>> u = GraphView(g, vfilt=lambda v: v.out_degree() > 4)
>>> tree = min_spanning_tree(u)
>>> u = GraphView(u, efilt=tree)
The resulting graph view can be used and visualized as normal:
>>> bv, be = betweenness(u)
>>> be.a /= be.a.max() / 5
>>> graph_draw(u, pos=pos, vertex_fill_color=bv,
... edge_pen_width=be, output="mst-view.svg")
<...>
.. figure:: mst-view.*
:align: center
:figwidth: 400
A composed view, obtained as the minimum spanning tree of all vertices in the
graph which have a degree larger than four. The edge thickness indicates the
betweeness values, as well as the node colors.
In-place graph filtering
^^^^^^^^^^^^^^^^^^^^^^^^
It is possible also to filter graphs "in-place", i.e. without creating an
additional object. To achieve this, vertices or edges which are to be filtered
should be marked with a :class:`~graph_tool.PropertyMap` with value type
``bool``, and then set with :meth:`~graph_tool.Graph.set_vertex_filter` or
:meth:`~graph_tool.Graph.set_edge_filter` methods. By default, vertex or edges
with value "1" are `kept` in the graphs, and those with value "0" are filtered
out. This behaviour can be modified with the ``inverted`` parameter of the
respective functions. All manipulation functions and algorithms will work as if
the marked edges or vertices were removed from the graph, with minimum overhead.
For example, to reproduce the same example as before for the facebook graph we
could have done:
.. doctest:: gview
>>> g = collection.ns["ego_social/facebook_combined"]
>>> vb, eb = betweenness(g)
>>> mask = g.new_ep("bool", vals = eb.fa < 1e-5)
>>> g.set_edge_filter(mask)
The ``mask`` property map has a bool type, with value ``1`` if the edge belongs to
the tree, and ``0`` otherwise.
Everything should work transparently on the filtered graph, simply as if the
masked edges were removed.
The original graph can be recovered by setting the edge filter to ``None``.
.. testcode:: gview
g.set_edge_filter(None)
Everything works in analogous fashion with vertex filtering.
Additionally, the graph can also have its edges reversed with the
:meth:`~graph_tool.Graph.set_reversed` method. This is also an :math:`O(1)`
operation, which does not really modify the graph.
As mentioned previously, the directedness of the graph can also be changed
"on-the-fly" with the :meth:`~graph_tool.Graph.set_directed` method.
.. testcleanup:: gview
conv_png("facebook-filtered.pdf")
Advanced iteration
------------------
Faster iteration over vertices and edges without descriptors
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The mode of iteration considered :ref:`above ` is convenient, but
requires the creation of vertex and edge descriptor objects, which incurs a
performance overhead. A faster approach involves the use of the methods
:meth:`~graph_tool.Graph.iter_vertices`, :meth:`~graph_tool.Graph.iter_edges`,
:meth:`~graph_tool.Graph.iter_out_edges`,
:meth:`~graph_tool.Graph.iter_in_edges`,
:meth:`~graph_tool.Graph.iter_all_edges`,
:meth:`~graph_tool.Graph.iter_out_neighbors`,
:meth:`~graph_tool.Graph.iter_in_neighbors`,
:meth:`~graph_tool.Graph.iter_all_neighbors`, which return vertex indices and
pairs thereof, instead of descriptors objects, to specify vertex and edges,
respectively.
For example, for the graph:
.. testcode::
g = Graph([(0, 1), (2, 3), (2, 4)])
we have
.. testcode::
for v in g.iter_vertices():
print(v)
for e in g.iter_edges():
print(e)
which yields
.. testoutput::
0
1
2
3
4
[0, 1]
[2, 3]
[2, 4]
and likewise for the iteration over the neighborhood of a vertex:
.. testcode::
for v in g.iter_vertices():
for e in g.iter_out_edges(v):
print(e)
for w in g.iter_out_neighbors(v):
print(w)
.. testoutput::
:hide:
[0, 1]
1
[2, 3]
[2, 4]
3
4
Even faster, loopless iteration over vertices and edges using arrays
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
While more convenient, looping over the graph as described in the previous
sections are not quite the most efficient approaches to operate on graphs. This
is because the loops are performed in pure Python, thus undermining the
main feature of the library, which is the offloading of loops from Python to
C++. Following the :mod:`numpy` philosophy, :mod:`graph_tool` also provides an
array-based interface that avoids loops in Python. This is done with the
:meth:`~graph_tool.Graph.get_vertices`, :meth:`~graph_tool.Graph.get_edges`,
:meth:`~graph_tool.Graph.get_out_edges`, :meth:`~graph_tool.Graph.get_in_edges`,
:meth:`~graph_tool.Graph.get_all_edges`,
:meth:`~graph_tool.Graph.get_out_neighbors`,
:meth:`~graph_tool.Graph.get_in_neighbors`,
:meth:`~graph_tool.Graph.get_all_neighbors`,
:meth:`~graph_tool.Graph.get_out_degrees`,
:meth:`~graph_tool.Graph.get_in_degrees` and
:meth:`~graph_tool.Graph.get_total_degrees` methods, which return
:class:`numpy.ndarray` instances instead of iterators.
For example, using this interface we can get the out-degree of each node via:
.. testcode::
print(g.get_out_degrees(g.get_vertices()))
.. testoutput::
[1 0 2 0 0]
or the sum of the product of the in and out-degrees of the endpoints of
each edge with:
.. testcode::
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())
.. testoutput::
5