..  -*- coding: utf-8 -*-

.. currentmodule:: networkx

Start here to begin working with NetworkX.


Creating a graph
----------------

Create an empty graph with no nodes and no edges.

>>> import networkx as nx
>>> G=nx.Graph()

By definition, a :class:`Graph` is a collection of nodes (vertices)
along with identified pairs of nodes (called edges, links, etc).
In NetworkX, nodes can be any hashable object e.g. a text string, an
image, an XML object, another Graph, a customized node object, etc.
(Note: Python's None object should not be used as a node as it
determines whether optional function arguments have been assigned 
in many functions.)

Nodes
-----

The graph G can be grown in several ways.
NetworkX includes many graph generator functions 
and facilities to read and write graphs in many formats.
To get started though we'll look at simple manipulations.
You can add one node at a time,

>>> G.add_node(1)

add a list of nodes,

>>> G.add_nodes_from([2,3])

or add any :term:`nbunch` of nodes.
An *nbunch* is any iterable container
of nodes that is not itself a node 
in the graph. (e.g. a list, set, graph, file, etc..)

>>> H=nx.path_graph(10)
>>> G.add_nodes_from(H)

Note that G now contains the nodes of H as nodes of G.
In contrast, you could use the graph H as a node in G. 

>>> G.add_node(H)

The graph G now contains H as a node.  This flexibility
is very powerful as it allows graphs of graphs, graphs of
files, graphs of functions and much more.  It is worth
thinking about how to structure your application so that
the nodes are useful entities.  Of course you can always
use a unique identifier in G and have a separate dictionary
keyed by identifier to the node information if you prefer.
(Note: You should not change the node object if the hash 
depends on its contents.)

Edges
-----

G can also be grown by adding one edge at a time,

>>> G.add_edge(1,2)
>>> e=(2,3)
>>> G.add_edge(*e) # unpack edge tuple*

by adding a list of edges, 

>>> G.add_edges_from([(1,2),(1,3)])

or by adding any :term:`ebunch` of edges.
An *ebunch* is any iterable container
of edge-tuples.  An edge-tuple can be a 2-tuple
of nodes or a 3-tuple with 2 nodes followed by 
an edge attribute dictionary, e.g. (2,3,{'weight':3.1415}).
Edge attributes are discussed further below

>>> G.add_edges_from(H.edges())

One can demolish the graph in a similar fashion; using 
:meth:`Graph.remove_node`,
:meth:`Graph.remove_nodes_from`, 
:meth:`Graph.remove_edge`
and 
:meth:`Graph.remove_edges_from`, e.g.

>>> G.remove_node(H)

There are no complaints when adding existing nodes or edges. For example,
after removing all nodes and edges,

>>> G.clear()

we add new nodes/edges and NetworkX quietly ignores any that are
already present.

>>> G.add_edges_from([(1,2),(1,3)])
>>> G.add_node(1)
>>> G.add_edge(1,2)
>>> G.add_node("spam")       # adds node "spam"
>>> G.add_nodes_from("spam") # adds 4 nodes: 's', 'p', 'a', 'm'

At this stage the graph G consists of 8 nodes and 2 edges, as can be seen by:

>>> G.number_of_nodes()
8
>>> G.number_of_edges()
2

We can examine them with

>>> G.nodes()
['a', 1, 2, 3, 'spam', 'm', 'p', 's']
>>> G.edges()
[(1, 2), (1, 3)]
>>> G.neighbors(1)
[2, 3]

Removing nodes or edges has similar syntax to adding:

>>> G.remove_nodes_from("spam")
>>> G.nodes()
[1, 2, 3, 'spam']
>>> G.remove_edge(1,3)

When creating a graph structure (by instantiating one of the graph
classes you can specify data in several formats.  

>>> H=nx.DiGraph(G)   # create a DiGraph using the connections from G
>>> H.edges()
[(1, 2), (2, 1)]
>>> edgelist=[(0,1),(1,2),(2,3)]
>>> H=nx.Graph(edgelist) 

What to use as nodes and edges
------------------------------
You might notice that nodes and edges are not specified as NetworkX
objects.  This leaves you free to use meaningful items as nodes and
edges. The most common choices are numbers or strings, but a node can
be any hashable object (except None), and an edge can be associated
with any object x using G.add_edge(n1,n2,object=x).

As an example, n1 and n2 could be protein objects from the RCSB Protein 
Data Bank, and x could refer to an XML record of publications detailing 
experimental observations of their interaction. 

We have found this power quite useful, but its abuse
can lead to unexpected surprises unless one is familiar with Python. 
If in doubt, consider using :func:`convert_node_labels_to_integers` to obtain
a more traditional graph with integer labels.


Accessing edges
---------------

In addition to the methods 
:meth:`Graph.nodes`, 
:meth:`Graph.edges`, and 
:meth:`Graph.neighbors`,
iterator versions (e.g. :meth:`Graph.edges_iter`) can save you from
creating large lists when you are just going to iterate 
through them anyway.

Fast direct access to the graph data structure is also possible
using subscript notation.

.. Warning::
   Do not change the returned dict--it is part of 
   the graph data structure and direct manipulation may leave the 
   graph in an inconsistent state.

>>> G[1]  # Warning: do not change the resulting dict
{2: {}}
>>> G[1][2]
{}

You can safely set the attributes of an edge using subscript notation
if the edge already exists.

>>> G.add_edge(1,3)
>>> G[1][3]['color']='blue'

Fast examination of all edges is achieved using adjacency iterators.
Note that for undirected graphs this actually looks at each edge twice.

>>> FG=nx.Graph()
>>> FG.add_weighted_edges_from([(1,2,0.125),(1,3,0.75),(2,4,1.2),(3,4,0.375)])
>>> for n,nbrs in FG.adjacency_iter():
...    for nbr,eattr in nbrs.items():
...        data=eattr['weight']
...        if data<0.5: print('(%d, %d, %.3f)' % (n,nbr,data))
(1, 2, 0.125)
(2, 1, 0.125)
(3, 4, 0.375)
(4, 3, 0.375)


Adding attributes to graphs, nodes, and edges
---------------------------------------------
Attributes such as weights, labels, colors, or whatever
Python object you like, can be attached to graphs, nodes, or edges.

Each graph, node, and edge can hold key/value attribute pairs
in an associated attribute dictionary (the keys must be hashable).
By default these are empty, but attributes can be added or changed using
add_edge, add_node or direct manipulation of the attribute 
dictionaries named G.graph, G.node and G.edge for a graph G.


Graph attributes
~~~~~~~~~~~~~~~~
Assign graph attributes when creating a new graph

>>> G = nx.Graph(day="Friday")
>>> G.graph
{'day': 'Friday'}

Or you can modify attributes later

>>> G.graph['day']='Monday'
>>> G.graph
{'day': 'Monday'}



Node attributes
~~~~~~~~~~~~~~~

Add node attributes using add_node(), add_nodes_from() or G.node

>>> G.add_node(1, time='5pm')
>>> G.add_nodes_from([3], time='2pm')
>>> G.node[1]
{'time': '5pm'}
>>> G.node[1]['room'] = 714
>>> G.nodes(data=True)
[(1, {'room': 714, 'time': '5pm'}), (3, {'time': '2pm'})]

Note that adding a node to G.node does not add it to the graph,
use G.add_node() to add new nodes.


Edge Attributes
~~~~~~~~~~~~~~~
Add edge attributes using add_edge(), add_edges_from(), subscript
notation, or G.edge.

>>> G.add_edge(1, 2, weight=4.7 )
>>> G.add_edges_from([(3,4),(4,5)], color='red')
>>> G.add_edges_from([(1,2,{'color':'blue'}), (2,3,{'weight':8})])
>>> G[1][2]['weight'] = 4.7
>>> G.edge[1][2]['weight'] = 4

The special attribute 'weight'
should be numeric and holds values used by algorithms requiring weighted edges.


Directed graphs
---------------

The DiGraph class provides additional methods specific to directed
edges, e.g. 
:meth:`DiGraph.out_edges`, 
:meth:`DiGraph.in_degree`, 
:meth:`DiGraph.predecessors`, 
:meth:`DiGraph.successors` etc.  
To allow algorithms to work with both classes easily, the directed 
versions of neighbors() and degree() are equivalent to successors() 
and the sum of in_degree() and out_degree() respectively even though 
that may feel inconsistent at times.

>>> DG=nx.DiGraph()
>>> DG.add_weighted_edges_from([(1,2,0.5), (3,1,0.75)])
>>> DG.out_degree(1,weight='weight')
0.5
>>> DG.degree(1,weight='weight')
1.25
>>> DG.successors(1)
[2]
>>> DG.neighbors(1)
[2]

Some algorithms work only for directed graphs and others are not well
defined for directed graphs.  Indeed the tendency to lump directed
and undirected graphs together is dangerous.  If you want to treat
a directed graph as undirected for some measurement you should probably
convert it using :meth:`Graph.to_undirected` or with

>>> H= nx.Graph(G) # convert H to undirected graph


Multigraphs
-----------

NetworkX provides classes for graphs which allow multiple edges
between any pair of nodes.  The :class:`MultiGraph` and
:class:`MultiDiGraph`
classes allow you to add the same edge twice, possibly with different
edge data.  This can be powerful for some applications, but many
algorithms are not well defined on such graphs.  Shortest path is one
example.  Where results are well defined,
e.g. :meth:`MultiGraph.degree` we provide the function.  Otherwise you
should convert to a standard graph in a way that makes the measurement
well defined.

>>> MG=nx.MultiGraph()
>>> MG.add_weighted_edges_from([(1,2,.5), (1,2,.75), (2,3,.5)])
>>> MG.degree(weight='weight')
{1: 1.25, 2: 1.75, 3: 0.5}
>>> GG=nx.Graph()
>>> for n,nbrs in MG.adjacency_iter():
...    for nbr,edict in nbrs.items():
...        minvalue=min([d['weight'] for d in edict.values()])
...        GG.add_edge(n,nbr, weight = minvalue)
...
>>> nx.shortest_path(GG,1,3)
[1, 2, 3]


Graph generators and graph operations
-------------------------------------

In addition to constructing graphs node-by-node or edge-by-edge, they
can also be generated by

1. Applying classic graph operations, such as::

    subgraph(G, nbunch)      - induce subgraph of G on nodes in nbunch
    union(G1,G2)             - graph union
    disjoint_union(G1,G2)    - graph union assuming all nodes are different
    cartesian_product(G1,G2) - return Cartesian product graph
    compose(G1,G2)           - combine graphs identifying nodes common to both
    complement(G)            - graph complement 
    create_empty_copy(G)     - return an empty copy of the same graph class
    convert_to_undirected(G) - return an undirected representation of G
    convert_to_directed(G)   - return a directed representation of G


2. Using a call to one of the classic small graphs, e.g.

>>> petersen=nx.petersen_graph()
>>> tutte=nx.tutte_graph()
>>> maze=nx.sedgewick_maze_graph()
>>> tet=nx.tetrahedral_graph()

3. Using a (constructive) generator for a classic graph, e.g.

>>> K_5=nx.complete_graph(5)
>>> K_3_5=nx.complete_bipartite_graph(3,5)
>>> barbell=nx.barbell_graph(10,10)
>>> lollipop=nx.lollipop_graph(10,20)
 
4. Using a stochastic graph generator, e.g.

>>> er=nx.erdos_renyi_graph(100,0.15)
>>> ws=nx.watts_strogatz_graph(30,3,0.1)
>>> ba=nx.barabasi_albert_graph(100,5)
>>> red=nx.random_lobster(100,0.9,0.9)

5. Reading a graph stored in a file using common graph formats, 
   such as edge lists, adjacency lists, GML, GraphML, pickle, LEDA and others.

>>> nx.write_gml(red,"path.to.file")
>>> mygraph=nx.read_gml("path.to.file")

Details on graph formats: :doc:`/reference/readwrite` 

Details on graph generator functions: :doc:`/reference/generators` 


Analyzing graphs 
----------------

The structure of G can be analyzed using various graph-theoretic 
functions such as:

>>> G=nx.Graph()
>>> G.add_edges_from([(1,2),(1,3)])
>>> G.add_node("spam")       # adds node "spam"

>>> nx.connected_components(G)
[[1, 2, 3], ['spam']]

>>> sorted(nx.degree(G).values())
[0, 1, 1, 2]

>>> nx.clustering(G)
{1: 0.0, 2: 0.0, 3: 0.0, 'spam': 0.0}

Functions that return node properties return dictionaries keyed by node label.

>>> nx.degree(G)
{1: 2, 2: 1, 3: 1, 'spam': 0}

For values of specific nodes, you can provide a single node or an nbunch 
of nodes as argument.  If a single node is specified, then a single value 
is returned.  If an nbunch is specified, then the function will 
return a dictionary.
 
>>> nx.degree(G,1)
2
>>> G.degree(1)
2
>>> G.degree([1,2])
{1: 2, 2: 1}
>>> sorted(G.degree([1,2]).values())
[1, 2]
>>> sorted(G.degree().values())
[0, 1, 1, 2]


Details on graph algorithms supported: :doc:`/reference/algorithms`


Drawing graphs
--------------

NetworkX is not primarily a graph drawing package but 
basic drawing with Matplotlib as well as an interface to use the
open source Graphviz software package are included.  
These are part of the networkx.drawing package
and will be imported if possible. 
See :doc:`/reference/drawing` for details.

Note that the drawing package in NetworkX is not yet compatible with
Python versions 3.0 and above.

First import Matplotlib's plot interface (pylab works too)

>>> import matplotlib.pyplot as plt

You may find it useful to interactively test code using "ipython -pylab", 
which combines the power of ipython and matplotlib and provides a convenient
interactive mode.

To test if the import of networkx.drawing was successful 
draw G using one of

>>> nx.draw(G)
>>> nx.draw_random(G)
>>> nx.draw_circular(G)
>>> nx.draw_spectral(G)

when drawing to an interactive display. 
Note that you may need to issue a Matplotlib 

>>> plt.show() 

command if you are not using matplotlib in interactive mode: (See 
`Matplotlib FAQ <http://matplotlib.org/faq/installing_faq.html#matplotlib-compiled-fine-but-nothing-shows-up-when-i-use-it>`_
)

To save drawings to a file, use, for example

>>> nx.draw(G)
>>> plt.savefig("path.png")

writes to the file "path.png" in the local directory. If Graphviz
and PyGraphviz, or pydot, are available on your system, you can also use

>>> nx.draw_graphviz(G)
>>> nx.write_dot(G,'file.dot')

Details on drawing graphs: :doc:`/reference/drawing`

