#
# ## Tutorial
#
# This guide can help you start 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 `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.
#
# # 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 iterable container of nodes. You can also add nodes along with node
# attributes if your container yields 2-tuples (node, node_attribute_dict).
# Node attributes are discussed further below.
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.
#
# # 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 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)
# 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'
G.add_edge(3, 'm')
# At this stage the graph `G` consists of 8 nodes and 3 edges, as can be seen by:
G.number_of_nodes()
G.number_of_edges()
# We can examine the nodes and edges. Four basic graph properties facilitate
# reporting: `G.nodes`, `G.edges`, `G.adj` and `G.degree`. These
# are set-like views of the nodes, edges, neighbors (adjacencies), and degrees
# of nodes in a graph. They offer a continually updated read-only view into
# the graph structure. They are also dict-like in that you can look up node
# and edge data attributes via the views and iterate with data attributes
# using methods `.items()`, `.data('span')`.
# If you want a specific container type instead of a view, you can specify one.
# Here we use lists, though sets, dicts, tuples and other containers may be
# better in other contexts.
list(G.nodes)
list(G.edges)
list(G.adj[1]) # or list(G.neighbors(1))
G.degree[1] # the number of edges incident to 1
# One can specify to report the edges and degree from a subset of all nodes
# using an *nbunch*. An *nbunch* is any of: None (meaning all nodes), a node,
# or an iterable container of nodes that is not itself a node in the graph.
G.edges([2, 'm'])
G.degree([2, 3])
# One can remove nodes and edges from the graph in a similar fashion to adding.
# Use methods
# `Graph.remove_node()`,
# `Graph.remove_nodes_from()`,
# `Graph.remove_edge()`
# and
# `Graph.remove_edges_from()`, e.g.
G.remove_node(2)
G.remove_nodes_from("spam")
list(G.nodes)
G.remove_edge(1, 3)
# When creating a graph structure by instantiating one of the graph
# classes you can specify data in several formats.
G.add_edge(1, 2)
H = nx.DiGraph(G) # create a DiGraph using the connections from G
list(H.edges())
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 `convert_node_labels_to_integers()` to obtain
# a more traditional graph with integer labels.
#
# # Accessing edges and neighbors
#
# In addition to the views `Graph.edges()`, and `Graph.adj()`,
# access to edges and neighbors is possible using subscript notation.
G[1] # same as G.adj[1]
G[1][2]
G.edges[1, 2]
# You can get/set the attributes of an edge using subscript notation
# if the edge already exists.
G.add_edge(1, 3)
G[1][3]['color'] = "blue"
G.edges[1, 2]['color'] = "red"
# Fast examination of all (node, adjacency) pairs is achieved using
# `G.adjacency()`, or `G.adj.items()`.
# Note that for undirected graphs, adjacency iteration sees 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.adj.items():
for nbr, eattr in nbrs.items():
wt = eattr['weight']
if wt < 0.5: print('(%d, %d, %.3f)' % (n, nbr, wt))
# Convenient access to all edges is achieved with the edges property.
for (u, v, wt) in FG.edges.data('weight'):
if wt < 0.5: print('(%d, %d, %.3f)' % (u, v, wt))
# # 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.nodes`, and
# `G.edges` for a graph `G`.
#
# ## Graph attributes
#
# Assign graph attributes when creating a new graph
G = nx.Graph(day="Friday")
G.graph
# Or you can modify attributes later
G.graph['day'] = "Monday"
G.graph
# # Node attributes
#
# Add node attributes using `add_node()`, `add_nodes_from()`, or `G.nodes`
G.add_node(1, time='5pm')
G.add_nodes_from([3], time='2pm')
G.nodes[1]
G.nodes[1]['room'] = 714
G.nodes.data()
# Note that adding a node to `G.nodes` does not add it to the graph, use
# `G.add_node()` to add new nodes. Similarly for edges.
#
# # Edge Attributes
#
# Add/change edge attributes using `add_edge()`, `add_edges_from()`,
# or subscript notation.
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.edges[3, 4]['weight'] = 4.2
# The special attribute `weight` should be numeric as it is used by
# algorithms requiring weighted edges.
#
# Directed graphs
#
# The `DiGraph` class provides additional properties specific to
# directed edges, e.g.,
# `DiGraph.out_edges()`, `DiGraph.in_degree()`,
# `DiGraph.predecessors()`, `DiGraph.successors()` etc.
# To allow algorithms to work with both classes easily, the directed versions of
# `neighbors()` is equivalent to `successors()` while `degree` reports
# the sum of `in_degree` and `out_degree` 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')
DG.degree(1, weight='weight')
list(DG.successors(1))
list(DG.neighbors(1))
# 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 `Graph.to_undirected()` or with
H = nx.Graph(G) # convert G to undirected graph
# # Multigraphs
#
# NetworkX provides classes for graphs which allow multiple edges
# between any pair of nodes. The `MultiGraph` and
# `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.
# Where results are well defined,
# e.g., `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, 0.5), (1, 2, 0.75), (2, 3, 0.5)])
dict(MG.degree(weight='weight'))
GG = nx.Graph()
for n, nbrs in MG.adjacency():
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)
# # 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) - induced subgraph view 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
# to_undirected(G) - return an undirected representation of G
# to_directed(G) - return a directed representation of G
# ```
#
# 1. 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()
# 1. 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)
# 1. 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)
# 1. 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")
# For details on graph formats see Reading and writing graphs
# and for graph generator functions see Graph 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"
list(nx.connected_components(G))
sorted(d for n, d in G.degree())
nx.clustering(G)
# Some functions with large output iterate over (node, value) 2-tuples.
# These are easily stored in a [dict](https://docs.python.org/2/library/stdtypes.html#dict) structure if you desire.
sp = dict(nx.all_pairs_shortest_path(G))
sp[3]
# See Algorithms for details on graph algorithms
# supported.
#
# # 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` module and will
# be imported if possible.
#
# 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
G = nx.petersen_graph()
plt.subplot(121)
nx.draw(G, with_labels=True, font_weight='bold')
plt.subplot(122)
nx.draw_shell(G, nlist=[range(5, 10), range(5)], with_labels=True, font_weight='bold')
# 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)
# ).
options = {
'node_color': 'black',
'node_size': 100,
'width': 3,
}
plt.subplot(221)
nx.draw_random(G, **options)
plt.subplot(222)
nx.draw_circular(G, **options)
plt.subplot(223)
nx.draw_spectral(G, **options)
plt.subplot(224)
nx.draw_shell(G, nlist=[range(5,10), range(5)], **options)
# You can find additional options via `draw_networkx()` and
# layouts via `layout`.
# You can use multiple shells with `draw_shell()`.
G = nx.dodecahedral_graph()
shells = [[2, 3, 4, 5, 6], [8, 1, 0, 19, 18, 17, 16, 15, 14, 7], [9, 10, 11, 12, 13]]
nx.draw_shell(G, nlist=shells, **options)
# 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_agraph.graphviz_layout(G)` or `nx_pydot.graphviz_layout(G)` to get the
# node positions, or write the graph in dot format for further processing.
from networkx.drawing.nx_pydot import write_dot
pos = nx.nx_agraph.graphviz_layout(G)
nx.draw(G, pos=pos)
write_dot(G, 'file.dot')
# See Drawing for additional details.