In [1]:
__AUTHORS__ = {'am': ("Andrea Marino",
"andrea.marino@unifi.it",),
'mn': ("Massimo Nocentini",
"massimo.nocentini@unifi.it",
"https://github.com/massimo-nocentini/",)}
__KEYWORDS__ = ['Python', 'Jupyter', 'notebooks', 'keynote', 'NetworkX', 'graphs']
NetworkXhttps://github.com/networkx/networkx
Aric A. Hagberg, Daniel A. Schult and Pieter J. Swart, “Exploring network structure, dynamics, and function using NetworkX”, in Proceedings of the 7th Python in Science Conference (SciPy2008), Gäel Varoquaux, Travis Vaught, and Jarrod Millman (Eds), (Pasadena, CA USA), pp. 11–15, Aug 2008 (pdf).
This content is originally downloaded from https://networkx.github.io/documentation/stable/tutorial.html and adapted to be shown as a presentation; moreover, we mix in additional resources such as examples (citing them and the original authors) in the last section.
In [2]:
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.
An object is hashable if it has a hash value which never changes during its lifetime (it needs a
__hash__()method), and can be compared to other objects (it needs an__eq__()method). Hashable objects which compare equal must have the same hash value.
In [3]:
G.add_node(1)
add a list of nodes,
In [4]:
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.
In [5]:
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.
In [6]:
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.
In [7]:
G.add_edge(1, 2)
e = (2, 3)
G.add_edge(*e) # unpack edge tuple*
by adding a list of edges,
In [8]:
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
In [9]:
G.add_edges_from(H.edges)
There are no complaints when adding existing nodes or edges. For example, after removing all nodes and edges,
In [10]:
G.clear()
we add new nodes/edges and NetworkX quietly ignores any that are already present.
In [11]:
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:
In [12]:
G.number_of_nodes()
Out[12]:
In [13]:
G.number_of_edges()
Out[13]:
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.
In [14]:
list(G.nodes)
Out[14]:
In [15]:
list(G.edges)
Out[15]:
In [16]:
list(G.adj[1]) # or list(G.neighbors(1))
Out[16]:
In [17]:
G.degree[1] # the number of edges incident to 1
Out[17]:
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.
In [18]:
G.edges([2, 'm']), G.degree([2, 3])
Out[18]:
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.
In [19]:
G.remove_node(2)
G.remove_nodes_from("spam")
list(G.nodes)
Out[19]:
In [20]:
G.remove_edge(1, 3)
When creating a graph structure by instantiating one of the graph classes you can specify data in several formats.
In [21]:
G.add_edge(1, 2)
H = nx.DiGraph(G) # create a DiGraph using the connections from G
list(H.edges())
Out[21]:
In [22]:
edgelist = [(0, 1), (1, 2), (2, 3)]
H = nx.Graph(edgelist)
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.
In [23]:
G[1] # same as G.adj[1]
Out[23]:
In [24]:
G[1][2], G.edges[1, 2]
Out[24]:
You can get/set the attributes of an edge using subscript notation if the edge already exists.
In [25]:
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.
In [26]:
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.
In [27]:
for (u, v, wt) in FG.edges.data('weight'):
if wt < 0.5: print('(%d, %d, %.3f)' % (u, v, wt))
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.
Assign graph attributes when creating a new graph
In [28]:
G = nx.Graph(day="Friday")
G.graph
Out[28]:
Or you can modify attributes later
In [29]:
G.graph['day'] = "Monday"
G.graph
Out[29]:
In [30]:
G.add_node(1, time='5pm')
G.add_nodes_from([3], time='2pm')
G.nodes[1]
Out[30]:
In [31]:
G.nodes[1]['room'] = 714
G.nodes.data()
Out[31]:
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.
In [32]:
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.
In [33]:
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')
Out[33]:
In [34]:
list(DG.successors(1)), list(DG.neighbors(1))
Out[34]:
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
In [35]:
H = nx.Graph(G) # convert G to undirected graph
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.
In [36]:
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'))
Out[36]:
In [37]:
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)
Out[37]:
In addition to constructing graphs node-by-node or edge-by-edge, they can also be generated by
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 GUsing a call to one of the classic small graphs, e.g.,
In [38]:
petersen = nx.petersen_graph()
nx.draw(petersen)
In [39]:
tutte = nx.tutte_graph()
nx.draw(tutte)
In [40]:
maze = nx.sedgewick_maze_graph()
nx.draw(maze)
In [41]:
tet = nx.tetrahedral_graph()
nx.draw(tet)
In [42]:
K_5 = nx.complete_graph(5)
nx.draw(K_5)
In [43]:
K_3_5 = nx.complete_bipartite_graph(3, 5)
nx.draw(K_3_5)
In [44]:
barbell = nx.barbell_graph(10, 10)
nx.draw(barbell)
In [45]:
lollipop = nx.lollipop_graph(10, 20)
nx.draw(lollipop)
In [46]:
er = nx.erdos_renyi_graph(100, 0.15)
nx.draw(er)
In [47]:
ws = nx.watts_strogatz_graph(30, 3, 0.1)
nx.draw(ws)
In [48]:
ba = nx.barabasi_albert_graph(100, 5)
nx.draw(ba)
In [49]:
red = nx.random_lobster(100, 0.9, 0.9)
nx.draw(red)
In [50]:
nx.write_gml(red, "path.to.file")
mygraph = nx.read_gml("path.to.file")
nx.draw(mygraph)
In [51]:
G = nx.Graph()
G.add_edges_from([(1, 2), (1, 3)])
G.add_node("spam") # adds node "spam"
list(nx.connected_components(G))
Out[51]:
In [52]:
sorted(d for n, d in G.degree())
Out[52]:
In [53]:
nx.clustering(G)
Out[53]:
Some functions with large output iterate over (node, value) 2-tuples. These are easily stored in a dict structure if you desire.
In [54]:
sp = dict(nx.all_pairs_shortest_path(G))
sp[3]
Out[54]:
See Algorithms for details on graph algorithms supported.
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)
In [55]:
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
In [56]:
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
In [57]:
plt.show()
command if you are not using matplotlib in interactive mode (see Matplotlib FAQ ).
In [58]:
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().
In [59]:
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
In [60]:
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.
In [61]:
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.
A complete gallery of examples can be found at https://networkx.github.io/documentation/stable/auto_examples/index.html
In [75]:
# Author: Aric Hagberg (hagberg@lanl.gov)
G = nx.grid_2d_graph(5, 5) # 5x5 grid
# print the adjacency list
#for line in nx.generate_adjlist(G):
# print(line)
# write edgelist to grid.edgelist
nx.write_edgelist(G, path="grid.edgelist", delimiter=":")
# read edgelist from grid.edgelist
H = nx.read_edgelist(path="grid.edgelist", delimiter=":")
nx.draw(H)
plt.show()
In [63]:
G = nx.lollipop_graph(4, 6)
pathlengths = []
print("source vertex {target:length, }")
for v in G.nodes():
spl = dict(nx.single_source_shortest_path_length(G, v))
print('{} {} '.format(v, spl))
for p in spl:
pathlengths.append(spl[p])
print('')
print("average shortest path length %s" %
(sum(pathlengths) / len(pathlengths)))
In [64]:
# histogram of path lengths
dist = {}
for p in pathlengths:
if p in dist:
dist[p] += 1
else:
dist[p] = 1
print('')
print("length #paths")
verts = dist.keys()
for d in sorted(verts):
print('%s %d' % (d, dist[d]))
In [65]:
print("radius: %d" % nx.radius(G))
print("diameter: %d" % nx.diameter(G))
print("eccentricity: %s" % nx.eccentricity(G))
print("center: %s" % nx.center(G))
print("periphery: %s" % nx.periphery(G))
print("density: %s" % nx.density(G))
In [66]:
nx.draw(G, with_labels=True)
plt.show()
In [67]:
# Author: Aric Hagberg (hagberg@lanl.gov)
G = nx.cycle_graph(24)
pos = nx.spring_layout(G, iterations=200)
nx.draw(G, pos, node_color=range(24),
node_size=800, cmap=plt.cm.Blues)
plt.show()
In [68]:
# Author: Aric Hagberg (hagberg@lanl.gov)
G = nx.star_graph(20)
pos = nx.spring_layout(G)
colors = range(20)
nx.draw(G, pos, node_color='#A0CBE2', edge_color=colors,
width=4, edge_cmap=plt.cm.Blues, with_labels=False)
plt.show()
In [69]:
options = {
'node_color': 'C0',
'node_size': 100,
}
G = nx.grid_2d_graph(6, 6)
plt.subplot(332)
nx.draw_spectral(G, **options)
G.remove_edge((2, 2), (2, 3))
plt.subplot(334)
nx.draw_spectral(G, **options)
G.remove_edge((3, 2), (3, 3))
plt.subplot(335)
nx.draw_spectral(G, **options)
In [70]:
G.remove_edge((2, 2), (3, 2))
plt.subplot(336)
nx.draw_spectral(G, **options)
G.remove_edge((2, 3), (3, 3))
plt.subplot(337)
nx.draw_spectral(G, **options)
G.remove_edge((1, 2), (1, 3))
plt.subplot(338)
nx.draw_spectral(G, **options)
G.remove_edge((4, 2), (4, 3))
plt.subplot(339)
nx.draw_spectral(G, **options)
In [71]:
# Author: Rodrigo Dorantes-Gilardi (rodgdor@gmail.com)
import matplotlib as mpl
import matplotlib.pyplot as plt
import networkx as nx
G = nx.generators.directed.random_k_out_graph(10, 3, 0.5)
pos = nx.layout.spring_layout(G)
node_sizes = [3 + 10 * i for i in range(len(G))]
M = G.number_of_edges()
edge_colors = range(2, M + 2)
edge_alphas = [(5 + i) / (M + 4) for i in range(M)]
In [72]:
nodes = nx.draw_networkx_nodes(G, pos, node_size=node_sizes, node_color='blue')
edges = nx.draw_networkx_edges(G, pos, node_size=node_sizes, arrowstyle='->',
arrowsize=10, edge_color=edge_colors,
edge_cmap=plt.cm.Blues, width=2)
# set alpha value for each edge
for i in range(M):
edges[i].set_alpha(edge_alphas[i])
pc = mpl.collections.PatchCollection(edges, cmap=plt.cm.Blues)
pc.set_array(edge_colors)
plt.colorbar(pc)
ax = plt.gca()
ax.set_axis_off()
plt.show()
In [73]:
# Authors: Brendt Wohlberg, Aric Hagberg (hagberg@lanl.gov)
import gzip
import re
import sys
import matplotlib.pyplot as plt
from networkx import nx
def roget_graph():
""" Return the thesaurus graph from the roget.dat example in
the Stanford Graph Base.
"""
# open file roget_dat.txt.gz (or roget_dat.txt)
fh = gzip.open('roget_dat.txt.gz', 'r')
G = nx.DiGraph()
for line in fh.readlines():
line = line.decode()
if line.startswith("*"): # skip comments
continue
if line.startswith(" "): # this is a continuation line, append
line = oldline + line
if line.endswith("\\\n"): # continuation line, buffer, goto next
oldline = line.strip("\\\n")
continue
(headname, tails) = line.split(":")
# head
numfind = re.compile("^\d+") # re to find the number of this word
head = numfind.findall(headname)[0] # get the number
G.add_node(head)
for tail in tails.split():
if head == tail:
print("skipping self loop", head, tail, file=sys.stderr)
G.add_edge(head, tail)
return G
In [74]:
G = roget_graph()
print("Loaded roget_dat.txt containing 1022 categories.")
print("digraph has %d nodes with %d edges"
% (nx.number_of_nodes(G), nx.number_of_edges(G)))
UG = G.to_undirected()
print(nx.number_connected_components(UG), "connected components")
options = {
'node_color': 'black',
'node_size': 1,
'line_color': 'grey',
'linewidths': 0,
'width': 0.1,
}
nx.draw_circular(UG, **options)
plt.show()