`NetworkX`

¶https://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.

Create an empty graph with no nodes and no edges.

In [20]:

```
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 [2]:

```
type(G)
```

Out[2]:

networkx.classes.graph.Graph

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,

In [21]:

```
G.add_node(1)
```

In [22]:

```
G.nodes
```

Out[22]:

NodeView((1,))

add a list of nodes,

In [23]:

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

In [24]:

```
nx.draw(G)
```

In [7]:

```
help(G.add_nodes_from)
```

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 [25]:

```
H = nx.path_graph(10)
```

In [26]:

```
nx.draw(H)
```

In [11]:

```
type(H)
```

Out[11]:

networkx.classes.graph.Graph

In [12]:

```
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 [9]:

```
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.

`G`

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

In [13]:

```
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 [14]:

```
G.add_edges_from(H.edges)
```

In [15]:

```
G.edges
```

Out[15]:

EdgeView([(1, 2), (1, 0), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9)])

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

In [16]:

```
G.clear()
```

In [17]:

```
len(G)
```

Out[17]:

0

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]:

8

In [13]:

```
G.number_of_edges()
```

Out[13]:

3

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]:

[1, 2, 3, 'spam', 's', 'p', 'a', 'm']

In [15]:

```
list(G.edges)
```

Out[15]:

[(1, 2), (1, 3), (3, 'm')]

In [16]:

```
list(G.adj[1]) # or list(G.neighbors(1))
```

Out[16]:

[2, 3]

In [17]:

```
G.degree[1] # the number of edges incident to 1
```

Out[17]:

2

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]:

(EdgeDataView([(2, 1), ('m', 3)]), DegreeView({2: 1, 3: 2}))

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]:

[1, 3, 'spam']

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]:

[(1, 2), (2, 1)]

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 addition to the views `Graph.edges()`

, and `Graph.adj()`

,
access to edges and neighbors is possible using subscript notation.

In [23]:

```
G[1] # same as G.adj[1]
```

Out[23]:

AtlasView({2: {}})

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))
```

(1, 2, 0.125) (2, 1, 0.125) (3, 4, 0.375) (4, 3, 0.375)

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))
```

(1, 2, 0.125) (3, 4, 0.375)

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 [18]:

```
G = nx.Graph(day="Friday")
G.graph
```

Out[18]:

{'day': 'Friday'}

In [19]:

```
type(_)
```

Out[19]:

dict

Or you can modify attributes later

In [29]:

```
G.graph['day'] = "Monday"
G.graph
```

Out[29]:

{'day': 'Monday'}

Add node attributes using `add_node()`

, `add_nodes_from()`

, or `G.nodes`

In [30]:

```
G.add_node(1, time='5pm')
G.add_nodes_from([3], time='2pm')
G.nodes[1]
```

Out[30]:

{'time': '5pm'}

In [31]:

```
G.nodes[1]['room'] = 714
G.nodes.data()
```

Out[31]:

NodeDataView({1: {'time': '5pm', 'room': 714}, 3: {'time': '2pm'}})

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.

Add/change edge attributes using `add_edge()`

, `add_edges_from()`

,
or subscript notation.

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]:

(0.5, 1.25)

In [34]:

```
list(DG.successors(1)), list(DG.neighbors(1))
```

Out[34]:

([2], [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 `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]:

{1: 1.25, 2: 1.75, 3: 0.5}

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]:

[1, 2, 3]

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 G`

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

In [3]:

```
petersen = nx.petersen_graph()
nx.draw(petersen)
```

In [4]:

```
tutte = nx.tutte_graph()
nx.draw(tutte)
```

In [5]:

```
maze = nx.sedgewick_maze_graph()
nx.draw(maze)
```

In [6]:

```
tet = nx.tetrahedral_graph()
nx.draw(tet)
```

In [7]:

```
K_5 = nx.complete_graph(5)
nx.draw(K_5)
```

In [8]:

```
K_3_5 = nx.complete_bipartite_graph(3, 5)
nx.draw(K_3_5)
```

In [9]:

```
barbell = nx.barbell_graph(10, 10)
nx.draw(barbell)
```

In [10]:

```
lollipop = nx.lollipop_graph(10, 20)
nx.draw(lollipop)
```

In [11]:

```
er = nx.erdos_renyi_graph(100, 0.15)
nx.draw(er)
```

In [12]:

```
ws = nx.watts_strogatz_graph(30, 3, 0.1)
nx.draw(ws)
```