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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Working with Graphs using Networkx Intro
When creating a graph object, it can either be empty (default) or you can pass data as an argument. The data can take multiple forms
Step1:  Notice that the edge list is empty, since we haven't added any edges yet. Also, because the number of edges in a graph can become very large, there is an iterator method for returning edges
Step2:  If we had a script that needs to add a single edge from a tuple, we would use * preceeding the tuple or it's assigned variable in the add_edge method
Step3:  We can also add nodes and edges using objects called nbunch and ebunch. These objects are any iterables or generators of nodes or edge tuples. We will do this below using a couple different methods.
Step4:  We can also remove nodes or edges using similar methods, just replacing 'add' with 'remove'
Step5:  Notice that removing nodes automatically removed the related edges for us. One last basic inspection method is to get a list of neighbors (adjacent nodes) for a specific node in a graph.
Step6:  While we have been using numbers to represent nodes, we can use any hashable object as a node. For example, this means that lists, sets and arrays can't be nodes, but frozensets can
Step7:  Edge properties
We can add weights or other properties to edges in a graph in different ways. The first is to add properties at creation time by passing triples instead of doubles for each edge. The third value will be the edge property.
Step8:  Subscript notation for accessing edges
We can use subscript notiation on a graph object to easily get edge data. Access edge data for a node by entering that node as the subscript. This will return a dict with connected nodes as keys, and their respective edge weights as values.
Step9:  We can also modify specific edge attributes
Step10:  And we can add other attributes
Step11:  1. Create a complete graph with 7 nodes and verify that it is complete by looking at the edges. Do this manually and using a built-in method.
Remember, a complete graph is an undirected graph that has every pair of nodes connected by a unique edge. In other words, every node is adjacent to every other.
Step12:  2. Create a function that will draw a given graph that has a layout type parameter and labels the nodes. Now draw the graph created in the last problem using circular layout.
Step13:  3. Create a graph with 10 nodes and 3 components. Draw this graph.
Recall that a component is a connected subgraph.
Step14:  4. Create a simple connected digraph with 4 nodes and a diameter of 2.
Step15:  5. Create another 4 node digraph with weighted edges. Draw this graph with node and edge weight labels.
Step16:  6. Create the adjacnency matrix from the edge data in edges_1.pkl
Step17:  7. Using networkx built-in functions, create the distance matrix for the same graph from the previous problem
Step18:  8. Identify and remove a cutpoint from this graph and re-draw it
Step19:  9. Use edges_2 to create a graph. List any subgraphs that are maximal cliques
Step20:  10. Determine the Degree, Closeness, and Betweenness measures of centrality for this network
Step21:  11. Based on the measures above, which actors have the greatest control over the flow of information? Why do some actors have betweenness measures of zero?
When considering control over flow of information, we look at the betweenness measure. In this case, actors 0, 1, and 2 have the greatest control over information flow. The actors with betweenness measures of zero have no geodesics through them connecting other pairs of nodes. For example, there is a path from 0 to 4 that goes through 9, but that has a length of 2 and 0 connects to 4 directly.
12. Create a copy of the last network and do the following
Step22:  13. Create a directed graph from edges_3.pkl and do the following
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Python Code:
# isntantiate a graph object
G = nx.Graph()
# add a single node
G.add_node(1)
# add multiple nodes from a list
G.add_nodes_from([2,3,5])
# return lists of nodes and edges in the graph
G.nodes(), G.edges()
Explanation: Working with Graphs using Networkx Intro
When creating a graph object, it can either be empty (default) or you can pass data as an argument. The data can take multiple forms:
an edge list
a numpy matrix or 2D ndarray
a Networkx graph object
a scipy sparse matrix
a PyGraphviz graph
Let's start by creating an empty graph, and then add nodes.
End of explanation
# add a single edge between 3 and 5
G.add_edge(3,5)
# add multiple edges using list of tuples
edge_list = [(1,2),(2,3),(2,5)]
G.add_edges_from(edge_list)
G.edges()
Explanation: Notice that the edge list is empty, since we haven't added any edges yet. Also, because the number of edges in a graph can become very large, there is an iterator method for returning edges: edges_iter().
End of explanation
# the asterisk indicates that the values should be extracted
G.add_edge(*(1,3))
G.edges()
Explanation: If we had a script that needs to add a single edge from a tuple, we would use * preceeding the tuple or it's assigned variable in the add_edge method:
End of explanation
# generate a graph of linearly connected nodes
# this is a graph of a single path with 5 nodes and 4 edges
H = nx.path_graph(5)
# a look at the nodes and edges produced
H.nodes(), H.edges()
# Create a graph using nbunch and ebunch from the graph H
G = nx.Graph()
G.add_nodes_from(H)
# we have to specify edges
G.add_edges_from(H.edges())
G.nodes(), G.edges()
# now add edges to a graph using an iterator instead of an iterable list
# this is another example of ebunch, and node iterators work too
G = nx.Graph()
G.add_nodes_from([1,2,3])
# create edge generator connecting all possible node pairs
from itertools import combinations
edge_generator = combinations([1,2,3], 2)
# to show this is a generator and not a list
print('not a list: ', edge_generator)
# now lets add the edges using the iterator
G.add_edges_from(edge_generator)
G.edges()
Explanation: We can also add nodes and edges using objects called nbunch and ebunch. These objects are any iterables or generators of nodes or edge tuples. We will do this below using a couple different methods.
End of explanation
H.nodes(), H.edges()
H.remove_nodes_from([0,4])
H.nodes(), H.edges()
Explanation: We can also remove nodes or edges using similar methods, just replacing 'add' with 'remove':
End of explanation
H = nx.path_graph(7)
# get the neighbors for node 5
H.neighbors(5)
Explanation: Notice that removing nodes automatically removed the related edges for us. One last basic inspection method is to get a list of neighbors (adjacent nodes) for a specific node in a graph.
End of explanation
G = nx.Graph()
# G.add_node([0,1]) <-- raises error
# G.add_node({0,1}) <-- raises error
G.add_node(frozenset([0,1]))  # this works
G.nodes()
Explanation: While we have been using numbers to represent nodes, we can use any hashable object as a node. For example, this means that lists, sets and arrays can't be nodes, but frozensets can:
End of explanation
G = nx.Graph()
G.add_nodes_from([1,2,3])
G.add_weighted_edges_from([(1,2,3.14), (2,3,6.5)])
# calling edges() alone will not return weights
print(G.edges(), '\n')
# we need to use the data parameter to get triples
print(G.edges(data='weight'), '\n')
# we can also get data for individual edges
print(G.get_edge_data(1,2))
Explanation: Edge properties
We can add weights or other properties to edges in a graph in different ways. The first is to add properties at creation time by passing triples instead of doubles for each edge. The third value will be the edge property.
End of explanation
# get edge data for node 2
print(G[2], '\n')
# subscript further to get only the weight for edge between 2 and 3
print(G[2][3])
Explanation: Subscript notation for accessing edges
We can use subscript notiation on a graph object to easily get edge data. Access edge data for a node by entering that node as the subscript. This will return a dict with connected nodes as keys, and their respective edge weights as values.
End of explanation
G[2][3]['weight'] = 17
G[2][3]
Explanation: We can also modify specific edge attributes:
End of explanation
G[2][3]['attr'] = 'value'
G[2][3]
Explanation: And we can add other attributes
End of explanation
# manually
from itertools import combinations
complete_edges = combinations(range(7), 2)
G_complete = nx.Graph(complete_edges)
G_complete.edges()
# built-in method
G_complete = nx.complete_graph(7)
G_complete.edges()
Explanation: 1. Create a complete graph with 7 nodes and verify that it is complete by looking at the edges. Do this manually and using a built-in method.
Remember, a complete graph is an undirected graph that has every pair of nodes connected by a unique edge. In other words, every node is adjacent to every other.
End of explanation
# function to draw and label nodes in a graph
def draw(G, layout):
    import warnings
    import matplotlib.cbook
    warnings.filterwarnings("ignore",category=matplotlib.cbook.mplDeprecation)
    warnings.filterwarnings("ignore",category=UserWarning)
    
    nx.draw(G, pos=layout(G))
    nx.draw_networkx_labels(G, pos=layout(G));
draw(G_complete, nx.circular_layout)
Explanation: 2. Create a function that will draw a given graph that has a layout type parameter and labels the nodes. Now draw the graph created in the last problem using circular layout.
End of explanation
from networkx.drawing.nx_agraph import graphviz_layout
edges_1 = [(0,1), (0,2)]
edges_2 = [(3,4), (3,5), (4,5), (4,6)]
edges_3 = [(7,8), (7,9)]
G = nx.Graph(edges_1 + edges_2 + edges_3)
draw(G, graphviz_layout)
Explanation: 3. Create a graph with 10 nodes and 3 components. Draw this graph.
Recall that a component is a connected subgraph.
End of explanation
# create in and out edge lists
out_edges = [(0,1), (0,2), (1,2), (2,3)]
# create the empty digraph
G = nx.DiGraph(out_edges)
draw(G, graphviz_layout)
Explanation: 4. Create a simple connected digraph with 4 nodes and a diameter of 2.
End of explanation
out_edges = [(0,1,0.5), (0,2,0.5), (1,2,1), (2,3,0.7)]
G = nx.DiGraph()
G.add_weighted_edges_from(out_edges)
draw(G, graphviz_layout)
labels = nx.get_edge_attributes(G, 'weight')
nx.draw_networkx_edge_labels(G, pos=graphviz_layout(G), edge_labels=labels);
Explanation: 5. Create another 4 node digraph with weighted edges. Draw this graph with node and edge weight labels.
End of explanation
import pickle
with open('../edges_1.pkl', 'rb') as f:
    edges = pickle.load(f)
G = nx.Graph(edges)
# lets see what it looks like
draw(G, graphviz_layout)
adj_matrix = nx.to_numpy_matrix(G)
DF(adj_matrix)
Explanation: 6. Create the adjacnency matrix from the edge data in edges_1.pkl
End of explanation
geodesics = nx.all_pairs_shortest_path_length(G)
# this gave us a dict of shortest path lengths between all connected pairs
geodesics
# we can easily convert this to a matrix using pandas
DF(geodesics)
Explanation: 7. Using networkx built-in functions, create the distance matrix for the same graph from the previous problem
End of explanation
# 4 is a cutpoint
G.remove_node(4)
draw(G, graphviz_layout)
Explanation: 8. Identify and remove a cutpoint from this graph and re-draw it
End of explanation
# G = nx.moebius_kantor_graph()
G = nx.dorogovtsev_goltsev_mendes_graph(3)
with open('../edges_2.pkl', 'rb') as f:
    edges = pickle.load(f)
    
G = nx.Graph(edges)
# draw(G, graphviz_layout)
draw(G, nx.circular_layout)
list(nx.find_cliques(G))
Explanation: 9. Use edges_2 to create a graph. List any subgraphs that are maximal cliques
End of explanation
degree = nx.degree_centrality(G)
closeness = nx.closeness_centrality(G)
betweenness = nx.betweenness_centrality(G)
Series(degree)
Series(closeness)
Series(betweenness)
Explanation: 10. Determine the Degree, Closeness, and Betweenness measures of centrality for this network
End of explanation
H = G.copy()
H.remove_node(0)
H.add_edge(10,14)
H.remove_edge(1,2)
# draw(H, graphviz_layout)
draw(H, nx.circular_layout)
# eccentricity of node 1
nx.eccentricity(H, 1)
# find cliques containing node 1
nx.cliques_containing_node(H, 1)
# density
nx.density(H)
# remove node 1
H.remove_node(1)
nx.density(H)
Explanation: 11. Based on the measures above, which actors have the greatest control over the flow of information? Why do some actors have betweenness measures of zero?
When considering control over flow of information, we look at the betweenness measure. In this case, actors 0, 1, and 2 have the greatest control over information flow. The actors with betweenness measures of zero have no geodesics through them connecting other pairs of nodes. For example, there is a path from 0 to 4 that goes through 9, but that has a length of 2 and 0 connects to 4 directly.
12. Create a copy of the last network and do the following:
remove node 0
add and edge between 10 and 14 and remove the edge between 1 and 2
draw the graph
determine the eccentricity of node 1
find all cliques containing node 1
compute the density of the graph
remove node 1 and compute the density of the resulting graph
End of explanation
with open('edges_3.pkl', 'rb') as f:
    edges = pickle.load(f)
    
G = nx.DiGraph(edges)
draw(G, graphviz_layout)
# adjacency matrix
adj_matrix = nx.to_numpy_matrix(G)
DF(adj_matrix)
# indegree and outdegree
indegree = adj_matrix.sum(axis=0) / (len(adj_matrix)-1)
outdegree = adj_matrix.sum(axis=1) / (len(adj_matrix)-1)
in_method = nx.in_degree_centrality(G)
out_method = nx.out_degree_centrality(G)
# indegree comparison
(Series(np.array(indegree).flatten()) == Series(in_method)).all()
# outdegree comparison
(Series(np.array(outdegree).flatten()) == Series(out_method)).all()
Series(in_method).sort_values(ascending=False)
Explanation: 13. Create a directed graph from edges_3.pkl and do the following:
create the adjacency matrix
compute the indegree and outdegree centrality for all actors in this network using the adjacency matrix
compare your results to the in and out_degree_centrality methods
End of explanation
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