Algorithms For Dummies

 Exploring the World of Graphs

Adding a graph to a matrix

Using NetworkX, you can easily move your graph to a NumPy matrix and back 

again as needed to perform various tasks. You use NumPy to perform all sorts of 

data manipulation tasks. By analyzing the data in a graph, you might see patterns 

that wouldn’t ordinarily be visible. Here’s the code used to convert the graph into 

a matrix that NumPy can understand:

import networkx as nx

import matplotlib.pyplot as plt

%matplotlib inline

AGraph = nx.Graph()

Nodes = range(1,6)

Edges = [(1,2), (2,3), (3,4), (4,5), (1,3), (1,5), (1,6)]

AGraph.add_nodes_from(Nodes)

AGraph.add_edges_from(Edges)

nx.to_numpy_matrix(AGraph)

matrix([[ 0.,  1.,  1.,  0.,  1.,  1.],

        [ 1.,  0.,  1.,  0.,  0.,  0.],

        [ 1.,  1.,  0.,  1.,  0.,  0.],

        [ 0.,  0.,  1.,  0.,  1.,  0.],

        [ 1.,  0.,  0.,  1.,  0.,  0.],

        [ 1.,  0.,  0.,  0.,  0.,  0.]])

The resulting rows and columns show where connections exist. For example, 

there is no connection between node 1 and itself, so row 1, column 1, has a 0 in it. 

However, there is a connection between node 1 and node 2, so you see a 1 in row 1, 

column 2, and row 2, column 1 (which means that the connection goes both ways 

as an undirected connection).

The size of this matrix is affected by the number of nodes (the marix has as many 

rows and columns as nodes), and when it grows huge, it has many nodes to rep-

resent because the total number of cells is the square of the number of nodes. For 

instance, you can’t represent the Internet using such a matrix because a conser-

vative estimate calculates that at 10^10 websites, you’d need a matrix with 10^20 

cells to store its structure, something impossible with the present computing 

capacity.

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CHAPTER 8