Book Image

Applying Math with Python - Second Edition

By : Sam Morley
Book Image

Applying Math with Python - Second Edition

By: Sam Morley

Overview of this book

The updated edition of Applying Math with Python will help you solve complex problems in a wide variety of mathematical fields in simple and efficient ways. Old recipes have been revised for new libraries and several recipes have been added to demonstrate new tools such as JAX. You'll start by refreshing your knowledge of several core mathematical fields and learn about packages covered in Python's scientific stack, including NumPy, SciPy, and Matplotlib. As you progress, you'll gradually get to grips with more advanced topics of calculus, probability, and networks (graph theory). Once you’ve developed a solid base in these topics, you’ll have the confidence to set out on math adventures with Python as you explore Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Table of Contents (13 chapters)

Getting the basic characteristics of networks

Networks have various basic characteristics beyond the number of nodes and edges that are useful for analyzing a graph. For example, the degree of a node is the number of edges that start (or end) at that node. A higher degree indicates that the node is better connected to the rest of the network.

In this recipe, we will learn how to access the basic attributes and compute various basic measures associated with a network.

Getting ready

As usual, we need to import the NetworkX package under the nx alias. We also need to import the Matplotlib pyplot module as plt.

How to do it...

Follow these steps to access the various basic characteristics of a network:

  1. Create the sample network that we will analyze in this recipe, like so:
    G = nx.Graph()
    G.add_nodes_from(range(10))
    G.add_edges_from([
        (0, 1), (1, 2), (2, 3), (2, 4),
        (2, 5), (3, 4), (4, 5), (6, 7),
        ...