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)

Generating the adjacency matrix for a network

One potent tool for analyzing graphs is the adjacency matrix, which has entries if there is an edge from node to node , and 0 otherwise. For most networks, the adjacency matrix will be sparse (most of the entries are 0). For networks that are not directed, the matrix will also be symmetric (). Numerous other matrices can be associated with a network. We will briefly discuss these in the There’s more... section of this recipe.

In this recipe, we will generate the adjacency matrix for a network and learn how to get some basic properties of the network from this matrix.

Getting ready

For this recipe, we will need the NetworkX package imported under the nx alias, and the NumPy module imported as np.

How to do it...

The following steps outline how to generate the adjacency matrix for a network and derive some simple properties of the network from this matrix:

  1. First, we will generate a network to work with throughout...