#### Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover 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.
Preface
Basic Packages, Functions, and Concepts
Free Chapter
Mathematical Plotting with Matplotlib
Working with Randomness and Probability
Geometric Problems
Finding Optimal Solutions
Miscellaneous Topics
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# Quantifying clustering in a network

There are various quantities associated with networks that measure the characteristics of the network. For example, the clustering coefficient of a node measures the interconnectivity between the nodes nearby (here, nearby means connected by an edge). In effect, it measures how close the neighboring nodes are to forming a complete network or clique.

The clustering coefficient of a node measures the proportion of the adjacent nodes that are connected by an edge; that is, two adjacent nodes form a triangle with the given node. We count the number of triangles and divide this by the total number of possible triangles that could be formed, given the degree of the node. Numerically, the clustering coefficient at a node, u, in a simple unweighted network is given by the following equation:

Here, Tu is the number of triangles at u and the denominator is the total possible number of triangles at u. If the...