Sparse Matrices and Graphs

We have gone through numerous examples of arrays and matrices that are essential in many aspects of numerical computing. And, we have represented arrays with the NumPy ndarray data structure, a heterogeneous representation that stores all the array elements it represents. This is often the most efficient way to represent an object, such as a vector, matrix, or higher-dimensional array. However, notable exceptions are matrices where most of the elements are zeros. Such matrices are known as sparse matrices, and they occur in many applications, for example, in connection networks (such as circuits) and large algebraic equation systems that arise, for example, when solving partial differential equations (see Chapter 11 for examples).