This chapter establishes the foundation for network machine learning. We begin with network fundamentals: adjacency matrices, edge directionality, node loops, and edge weights. We then explore node-specific properties such as degree and path length, followed by network-wide metrics including density, clustering coefficients, and average path lengths. The chapter progresses to advanced matrix representations, notably degree matrices and various Laplacian forms, which are crucial for spectral analysis methods. We examine subnetworks and connected components, tools for focusing on relevant network structures. The latter half of the chapter delves into preprocessing techniques. We cover node pruning methods to manage outliers and low-degree nodes. Edge regularization techniques, including thresholding and sparsification, address issues in weighted and dense networks. Finally, we explore edge-weight rescaling methods such as z-score standardization and ranking-based approaches. Throughout, we emphasize practical applications, illustrating concepts with examples and code snippets. These preprocessing steps are vital for addressing noise, sparsity, and computational challenges in network data. By mastering these concepts and techniques, readers will be well-equipped to prepare network data for sophisticated machine learning tasks, setting the stage for the advanced methods presented in subsequent chapters.

This chapter explores deep learning methods for network analysis, focusing on graph neural networks (GNNs) and diffusion-based approaches. We introduce GNNs through a drug discovery case study, demonstrating how molecular structures can be analyzed as networks. The chapter covers GNN architecture, training processes, and their ability to learn complex network representations without explicit feature engineering. We then examine diffusion-based methods, which use random walks to develop network embeddings. These techniques are compared and contrasted with earlier spectral approaches, highlighting their capacity to capture nonlinear relationships and local network structures. Practical implementations using frameworks such as PyTorch Geometric illustrate the application of these methods to large-scale network datasets, showcasing their power in addressing complex network problems across various domains.

This chapter explores advanced applications of network machine learning for multiple networks. We introduce anomaly detection in time series of networks, identifying significant structural changes over time. The chapter then focuses on signal subnetwork estimation for network classification tasks. We present both incoherent and coherent approaches, with incoherent methods identifying edges that best differentiate between network classes, and coherent methods leveraging additional network structure to improve classification accuracy. Practical applications, such as classifying brain networks, are emphasized throughout. These techniques apply to collections of networks, providing a toolkit for analyzing and classifying complex, multinetwork datasets. By integrating previous concepts with new methodologies, we offer a framework for extracting insights and making predictions from diverse network structures with associated attributes.