Название: Dots and Lines: Hidden Networks in Social Media, AI, and Nature
Автор: Anthony Bonato
Издательство: Johns Hopkins University Press
Год: 2025
Страниц: 288
Язык: английский
Формат: pdf, epub (true)
Размер: 13.3 MB

Can networks unlock secrets of AI or make sense of a social media mess? A behind-the-scenes look at how networks reveal reality.

According to mathematician Anthony Bonato, the hidden world of networks permeates our lives in astounding ways. From Bitcoin transactions to neural connections, his book explains how networks shape everything from political landscapes to climate patterns and how deceptively simple dots and lines can unveil the wonders of technology, society, and even nature.

From a fresh and startling look at the true impact of clever keywords in politicians' social media posts to a fun breakdown of survival strategies in reality TV shows, Bonato shows us how network theory operates everywhere. Each chapter focuses on a unique aspect of networks to reveal how they provide a captivating lens for bringing diverse phenomena into clearer focus.

Networks are dots and lines connecting them. They are also called graphs, and graph theory is a well-established discipline intersecting pure and applied mathematics. While graph theory texts often discuss the theoretical side of mathematics, it is less common to see a book devoted to its modern applications. By modern, I mean happening this century, this decade, or even these past few years.

The last twenty years especially have seen an explosion of network methods applied to every discipline imaginable. From early examples like the web graph, we now study networks in food webs, mobile calls, political votes, smart grids, characters in novels, conflicts, protein interactions in living cells, supply chains, Bitcoin transactions, and neural connections in the brain. Network science, as it is called, is an interdisciplinary endeavor within the formal, mathematical framework of graph theory. While network science has matured over the decades, it remains less familiar to people not working in the field.

What is the book about? My main goal for the book is to give the reader a snapshot of modern network science, told through timely applications. The topics presented are not meant to be exhaustive but will give the reader a sampling of flavors of the discipline. Many, but not all, are topics I’ve worked on in my research, with each chapter focused on a particular theme.

The chapters are meant to be read in order, but you should feel free to skip around, to look at whatever topic captures your imagination. We begin in chapter 0 with an introduction to networks, focusing on their origins, their universal role in the modern world, and why they matter. Twitter keywords of various political figures are the topic of chapter 1, including what the keywords reveal about them and the central role of communities in networks. Chapter 2 unravels the voting network of the game show Survivor and, more generally, adversarial networks ranging from food webs to conflicts between groups in Pakistan. Here, we’ll also meet the influential PageRank algorithm from Google, with applications far beyond searching the web. Chapter 3 focuses on how six degrees of separation is ubiquitous in networks, stretching back to Stanley Milgram’s chain letter experiments, to the Kevin Bacon parlor game, and to our modern understanding provided by big data. In chapter 4 we’ll learn about memes popping up on social media, paralleling the spread of viruses like COVID-19. For this topic, we’ll cover graph burning and the burning number of networks. Detecting and eliminating threats in networks is the focus of chapter 5. You’ll discover how networks can help guard priceless paintings, find a person lost in a cave, and spur applications to driverless cars and real-life Transformers.

Chapter 6 focuses on the networks of characters in our stories and reveals hidden power brokers in Game of Thrones. Artificial Intelligence plays a role in analyzing stories and well beyond, with chapter 7 focusing on using geometry and machine learning to uncover the hidden architecture of networks. In chapter 8 we’ll discuss networks in biology, including proteins interacting in our cells and neurons in our brains, and what networks tell us about our banking systems and cryptocurrency. Chapter 9 dips into graph theory’s cool but refreshing waters, recounting Ramsey theory, hypergraphs, and graph coloring. The final chapter, chapter 10, looks forward, expounding the role of networks as quantitative views to transform our outlook on the world around us. We’ll see some unexpected applications of networks to anti–money laundering, success in the art world, and El Niño’s influence on our weather.

The book offers an accessible snapshot of networks for anyone curious about what makes the modern world tick. Bonato's insights will give readers a deeper appreciation and understanding of networks and their relevance to our everyday lives.

Who is the book for?
The book is for any reader curious to learn more about networks and for those unfamiliar with networks in any formal way. It can be understood by most anyone with a high school math background. That means no calculus, no advanced algebra, limited use of jargon or formulas, and only a few forays into discussion that uses letters like n to represent an integer. When I introduce the occasional formula, for completeness, say, I do my best to motivate it. These can be skipped with no disruption to the reader. The editor of Stephen Hawking’s book A Brief History of Time, Simon Mitton, warned him that every formula he included would halve the number of readers, and I’ve taken this advice to heart. Networks are so compellingly visual, as much as or more so than other areas of mathematics, that I feature figures throughout.

"Dots and Lines provides a lively account of the rich interactions between the abstract mathematical study of networks and everything else". - Emily Riehl, Johns Hopkins University

"A must-read for anyone trying to keep up with the technology that drives today's world. A glance into network science and its many applications, written with the rigor of an expert but intended for everyone. As engaging as it is informative". - Maria Chudnovsky, Princeton University

"Dots and Lines is an entertaining introduction to modern network science covering topics ranging from the lighthearted to the serious. But more than that, it is an authentic and heartfelt chronicle of one mathematician's decades long love affair with graph theory and network science, and an invitation to share in that love by appreciating the dots and lines that surround each of us". - Stephen J. Young, Pacific Northwest National Laboratory