Networks & Graphs

Watch

• The Scariest Chart in Electrical Engineering ↗Veritasium
• The Science of Six Degrees of Separation ↗Veritasium
• Decoding the Universe: Quantum | Full Documentary | NOVA | PBS ↗NOVA PBS Official
• But what is a neural network? | Deep learning chapter 1 ↗3Blue1Brown
• But what is the Fourier Transform? A visual introduction. ↗3Blue1Brown
• How Cell Service Actually Works ↗Wendover Productions

Read

• Graph Representation Learning ↗A lucid exposition for those seeking a foundational understanding of how to translate complex graph structures into machine-digestible representations.William L. Hamilton
• Graph Neural Networks: Foundations, Frontiers, and Applications ↗This comprehensive volume offers a rigorous exploration of GNN architectures, theoretical underpinnings, and their burgeoning applications across diverse domains.Lingfei Wu, Peng Cui, Jian Pei, Liang Zhao, Shiqiang Yang, Philip S. Yu
• Semi-Supervised Classification with Graph Convolutional Networks ↗The seminal work that introduced Graph Convolutional Networks, providing a scalable and effective framework for learning on graph-structured data.Thomas N. Kipf, Max Welling
• Graph Attention Networks ↗This paper introduced the attention mechanism to graph neural networks, enabling models to weigh the importance of different neighbours dynamically.Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, Yoshua Bengio
• Graph Neural Networks: A Review of Methods and Applications ↗An exhaustive survey charting the landscape of GNNs, from foundational models to cutting-edge applications, essential for navigating this rapidly evolving field.Jie Zhou, Ganqu Cui, Shengding Hu, Zhengyu Zhang, Cheng Yang, Zhiyuan Liu, Maosong Sun, Chi Li, Zhaokang Sun, Lifeng Wang, Xing Xie, Jian Tang

Voices to follow

• Yoshua Bengio ↗A titan of deep learning, his work on neural networks underpins much of modern AI, including foundational contributions to graph-based architectures.Professor, Université de Montréal; Scientific Director, MILA
• Jure Leskovec ↗A leading authority on large-scale graph analysis and network science, his research has significantly advanced the application of deep learning to complex graph structures.Professor of Computer Science, Stanford University
• Michael Bronstein ↗A pioneer in geometric deep learning, he has been instrumental in developing theoretical frameworks and practical applications for neural networks on non-Euclidean data like graphs.Professor, Imperial College London; Head of Graph Learning, Twitter
• Petar Veličković ↗Known for his seminal work on Graph Attention Networks (GATs), he continues to push the boundaries of graph representation learning with practical and theoretical insights.Staff Research Scientist, Google DeepMind; Affiliated Lecturer, University of Cambridge

Glossary

• EdgeAn edge is a connection or a link between two nodes in a graph. It shows that these two items are related in some way. For example, if two students are friends, the line connecting their nodes in a social graph would be an edge.
• FeatureA feature is a piece of information or a characteristic that describes a node or an edge. It helps us understand more about that specific part of the graph. For example, for a student node, features could be their age, grade, or favorite subject.
• GraphA graph is like a map that shows how different things are connected. It's made up of individual items (called "nodes") and the links between them (called "edges"). For example, a social media network where each person is a node and a friendship is an edge is a type of graph.
• Graph EmbeddingGraph embedding is the process where a GNN turns a node, an edge, or even an entire graph into a compact numerical code or vector. This code captures the important information and relationships, making it easier for computers to process. For example, imagine summarizing a long story into a short, secret code that still holds all the main points, so a computer can quickly understand what the story is about.
• Graph Neural Network (GNN)A Graph Neural Network (GNN) is a special type of artificial intelligence program that can "understand" and learn from data that is structured as a graph. It's designed to figure out patterns in how things are connected. For example, a GNN could be used to recommend new friends to you on social media by looking at your existing friends and their connections.
• Message PassingMessage passing is the main way a GNN learns. It's like nodes in a graph sending and receiving "messages" (which are actually pieces of information or features) to and from their neighbors. This helps each node update its understanding based on its connections. For example, imagine students in a group project sharing their ideas (messages) with their teammates (neighbors) to come up with a better final plan.
• NeighborhoodA node's neighborhood includes that node itself and all the other nodes it is directly connected to by an edge. It's like a node's immediate circle of friends. For example, if you are a node in a friendship graph, your neighborhood would be you and all your direct friends.
• NodeA node (sometimes called a vertex) is one of the individual items or points in a graph. Think of it as a single spot on your map. For example, in a graph of your school, each student or each classroom could be a node.
• PredictionPrediction is what a GNN does after it has learned from the graph data. It uses what it has learned to make a guess or a decision about new or unknown parts of the graph. For example, a GNN might predict if a new movie will be popular based on how similar movies (nodes) were connected to popular actors (other nodes) and genres (features).

Threads 14

Where this connects to other fields, and why it's worth knowing.

• Empires & Imperial Power History

  Ancient empires were basically a race against messenger speed. If an order from the capital took longer to arrive than a rebellion took to erupt, the far edges spun out of control. So the maximum size of an empire was set by one number: how many days it took news to cross the network before authority went stale.

• Rivers, Watersheds, and Water Systems Geography

  Look at a river system from above, the veins in your hand, and a lightning bolt, and they branch in eerily similar patterns. That's not a coincidence. Each one is nature's cheapest way to funnel stuff, water, blood, electric charge, from a whole spread-out area down to a single point, using the least energy possible.

• Political Economy Political Science

  Draw a map of which companies own shares of which other companies, and it doesn't spread out evenly, it collapses into a tiny tangled core. One study found just 147 firms secretly control 40% of the world's corporate value through these ownership webs. Real economic power isn't on any org chart; it's a hidden pattern in the network.

• Kinship & Family Sociology

  Aboriginal Australian communities have strict rules about who can marry whom, passed down for thousands of years. When mathematicians wrote those rules out, they matched a 'group' exactly, the same math structure that describes rotating a cube. Nobody designed it that way on purpose, yet the family system runs on flawless algebra.

• Immigration & Border Policy Political Science

  Once a few people from one village settle in a new country, they make it cheaper and less scary for their neighbors to follow, texting back tips, jobs, and a couch to crash on. So migration feeds itself and keeps going long after the first reason to leave is gone. That's why migrants cluster by hometown; it's chains of connections, not a random flood.

• Globalisation History

  You'd think hooking the whole world tightly together makes it sturdier. It does the opposite. In a densely linked financial network, one bank's collapse yanks on everyone wired to it, so a single local default can cascade into a worldwide crash. Tight connection spreads the damage instead of cushioning it.

• Cybercrime Law Law

  You can't chase an online hacker across a map, because they could be anywhere. Instead police trace the connections: which computers talked to which, which crypto wallets link up, what infrastructure they share. Catching them becomes less about geography and more about following the web of links.

• Pandemics Science

  A disease doesn't spread evenly, one person to the next. A few super-connected people (a nurse, a party host) infect huge numbers, while most infect almost no one. That's why the smart move is targeting those hubs, not vaccinating random people, and why one 'average' spread number hides what really matters.

• English as a Global Language Literature

  Every new person who learns English makes English more useful for everyone else to learn. That snowball locks it in as the world's default, even if another language might be 'better,' just like we're all stuck with the awkward QWERTY keyboard.

• Education and Social Mobility Sociology

  A researcher found that most people get their jobs not from close friends, but from people they barely know, a cousin's coworker, an old classmate. Those loose 'weak' connections reach into worlds your inner circle can't. So climbing in life runs a lot on the shape of your network, not just your grades.

• Cryptocurrency & Digital Money Economics

  People think Bitcoin is anonymous. Actually every transaction is written on a permanent public list anyone can read, and "chain analysis" experts routinely trace it back to real people. It's one of the least private kinds of money ever invented.

• Chokepoints & Strategic Waterways Geography

  Draw the world as dots and lines, and some lines carry a huge share of all the traffic. Cut one, and the whole map splits into disconnected pieces. Math can spot those weak links in advance, which is why the narrow Strait of Hormuz is dangerous on paper before any navy shows up.

• The Loneliness Epidemic Sociology

  Loneliness can ripple through a friend group up to three people away, like catching a cold you never touched. And it tends to push lonely people out toward the ragged edges of the network. An emotion is spreading with a shape and a pattern, like a contagion.

• Systemic & Cascading Risk Global Challenges

  Graph theory makes dependencies visible: nodes represent services and edges represent requirements or transmission pathways. Systemic-risk analysis adds the meaning of those links and the consequences of losing them.

  Sources: Briefing note on systemic risk ↗