Hacker News with Generative AI: Graph Theory

Ask HN: Dense Tree Layout Algorithms (ycombinator.com)
I recently bought a poster which features a really beautiful rendering of a phylogenetic tree of the world's bird families (a rooted binary tree).<p>https://lynxnaturebooks.com/product/orders-and-families-of-the-birds-of-the-world-poster/<p>I am sure it was carefully designed by hand. What algorithms could automatically generate a layout like this? The graphviz layout algorithms are poorly suited to the problem because they cannot seem to avoid edge/node coincidence beyond a certain node density.
Treewidth? (ams.org)
The treewidth of a graph, a positive integer defined using a tree of sets of vertices, is central to graph structure theory and the parametrized complexity of algorithms.
A Gentle Introduction to Graph Neural Networks (2021) (distill.pub)
Neural networks have been adapted to leverage the structure and properties of graphs. We explore the components needed for building a graph neural network - and motivate the design choices behind them.
The science of routing print orders (canva.dev)
How Canva uses graph traversal to handle the complexity of getting print orders to our customers.
Curve Families (linebender.org)
This graph has an arrow when one curve family fully includes the parameter space of another. A dotted line represents an approximation which is better than can be expected from scaling based on the number of parameters.
Languages ... by finite semigroups [generalised to] trees and graphs (2020)[pdf] (mimuw.edu.pl)
Computer Scientists Establish the Best Way to Traverse a Graph (quantamagazine.org)
Dijkstra’s algorithm was long thought to be the most efficient way to find a graph’s best routes. Researchers have now proved that it’s “universally optimal.”
The bunkbed conjecture is false (wordpress.com)
The bunkbed conjecture (BBC) is a basic claim about random subgraphs.
Hierarchical Navigable Small World: a scalable nearest neighbor search (github.com/brtholomy)
"Hierarchical Navigable Small World" (HNSW): an intriguing mouthful, designating a dense bouquet of concepts developed in the last 70 years in sociology, graph theory, and algorithmic science. In this brief tutorial, we'll examine these concepts carefully and attempt to solidify our understanding with proof-of-concept code and as many visualizations as possible.
Graph Coloring Methods (graphcoloringmethods.com)
This is a graduate textbook about how to color graphs.
Possibly all the ways to get loop-finding in graphs wrong (greenend.org.uk)
Over the years I’ve been developing these puzzles, I’ve gone through an amazing number of algorithms for doing that job. Each one was unsatisfactory for some reason, and I threw it away, and moved on to the next.
Vizdom: A Fast and Declarative Graph Layout and Rendering Library (reddit.com)
Compressing graphs and indexes with recursive graph bisection (2016) (arxiv.org)
In highly connected networks, there's always a loop (quantamagazine.org)
Not all graphs are trees (buttondown.email)
Solving the minimum cut problem for undirected graphs (research.google)