Finding knots in graph embeddings

A while ago I wrote a post about indistinguishable sceneries on the Boolean hypercube. The post contained this (pretty, if I may so myself) image: This is a three dimensional embedding of the four dimensional Boolean hypercube; by “embedding”, I mean putting the vertices and edges of the 4d cube in some way in space, … More Finding knots in graph embeddings

Random graphs: The exponential random graph model

Some mathematicians like probability, and some mathematicians like graphs, so it’s only natural that some mathematicians like probabilistic graphs. That is, they like to generate graphs at random, and then ask all sorts of questions about them: What are the features of a random graph? Will it be connected? Will it contain many triangles? Will … More Random graphs: The exponential random graph model

Random graphs: The Erdős–Rényi G(n,p) model

Some mathematicians like probability, and some mathematicians like graphs, so it’s only natural that some mathematicians like probabilistic graphs. That is, they like to generate graphs at random, and then ask all sorts of questions about them: What are the features of a random graph? Will it be connected? Will it contain many triangles? Will … More Random graphs: The Erdős–Rényi G(n,p) model