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

Random Chess Conquests

In our last statistical analysis of chess, we looked at the relative frequencies on which the different squares of the chessboard are stepped on, by any pieces. The games analyzed were carried out by masters and grandmasters, who exhibit remarkable intuition and control of the game. I speculate that the distribution amongst amateur players and … More Random Chess Conquests