In 2004, two mathematicians hypothesized a powerful kind of sandwich. They were studying graphs, which are collections of points (called vertices) and lines (called edges). Graphs might represent ...

Random graph theory provides a probabilistic framework for modelling and analysing networks in which connections between entities are assigned according to specified random processes. From its origins ...

Random graphs provide a mathematical framework for modelling networks in which connections between nodes occur with prescribed probabilities. Classical models such as the Erdős–Rényi graph establish ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

This lecture course is devoted to the study of random geometrical objects and structures. Among the most prominent models are random polytopes, random tessellations, particle processes and random ...

Amazon Web Services (AWS) has detailed a new cloud networking architecture based on random graph theory that it says is now the default fabric for its general-purpose cloud infrastructure worldwide.