A graph database with a quadrillion nodes? Such a monstrous entity is beyond the scope of what technologist are trying to do now. But with the latest release of the Neo4j database from Neo Technology, ...

Graph limit theory provides a rigorous framework for analysing sequences of large graphs by representing them as continuous objects known as graphons – symmetric measurable functions on the unit ...

We study the uniform random graph Cn with n vertices drawn from a subcriticai class of connected graphs. Our main result is that the rescaled graph On ${C_n}/\sqrt n $ converges to the Brownian ...

We consider a stochastic SIR (susceptible → infective → recovered) epidemic defined on a configuration model random graph, in which infective individuals can infect only their neighbours in the graph ...