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 a broad class of stochastic process models for dynamic networks that satisfy the minimal regularity conditions of (i) exchangeability and (ii) càdlàg sample paths. Our main theorems ...

Given a sequence {a n } in (0,1) converging to a rational, we examine the model theoretic properties of structures obtained as limits of Shelah-Spencer graphs G(m, m -αn ). We show that in most cases ...