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 prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform infinite ...

Consider a family of random ordered graph trees (T n ) n≥1 , where T n has n vertices. It has previously been established that if the associated search-depth processes converge to the normalised ...