These are exciting times for quantum physics as new quantum technologies are expected to
soon transform computing at an unprecedented level. Simultaneously network science is …

We consider models of evolving networks G n: n≥ 0 modulated by two parameters: an
attachment function f: N 0→ R+ and a (possibly random) attachment sequence mi: i≥ 1 …

We study a general model of recursive trees where vertices are equipped with independent
weights and at each time-step a vertex is sampled with probability proportional to its fitness …

Preferential attachment models form a popular class of growing networks, where incoming
vertices are preferably connected to vertices with high degree. We consider a variant of this …

We study the structure of genealogical trees associated with explosive Crump-Mode-Jagers
branching processes (stopped at the explosion time), proving criteria for the associated tree …

A sequence of trees $(\mathcal {T} _ {n}) _ {n\in\mathbb {N}} $ contains a\emph {persistent
hub}, or displays\emph {degree centrality}, if there is a fixed node of maximal degree for all …

In this paper we initiate the theory of Crump-Mode-Jagers branching processes (BP) in the
setting where no Malthusian parameter exist, ie, the process grows faster than exponential …

We provide sufficient criteria for explosion in Crump-Mode-Jagers branching process, via
the process producing an infinite path in finite time. As an application, we deduce a phase …

We study the evolution of the graph distance and weighted distance between two fixed
vertices in dynamically growing random graph models. More precisely, we consider …

We introduce a model of a preferential attachment based random graph which extends the
family of models in which condensation phenomena can occur. Each vertex has an …