Related papers: Growing random graphs with a preferential attachme…
We study the random simple connected cubic planar graph $\mathsf{C}_n$ with an even number $n$ of vertices. We show that the Brownian map arises as Gromov--Hausdorff--Prokhorov scaling limit of $\mathsf{C}_n$ as $n \in 2 \ndN$ tends to…
We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes…
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…
We study two models of an age-biased graph process: the $\delta$-version of the preferential attachment graph model (PAM) and the uniform attachment graph model (UAM), with $m$ attachments for each of incoming vertices. We show that almost…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
We introduce and study a universal model of random geometry in two dimensions. To this end, we start from a discrete graph drawn on the sphere, which is chosen uniformly at random in a certain class of graphs with a given size $n$, for…
The theme in this paper is a composition of random graphs and P\'olya urns. The random graphs are generated through a small structure called the seed. Via P\'olya urns, we study the asymptotic degree structure in a random $m$-ary hooking…
Modelling the growth histories of specific galaxies often involves generating the entire population of objects that arise in a given cosmology and selecting systems with appropriate properties. This approach is highly inefficient when…
We introduce a new model of correlated randomly growing graphs and study the fundamental questions of detecting correlation and estimating aspects of the correlated structure. The model is simple and starts with any model of randomly…
In this paper we introduce a new model of random spanning trees that we call choice spanning trees, constructed from so-called choice random walks. These are random walks for which each step is chosen from a subset of random options,…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
We present a new technique for proving logarithmic upper bounds for diameters of evolving random graph models, which is based on defining a coupling between random graphs and variants of random recursive trees. The advantage of the…
We establish limit theorems that describe the asymptotic local and global geometric behaviour of random enriched trees considered up to symmetry. We apply these general results to random unlabelled weighted rooted graphs and uniform random…
We give an explicit construction of the scaling limit of the minimum spanning tree of the complete graph. The limit object is described using a recursive construction involving the convex minorants of a Brownian motion with parabolic drift…
We study random digraphs on sequences of expanders with bounded average degree {which converge locally in probability}. We prove that the threshold for the existence of a giant strongly connected component, as well as the asymptotic…
For a contractive iterated function system (IFS), it is known that there is a natural hyperbolic graph structure (augmented tree) on the symbolic space of the IFS that reflects the relationship among neighboring cells, and its hyperbolic…
We study a new class of preferential attachment trees with \emph{self-reinforcement}. At each time, each vertex is assigned a weight equal to the cumulative sum over past times of an affine function of its degree. A new vertex attaches…
Based on solid theoretical foundations, we present strong evidences that a number of real-life networks, taken from different domains like Internet measurements, biological data, web graphs, social and collaboration networks, exhibit…
The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…
We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…