Related papers: Threshold graph limits and random threshold graphs
We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the random graph obtained when using the…
Distributed processing of large-scale graph data has many practical applications and has been widely studied. In recent years, a lot of distributed graph processing frameworks and algorithms have been proposed. While many efforts have been…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
We give several algebraic bounds for percolation on directed and undirected graphs: proliferation of strongly-connected clusters, proliferation of in- and out-clusters, and the transition associated with the number of giant components.
We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of so called graphons we…
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…
We survey recent results on graphs and their Laplacians related to the behavior of the graph at large. In particular, we focus on Liouville theorems, recurrence and characterizations of Dirichlet forms via boundary terms.
We determine the probability thresholds for the existence of monotone paths, of finite and infinite length, in random oriented graphs with vertex set $\mathbb N^{[k]}$, the set of all increasing $k$-tuples in $\mathbb N$. These graphs…
In this thesis we consider ordered graphs (that is, graphs with a fixed linear ordering on their vertices). We summarize and further investigations on the number of edges an ordered graph may have while avoiding a fixed forbidden ordered…
The bloom of complex network study, in particular, with respect to scale-free ones, is considerably triggering the research of scale-free graph itself. Therefore, a great number of interesting results have been reported in the past,…
We offer a new perspective on the closed graph theorem and the open mapping theorem for separated barrelled spaces and fully complete spaces.
We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…
The theory of convergent graph sequences has been worked out in two extreme cases, dense graphs and bounded degree graphs. One can define convergence in terms of counting homomorphisms from fixed graphs into members of the sequence…
Consider the complete n-vertex graph whose edge-lengths are independent exponentially distributed random variables. Simultaneously for each pair of vertices, put a constant flow between them along the shortest path. Each edge gets some…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
We study the integral and measure theory of the ultraproduct of finite sets. As a main application we construct limit objects for hypergraph sequences. We give a new proof for the Hypergraph Removal Lemma and the Hypergraph Regularity…
We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…
We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…
We give upper and lower bounds on the number of graphs of fixed degree which have a positive density of triangles. In particular, we show that there are very few such graphs, when compared to the number of graphs without this restriction.…