Related papers: Random homomorphisms into the orthogonality graph
We generalize subgraph densities, arising in dense graph limit theory, to Markov spaces (symmetric measures on the square of a standard Borel space). More generally, we define an analogue of the set of homomorphisms in the form of a measure…
A growing set of on-line applications are generating data that can be viewed as very large collections of small, dense social graphs -- these range from sets of social groups, events, or collaboration projects to the vast collection of…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
We propose a notion of graph convergence that interpolates between the Benjamini--Schramm convergence of bounded degree graphs and the dense graph convergence developed by L\'aszl\'o Lov\'asz and his coauthors. We prove that spectra of…
We introduce probability-graphons which are probability kernels that generalize graphons to the case of weighted graphs. Probability-graphons appear as the limit objects to study sequences of large weighted graphs whose distribution of…
We highlight a topological aspect of the graph limit theory. Graphons are limit objects for convergent sequences of dense graphs. We introduce the representation of a graphon on a unique metric space and we relate the dimension of this…
We show that if a sequence of dense graphs has the property that for every fixed graph F, the density of copies of F in these graphs tends to a limit, then there is a natural ``limit object'', namely a symmetric measurable 2-variable…
In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable…
We generalize the notion of quasirandom which concerns a class of equivalent properties that random graphs satisfy. We show that the convergence of a graph sequence under the spectral distance is equivalent to the convergence using the…
Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts in random graphs generated by a general graphon and independent vertex labels. We are interested in these statistics because they…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Subgraph densities play a crucial role in network analysis, especially for the identification and interpretation of meaningful substructures in complex graphs. Localized subgraph densities, in particular, can provide valuable insights into…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…
We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…
Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures as building blocks. However, it has not been thoroughly…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…