Related papers: Generalized quasirandom properties of expanding gr…
We prove that any quasirandom uniform hypergraph $H$ can be approximately decomposed into any collection of bounded degree hypergraphs with almost as many edges. In fact, our results also apply to multipartite hypergraphs and even to the…
The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…
We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
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.…
The well-known regularity lemma of E. Szemer\'edi for graphs (i.e. 2-uniform hypergraphs) claims that for any graph there exists a vertex partition with the property of quasi-randomness. We give a simple construction of such a partition. It…
Generally speaking, `almost distance-regular' graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity,…
Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph G is distance-regular if and only if its spectral excess (a number that can be…
In previous papers, threshold probabilities for the properties of a random distance graph to contain strictly balanced graphs were found. We extend this result to arbitrary graphs and prove that the number of copies of a strictly balanced…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
Given a hereditary graph property $\mathcal{P}$, consider distributions of random orderings of vertices of graphs $G\in\mathcal{P}$ that are preserved under isomorphisms and under taking induced subgraphs. We show that for many properties…
We describe a natural topological generalization of edge expansion for graphs to regular CW complexes and prove that this property holds with high probability for certain random complexes.
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
To each colored graph, one can associate its closure in the universal space of isomorphism classes of pointed colored graphs, and this subspace can be regarded as a generalized subshift. Based on this correspondence, we extend the notion of…
Random graph models are a recurring tool-of-the-trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test-bed generators for studying diffusion and…
Let $\mathbb{G}^{D}$ be the set of graphs $G(V,\, E)$ with $\left|V\right|=n$, and the degree sequence equal to $D=(d_{1},\, d_{2},\,\dots,\, d_{n})$. In addition, for $\frac{1}{2}<a<1$, we define the set of graphs with an almost given…
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…