Related papers: Structural properties and average tapping time on …
Preferential attachment models are a common class of graph models which have been used to explain why power-law distributions appear in the degree sequences of real network data. One of the things they lack, however, is higher-order network…
This work provides a structural characterisation of hereditary graph classes that do not contain a star forest, several graphs obtained from star forests by subset complementation, a union of cliques, and the complement of a union of…
Continuous graph neural models based on differential equations have expanded the architecture of graph neural networks (GNNs). Due to the connection between graph diffusion and message passing, diffusion-based models have been widely…
Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…
In recent years there has been much progress in graph theory on questions of the following type. What is the threshold for a certain large substructure to appear in a random graph? When does a random graph contain all structures from a…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
We consider relations between the size, treewidth, and local crossing number (maximum number of crossings per edge) of graphs embedded on topological surfaces. We show that an $n$-vertex graph embedded on a surface of genus $g$ with at most…
We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global…
We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the…
We study two global structural properties of a graph $\Gamma$, denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erd\"os--R\'enyi random graph model G(n,p), proving a sharp…
Understanding the structure of minor-free metrics, namely shortest path metrics obtained over a weighted graph excluding a fixed minor, has been an important research direction since the fundamental work of Robertson and Seymour. A…
Let $\pi: (X,T)\rightarrow (Y,T)$ be a factor map of topological dynamics and $d\in {\mathbb {N}}$. $(Y,T)$ is said to be a $d$-step topological characteristic factor if there exists a dense $G_\delta$ set $X_0$ of $X$ such that for each…
A flip of a graph is obtained by complementing the edge relation within a set of vertices. Flips are typically used to separate vertices in a graph, by increasing the distances between them. We show that in $K_{t,t}$-free graphs, every…
$ \def\vecc#1{\boldsymbol{#1}} $We design a polynomial time algorithm that for any weighted undirected graph $G = (V, E,\vecc w)$ and sufficiently large $\delta > 1$, partitions $V$ into subsets $V_1, \ldots, V_h$ for some $h\geq 1$, such…
Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property…
Given an undirected graph $G$ and an error parameter $\epsilon > 0$, the {\em graph sparsification} problem requires sampling edges in $G$ and giving the sampled edges appropriate weights to obtain a sparse graph $G_{\epsilon}$ with the…
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
Stability and dependence are model-theoretic notions that have recently proved highly effective in the study of structural and algorithmic properties of hereditary graph classes, and are considered key notions for generalizing to hereditary…
In this paper, we analyze the behavior of the global clustering coefficient in scale free graphs. We are especially interested in the case of degree distribution with an infinite variance, since such degree distribution is usually observed…
Given connected graph $H$ which is not a star, we show that the number of copies of $H$ in a dense uniformly random regular graph is asymptotically Gaussian, which was not known even for $H$ being a triangle. This addresses a question of…