Related papers: Connectivity and Giant Component of Stochastic Kro…
Data-driven analysis of large social networks has attracted a great deal of research interest. In this paper, we investigate 120 real social networks and their measurement-calibrated synthetic counterparts generated by four well-known…
Gy\'arf\'as famously showed that in every $r$-coloring of the edges of the complete graph $K_n$, there is a monochromatic connected component with at least $\frac{n}{r-1}$ vertices. A recent line of study by Conlon, Tyomkyn, and the second…
In this paper, we study the large-scale structure of dense regular graphs. This involves the notion of robust expansion, a recent concept which has already been used successfully to settle several longstanding problems. Roughly speaking, a…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
This paper is a short introduction to the theory of tangles, both in graphs and general connectivity systems. An emphasis is put on the correspondence between tangles of order k and k-connected components. In particular, we prove that there…
In this work, for the given adjacency matrix of a graph, we present an algorithm which checks the connectivity of a graph and computes all of its connected components. Also, it is mathematically proved that the algorithm presents all the…
We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…
Consider a family $\mathcal{T}$ of 3-connected graphs of moderate growth, and let $\mathcal{G}$ be the class of graphs whose 3-connected components are graphs in $\mathcal{T}$. We present a general framework for analyzing such graphs…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$ was introduced by Hager before 1985. As its a natural counterpart, we introduced the concept of generalized edge-connectivity $\lambda_k(G)$, recently. In this paper we summarize…
The stochastic Kronecker graph model introduced by Leskovec et al. is a random graph with vertex set $\mathbb Z_2^n$, where two vertices $u$ and $v$ are connected with probability…
In this paper we study the threshold model of \emph{geometric inhomogeneous random graphs} (GIRGs); a generative random graph model that is closely related to \emph{hyperbolic random graphs} (HRGs). These models have been observed to…
We consider the count of subgraphs with an arbitrary configuration of endpoints in the random-connection model based on a Poisson point process on ${\Bbb R}^d$. We present combinatorial expressions for the computation of the cumulants and…
Generative models for graphs are increasingly becoming a popular tool for researchers to generate realistic approximations of graphs. While in the past, focus was on generating graphs which follow general laws, such as the power law for…
In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects 'k' possible partners from the existing…
Local convergence techniques have become a key methodology to study sparse random graphs. However, convergence of many random graph properties does not directly follow from local convergence. A notable, and important, such random graph…
We interpret the subgraph centrality as the partition function of a network. The entropy, the internal energy and the Helmholtz free energy are defined for networks and molecular graphs on the basis of graph spectral theory. Various…
We study the problem of the existence of a giant component in a random multipartite graph. We consider a random multipartite graph with $p$ parts generated according to a given degree sequence $n_i^{\mathbf{d}}(n)$ which denotes the number…
The problem of graph learning concerns the construction of an explicit topological structure revealing the relationship between nodes representing data entities, which plays an increasingly important role in the success of many graph-based…