Related papers: Are Erd\"os- R\'enyi Random Graphs Topologically R…
We consider the Erdos-Renyi random graph G(n,p) inside the critical window, that is when p=1/n+ lambda*n^{-4/3}, for some fixed lambda in R. Then, as a metric space with the graph distance rescaled by n^{-1/3}, the sequence of connected…
We modify the usual Erdos-Renyi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the intensity of rate of lightnings the…
We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the…
A significant generalization of the Erd\"os-R\'enyi random graph model is an `inhomogeneous' random graph where the edge probabilities vary according to vertex types. We identify the threshold value for this random graph with a finite…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
Delete the edges of a Kneser graph independently of each other with some probability: for what probabilities is the independence number of this random graph equal to the independence number of the Kneser graph itself? We prove a sharp…
In this paper we prove the semi-circular law for the eigenvalues of regular random graph $G_{n,d}$ in the case $d\rightarrow \infty$, complementing a previous result of McKay for fixed $d$. We also obtain a upper bound on the infinity norm…
Graphs are powerful abstractions for capturing complex relationships in diverse application settings. An active area of research focuses on theoretical models that define the generative mechanism of a graph. Yet given the complexity and…
Consider a `dense' Erd\H{o}s--R\'enyi random graph model $G=G_{n,M}$ with $n$ vertices and $M$ edges, where we assume the edge density $M/\binom{n}{2}$ is bounded away from 0 and 1. Fix $k=k(n)$ with $k/n$ bounded away from 0 and~1, and let…
Consider a sequence of possibly random graphs $G_N=(V_N, E_N)$, $N\ge 1$, whose vertices's have i.i.d. weights $\{W^N_x : x\in V_N\}$ with a distribution belonging to the basin of attraction of an $\alpha$-stable law, $0<\alpha<1$. Let…
Consider a random graph model with $n$ vertices where each vertex has a vertex-type drawn from some discrete distribution. Suppose that the number of arcs to be placed between each pair of vertex-types is known, and that each arc is placed…
Neuronal network dynamics depends on network structure. In this paper we study how network topology underpins the emergence of different dynamical behaviors in neuronal networks. In particular, we consider neuronal network dynamics on…
In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos-Renyi random graph $G(n,p)$, where $p \in (0,1)$ is a fixed constant. Our proof is based on bounding the characteristic function…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs); a graph model used to study the structure and dynamics of complex systems embedded in a two dimensional space.…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
We determine the asymptotic behavior of the maximum subgraph density of large random graphs with a prescribed degree sequence. The result applies in particular to the Erd\H{o}s-R\'{e}nyi model, where it settles a conjecture of Hajek [IEEE…
We consider universal source coding of unlabeled graphs which are commonly referred to as graphical structures. We adopt an Erd\"{o}s-R\'enyi model to generate the random graphical structures. We propose a variant of the previously…