Related papers: Do random initial degrees suppress concentration i…
We show that the distribution of the first return time $\tau$ to the origin, v, of a simple random walk on an infinite recurrent graph is heavy tailed and nonconcentrated. More precisely, if $d_v$ is the degree of v, then for any $t\geq1$…
This paper studies how close random graphs are typically to their expectations. We interpret this question through the concentration of the adjacency and Laplacian matrices in the spectral norm. We study inhomogeneous Erd\"os-R\'enyi random…
In this paper, we study some important statistics of the random graph in the Buckley-Osthus model. This model is a modification of the well-known Bollob\'as-Riordan model. We denote the number of nodes by t, the so-called initial…
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
We establish the asymptotic degree distribution of the typical vertex of inhomogeneous and passive random intersection graphs under the minimal moment conditions.
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies} between neighbouring nodes. One of the problems with the…
In this paper we introduce the perturbed version of the Barab\'asi-Albert random graph with multiple type edges and prove the existence of the (generalized) asymptotic degree distribution. Similarly to the non-perturbed case, the asymptotic…
In the infinite configuration network the links between nodes are assigned randomly with the only restriction that the degree distribution has to match a predefined function. This work presents a simple equation that gives for an arbitrary…
Preferential attachment, homophily and, their consequences such as the glass ceiling effect have been well-studied in the context of undirected networks. However, the lack of an intuitive, theoretically tractable model of a directed,…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent…
Scale-free networks with moderate edge dependence experience a phase transition between ultrasmall and small world behaviour when the power law exponent passes the critical value of three. Moreover, there are laws of large numbers for the…
It is widely believed that the Internet's AS-graph degree distribution obeys a power-law form. Most of the evidence showing the power-law distribution is based on BGP data. However, it was recently argued that since BGP collects data in a…
We provide large deviations estimates for the upper tail of the number of triangles in scale-free inhomogeneous random graphs where the degrees have power law tails with index $-\alpha, \alpha \in (1,2)$. We show that upper tail…
In this paper we study the degree sequence of the permutation graph $G_{\pi_n}$ associated with a sequence $\pi_n\in S_n$ of random permutations. Joint limiting distributions of the degrees are established using results from graph and…
If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences 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…