Related papers: Degree distributions in AB random geometric graphs
Preferential attachment models have been widely studied in complex networks, because they can explain the formation of many networks like social networks, citation networks, power grids, and biological networks, to name a few. Motivated by…
We present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution. This approach extends the construction toolbox of random networks beyond the…
This paper presents an analytical framework to model fault-tolerance in unstructured peer-to-peer overlays, represented as complex networks. We define a distributed protocol peers execute for managing the overlay and reacting to node…
We analyze the properties of Degree-Ordered Percolation (DOP), a model in which the nodes of a network are occupied in degree-descending order. This rule is the opposite of the much studied degree-ascending protocol, used to investigate…
In this note we consider the $k$th level of the uniform random recursive tree after $n$ steps, and prove that the proportion of nodes with degree greater than $t\log n$ converges to $(1-t)^k$ almost surely, as $n\to\infty$, for every…
The stochastic block model is a powerful tool for inferring community structure from network topology. However, it predicts a Poisson degree distribution within each community, while most real-world networks have a heavy-tailed degree…
We consider uniform random cographs (either labeled or unlabeled) of large size. Our first main result is the convergence towards a Brownian limiting object in the space of graphons. We then show that the degree of a uniform random vertex…
The degree distribution is one of the most fundamental graph properties of interest for real-world graphs. It has been widely observed in numerous domains that graphs typically have a tailed or scale-free degree distribution. While the…
This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…
This work introduces a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
We investigate a variety of statistical properties associated with the number of distinct degrees that exist in a typical network for various classes of networks. For a single realization of a network with N nodes that is drawn from an…
The paper orders certain important issues related to both uncorrelated and correlated networks with hidden variables. In particular, we show that networks being uncorrelated at the hidden level are also lacking in correlations between node…
We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…
For a graph $G$ with $n$ vertices and a positive integer $k \leq n$, let $s_k(G)$ be the number of subtrees (subgraphs that are trees, not necessarily induced) of $G$ with $k$ vertices. The subtree polynomial of $G$ is $S(G;x) =…
Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called…
In this paper we present a generalization of the classical configuration model. Like the classical configuration model, the generalized configuration model allows users to specify an arbitrary degree distribution. In our generalized…
Due to their conceptual and mathematical simplicity, Erd\"os-R\'enyi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely…
We consider the number of common edges in two independent random spanning trees of a graph $G$. For complete graphs $K_n$, we give a new proof of the fact, originally obtained by Moon, that the distribution converges to a Poisson…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…