Related papers: A simple and flexible algorithm to generate real-w…

We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm designed for practical use both because of its ability to…

This work introduces NetDiff, an expressive graph denoising diffusion probabilistic architecture that generates wireless ad hoc network link topologies. Such networks, with directional antennas, can achieve unmatched performance when the…

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…

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…

We uncover the global organization of clustering in real complex networks. As it happens with other fundamental properties of networks such as the degree distribution, we find that real networks are neither completely random nor ordered…

Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…

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 propose NetGAN - the first implicit generative model for graphs able to mimic real-world networks. We pose the problem of graph generation as learning the distribution of biased random walks over the input graph. The proposed model is…

In this study, the concept of small worlds is investigated in the context of large-scale wireless ad hoc and sensor networks. Wireless networks are spatial graphs that are usually much more clustered than random networks and have much…

Let $F$ be a probability distribution with support on the non-negative integers. Four methods for generating a simple undirected graph with (approximate) degree distribution $F$ are described and compared. Two methods are based on the so…

We give a simple, local process for nodes in an undirected graph to form non-adjacent clusters that (1) have at most a polylogarithmic diameter and (2) contain at least half of all vertices. Efficient deterministic distributed clustering…

The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…

We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and…

Real-world networks, e.g. the social relations or world-wide-web graphs, exhibit both small-world and scale-free behaviour. We interpret lattice triangulations as planar graphs by identifying triangulation vertices with graph nodes and…

The past decade highlighted the usefulness of social network simulations that run on k-regular, n-size, connected graphs. These can be seen as small-scale models of human social networks of large societies. By narrowing down onto k-regular…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

Real social networks are often compared to random graphs in order to assess whether their typological structure could be the result of random processes. However, an Erd\H{o}s-R\'enyi random graph in large scale is often lack of local…

We present a novel algorithm that generates scale free small world graphs such as those found in the World Wide Web,social and metabolic networks. We use the generated graphs to study the dynamics of a realistic search strategy on the…

In this paper, we propose a simple rule that generates scale-free small-world networks with tunable assortative coefficient. These networks are constructed by two-stage adding process for each new node. The model can reproduce scale-free…

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to…