Related papers: Constructing and sampling directed graphs with giv…

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…

We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…

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…

In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the…

Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…

The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…

Random graphs with prescribed degree sequences have been widely used as a model of complex networks. Comparing an observed network to an ensemble of such graphs allows one to detect deviations from randomness in network properties. Here we…

Sampling from combinatorial families can be difficult. However, complicated families can often be embedded within larger, simpler ones, for which easy sampling algorithms are known. We take advantage of such a relationship to describe a…

Choosing a uniformly sampled simple directed graph realization of a degree sequence has many applications, in particular in social networks where self-loops are commonly not allowed. It has been shown in the past that one can perform a…

Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…

Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…

Markov chain Monte Carlo is a widely-used technique for generating a dependent sequence of samples from complex distributions. Conventionally, these methods require a source of independent random variates. Most implementations use…

Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…

Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…

We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…

Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties,…

Sampling random graphs is essential in many applications, and often algorithms use Markov chain Monte Carlo methods to sample uniformly from the space of graphs. However, often there is a need to sample graphs with some property that we are…

We discuss various ensembles of homogeneous complex networks and a Monte-Carlo method of generating graphs from these ensembles. The method is quite general and can be applied to simulate micro-canonical, canonical or grand-canonical…

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory…