Related papers: Uniformly sampling random directed hypergraphs wit…
Comparative analysis between a network and a random graph model can uncover network properties that significantly deviate from those in random networks. The standard random graph model used for comparison uniformly samples random graphs…
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…
With sufficient time, double edge-swap Markov chain Monte Carlo (MCMC) methods are able to sample uniformly at random from many different and important graph spaces. For instance, for a fixed degree sequence, MCMC methods can sample any…
Random hypergraphs extend the classical notion of random graphs by allowing hyperedges to join more than two vertices, making them well-suited for modeling higher-order interactions in complex systems. Despite their broad applicability,…
The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in- and out-degrees. As the number of…
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…
In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…
Graph Sampling provides an efficient yet inexpensive solution for analyzing large graphs. While extracting small representative subgraphs from large graphs, the challenge is to capture the properties of the original graph. Several sampling…
`Double edge swaps' transform one graph into another while preserving the graph's degree sequence, and have thus been used in a number of popular Markov chain Monte Carlo (MCMC) sampling techniques. However, while double edge-swaps can…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
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…
We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models…
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…
A heterogeneous graph consists of different vertices and edges types. Learning on heterogeneous graphs typically employs meta-paths to deal with the heterogeneity by reducing the graph to a homogeneous network, guide random walks or capture…
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…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a…
Hypergraphs provide a fundamental framework for representing complex systems involving interactions among three or more entities. As empirical hypergraphs grow in size, characterizing their structural properties becomes increasingly…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…