Related papers: Making multigraphs simple by a sequence of double …
The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…
A 2-switch is an edge addition/deletion operation that changes adjacencies in the graph while preserving the degree of each vertex. A well known result states that graphs with the same degree sequence may be changed into each other via…
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…
Many complex systems show non-pairwise interactions, which can be captured by hypergraphs. In this work, we propose an edge-swapping method to sample random directed hypergraphs with fixed vertex and hyperarc degrees, which can be applied…
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…
Switches are operations which make local changes to the edges of a graph, usually with the aim of preserving the vertex degrees. We study a restricted set of switches, called triangle switches. Each triangle switch creates or deletes at…
Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is…
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…
Sampling uniform simple graphs with power-law degree distributions with degree exponent $\tau\in(2,3)$ is a non-trivial problem. We propose a method to sample uniform simple graphs that uses a constrained version of the configuration model…
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…
The switch Markov chain has been extensively studied as the most natural Markov Chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We use comparison arguments with other, less natural but simpler to analyze,…
We consider the following common network analysis problem: given a degree sequence $\mathbf{d} = (d_1, \dots, d_n) \in \mathbb N^n$ return a uniform sample from the ensemble of all simple graphs with matching degrees. In practice, the…
This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under which a sequence is necessarily connected i.e. the sequence…
Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…
Let J and J* be subsets of Z+ such that 0,1\in J and 0\in J*. For infinitely many n, let k=(k_1,..., k_n) be a vector of nonnegative integers whose sum M is even. We find an asymptotic expression for the number of multigraphs on the vertex…
The problem of efficiently sampling from a set of (undirected, or directed) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the…
Let $G$ be a uniformly chosen simple (labelled) random graph with given degree sequence $\boldsymbol{d}$ and let $X,Y,L$ be edge-disjoint graphs on the same vertex set as $G$. We investigate the probability that $X \subseteq G$ and that $G…
Suppose a finite, unweighted, combinatorial graph $G = (V,E)$ is the union of several (degree-)regular graphs which are then additionally connected with a few additional edges. $G$ will then have only a small number of vertices $v \in V$…
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…
Learning-based methods for routing have gained significant attention in recent years, both in single-objective and multi-objective contexts. Yet, existing methods are unsuitable for routing on multigraphs, which feature multiple edges with…