Related papers: Uniform sampling of undirected and directed graphs…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
We consider the problem of sampling a proper $k$-coloring of a graph of maximal degree $\Delta$ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of bounded treewidth if…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
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 explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social…
Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…
Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for…
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…
A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of…
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…
Graph randomisation is a crucial task in the analysis and synthesis of networks. It is typically implemented as an edge switching process (ESMC) repeatedly swapping the nodes of random edge pairs while maintaining the degrees involved.…
We consider the problem of sampling from the uniform distribution on the set of Eulerian orientations of subgraphs of the triangular lattice. Although it is known that this can be achieved in polynomial time for any graph, the algorithm…
The graph alignment problem, which considers the optimal node correspondence across networks, has recently gained significant attention due to its wide applications. There are graph alignment methods suited for various network types, but we…
Decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD) algorithm - a variant of the decentralized…
Given a set of snapshots from a temporal network we develop, analyze, and experimentally validate a so-called network interpolation scheme. Our method allows us to build a plausible, albeit random, sequence of graphs that transition between…
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…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The…
We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…