Related papers: Priors on exchangeable directed graphs

We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…

In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected…

Bidirected graphs are a generalisation of directed graphs that arises in the study of undirected graphs with perfect matchings. Menger's famous theorem - the minimum size of a set separating two vertex sets $X$ and $Y$ is the same as the…

Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…

We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In…

We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers. In particular, we prove the homotopy…

We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed…

In a directed graph, the imbalance of a vertex is its outdegree minus its indegree. We characterize the sequences that are realizable as the sequence of imbalances of a simple directed graph. Moreover, a realization of a realizable sequence…

We introduce two new bootstraps for exchangeable random graphs. One, the "empirical graphon bootstrap", is based purely on resampling, while the other, the "histogram bootstrap", is a model-based "sieve" bootstrap. We show that both of them…

We propose some kinetic models of wealth exchange and investigate their behavior on directed networks though numerical simulations. We observe that network topology and directedness yields a variety of interesting features in these models.…

We present a novel model architecture which leverages deep learning tools to perform exact Bayesian inference on sets of high dimensional, complex observations. Our model is provably exchangeable, meaning that the joint distribution over…

This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial…

Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured,…

In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most graph generating…

We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…

Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing…

Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…

Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…

Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same…

We call a topological ordering of a weighted directed acyclic graph non-negative if the sum of weights on the vertices in any prefix of the ordering is non-negative. We investigate two processes for constructing non-negative topological…