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Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…
We investigate to what extent the degree sequence of a directed network constrains the number of driver nodes. We develop a pair of algorithms that take a directed degree sequence as input and aim to output a network with the maximum or…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
In this paper, we prove the first-order convergence law for the uniform attachment random graph with almost all vertices having the same degree. In the considered model, vertices and edges are introduced recursively: at time $m+1$ we start…
We introduce a new class of graphical models that generalizes Lauritzen-Wermuth-Frydenberg chain graphs by relaxing the semi-directed acyclity constraint so that only directed cycles are forbidden. Moreover, up to two edges are allowed…
We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random…
We consider the configuration model and the uniform simple graph with given degree sequence $\boldsymbol{d}=\left(d_i\right)_{i=1}^n$. We derive quantitative bounds for the errors in (i) joint normal-Poisson approximation to the numbers of…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
A directed graph G = (V,E) is singly connected if for any two vertices v, u of V, the directed graph G contains at most one simple path from v to u. In this paper, we study different algorithms to find a feasible but necessarily optimal…
We propose efficient algorithms for two key tasks in the analysis of large nonuniform networks: uniform node sampling and cluster detection. Our sampling technique is based on augmenting a simple, but slowly mixing uniform MCMC sampler with…
Directed graphs are ubiquitous models for networks, and topological spaces they generate, such as the directed flag complex, have become useful objects in applied topology. The simplices are formed from directed cliques. We extend Atkin's…
Despite the enormous success of graph neural networks (GNNs), most existing GNNs can only be applicable to undirected graphs where relationships among connected nodes are two-way symmetric (i.e., information can be passed back and forth).…
Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning algorithms for the problem of parallelizing computation for multiprocessor…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
We study the expected adjacency matrix of a uniformly random multigraph with fixed degree sequence $\mathbf{d} \in \mathbb{Z}_+^n$. This matrix arises in a variety of analyses of networked data sets, including modularity-maximization and…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
Directed acyclic graphical models, or DAG models, are widely used to represent complex causal systems. Since the basic task of learning such a model from data is NP-hard, a standard approach is greedy search over the space of directed…
This paper proposes a new class of assortativity measures for weighted and directed networks. We extend the classical Newman's degree-degree assortativity by considering nodes' attributes different from the degree. Moreover, we propose…
Bounding chains are a technique that offers three benefits to Markov chain practitioners: a theoretical bound on the mixing time of the chain under restricted conditions, experimental bounds on the mixing time of the chain that are provably…
Despite great effort spent measuring topological features of large networks like the Internet, it was recently argued that sampling based on taking paths through the network (e.g., traceroutes) introduces a fundamental bias in the observed…