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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…

There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…

We consider a system of $N$ servers inter-connected by some underlying graph topology $G_N$. Tasks arrive at the various servers as independent Poisson processes of rate $\lambda$. Each incoming task is irrevocably assigned to whichever…

In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…

Let $N$ local decision makers in a sensor network communicate with their neighbors to reach a decision \emph{consensus}. Communication is local, among neighboring sensors only, through noiseless or noisy links. We study the design of the…

Control of large-scale networked systems often necessitates the availability of complex models for the interactions amongst the agents. However in many applications, building accurate models of agents or interactions amongst them might be…

Graph convolutional networks (GCNs) are a family of neural network models that perform inference on graph data by interleaving vertex-wise operations and message-passing exchanges across nodes. Concerning the latter, two key questions…

Multi-agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-agent network to perturbations such as failures, noise, or malicious…

We develop a novel key routing algorithm for quantum key distribution (QKD) networks that utilizes a distribution of keys between remote, i.e., not directly connected by a QKD link, nodes through multiple non-overlapping paths. This…

We consider the Eschenauer-Gligor key predistribution scheme under the condition of partial visibility with i.i.d. on-off links between pairs of nodes. This situation is modeled as the intersection of two random graphs, namely a random key…

There are a number of existing studies analysing the convergence behaviour of graph neural networks on large random graphs. Unfortunately, the majority of these studies do not model correlations between node features, which would naturally…

Quantum interference (QI) in molecular transport junctions can lead to dramatic reductions of the electron transmission at certain energies. In a recent work [Markussen et al., Nano Lett. 2010, 10, 4260] we showed how the presence of such…

With the growing complexity of quantum key distribution (QKD) network structures, aforehand topology design is of great significance to support a large-number of nodes over a large-spatial area. However, the exclusivity of quantum channels,…

In recommender systems, user-item interactions can be modeled as a bipartite graph, where user and item nodes are connected by undirected edges. This graph-based view has motivated the rapid adoption of graph neural networks (GNNs), which…

Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…

Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses…

Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…

In the classical Erd\"os-R\'enyi random graph G(n,p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n,p) is homogeneous in the sense that all vertices have the same…

We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that when a quantum network is described by such a graph, the network is efficiently controllable, in…

Contemporary technological challenges often involve many degrees of freedom in a distributed or networked setting. Three aspects are notable: the variables are usually associated with the nodes of a graph with limited communication…