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This article investigates the ability of graph neural networks (GNNs) to identify risky conditions in a power grid over the subsequent few hours, without explicit, high-resolution information regarding future generator on/off status (grid…
Random walks on simple graphs in connection with electrical resistor networks lead to the definition of Markov chains with transition probability matrix in terms of electrical conductances. We extend this definition to an effective…
In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…
We study a method for key predistribution in a network of $n$ users where pairwise keys are computed by hashing users' IDs along with secret information that has been (pre)distributed to the network users by a trusted entity. A…
Due to the fact much of today's data can be represented as graphs, there has been a demand for generalizing neural network models for graph data. One recent direction that has shown fruitful results, and therefore growing interest, is the…
Graph Neural Networks (GNNs) have emerged as a powerful technique for learning on relational data. Owing to the relatively limited number of message passing steps they perform -- and hence a smaller receptive field -- there has been…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
Random intersection graphs have received much attention for nearly two decades, and currently have a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. In this paper, we…
We investigate a process of joining $k$ random spanning trees on a fixed clique $K_n$. The joined trees may not be disjoint and multiple edges are replaced by one simple edge. This process produces a simple graph $G$ on $n$~vertices with an…
An Automata Network is a map ${f:Q^n\rightarrow Q^n}$ where $Q$ is a finite alphabet. It can be viewed as a network of $n$ entities, each holding a state from $Q$, and evolving according to a deterministic synchronous update rule in such a…
Quantum key distribution (QKD), which promises secure key exchange between two remote parties, is now moving toward the realization of scalable and secure QKD networks (QNs). Fully connected, trusted node-free QNs have been realized based…
Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…
Quantum key distribution (QKD) networks hold promise for sharing secure randomness over multi-partities. Most existing QKD network schemes and demonstrations are based on trusted relays or limited to point-to-point scenario. Here, we…
We consider random-access networks where nodes represent servers with a queue and can be either active or inactive. A node deactivates at unit rate, while it activates at a rate that depends on its queue length, provided none of its…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
A new complex network model, called q-snapback network, is introduced. Basic topological characteristics of the network, such as degree distribution, average path length, clustering coefficient and Pearson correlation coefficient, are…
A uniform attachment graph (with parameter $k$), denoted $G_{n,k}$ in the paper, is a random graph on the vertex set $[n]$, where each vertex $v$ makes $k$ selections from $[v-1]$ uniformly and independently, and these selections determine…
Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. Here, we present a specific realization of a class of random…
Existing Graph Neural Networks (GNNs) compute the message exchange between nodes by either aggregating uniformly (convolving) the features of all the neighboring nodes, or by applying a non-uniform score (attending) to the features. Recent…
We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension $q$, as well as explicit decoding operations for quantum secret sharing based on…