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Spectral Graph Neural Networks (SGNNs) have achieved remarkable performance in tasks such as node classification due to their ability to learn flexible filters. Typically, these filters are learned under the supervision of downstream tasks,…
We focus on designing Peer-to-Peer (P2P) networks that enable efficient communication. Over the last two decades, there has been substantial algorithmic research on distributed protocols for building P2P networks with various desirable…
A family of graphs optimized as the topologies for supercomputer interconnection networks is proposed. The special needs of such network topologies, minimal diameter and mean path length, are met by special constructions of the weight…
By leveraging information technologies, organizations now have the ability to design their communication networks and crowdsourcing platforms to pursue various performance goals, but existing research on network design does not account for…
This paper presents an optimal network topology control framework using cutting-plane methods for efficient network partitioning with controllable edges. The objective is to enable real-time reconfiguration of interconnected sub-networks…
The aim of this paper is to investigate the spectral theory of unimodular random graphs and graphings representing them. We prove that Bernoulli graphings are relatively Ramanujan with respect to their skeleton Markov chain. That is, the…
We present a framework based on spectral graph theory that captures the interplay among network topology, system inertia, and generator and load damping in determining the overall grid behavior and performance. Specifically, we show that…
In this paper, we introduce a novel unsupervised, graph-based filter feature selection technique which exploits the power of topologically constrained network representations. We model dependency structures among features using a family of…
Graph heterophily poses a formidable challenge to the performance of Message-passing Graph Neural Networks (MP-GNNs). The familiar low-pass filters like Graph Convolutional Networks (GCNs) face performance degradation, which can be…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
Connection graphs (CGs) extend traditional graph models by coupling network topology with orthogonal transformations, enabling the representation of global geometric consistency. They play a key role in applications such as synchronization,…
We consider finite graphs whose vertexes are supersingular elliptic curves, possibly with level structure, and edges are isogenies. They can be applied to the study of modular forms and to isogeny based cryptography. The main result of this…
Our goal in this paper is the robust design of filters acting on signals observed over graphs subject to small perturbations of their edges. The focus is on developing a method to identify spectral and polynomial graph filters that can…
It was recently shown by Lubetzky and Peres (2016) and by Sardari (2018) that Ramanujan graphs, i.e., graphs with the optimal spectrum, exhibit cutoff of the simple random walk in an optimal time and have an optimal almost-diameter. We show…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
Spectral features are widely incorporated within Graph Neural Networks (GNNs) to improve their expressive power, or their ability to distinguish among non-isomorphic graphs. One popular example is the usage of graph Laplacian eigenvectors…
The interconnection network comprises a significant portion of the cost of large parallel computers, both in economic terms and power consumption. Several previous proposals exploit large-radix routers to build scalable low-distance…
The multihop relay wireless networks have gained traction due to the emergence of Reconfigurable Intelligent Surfaces (RISs) which can be used as relays in high frequency range wireless network, including THz or mmWave. To select paths in…
The work in this thesis concerns the investigation of eigenvalues of the Laplacian matrix, normalized Laplacian matrix, signless Laplacian matrix and distance signless Laplacian matrix of graphs. In Chapter 1, we present a brief…
Graph Laplacians as well as related spectral inequalities and (co-)homology provide a foray into discrete analogues of Riemannian manifolds, providing a rich interplay between combinatorics, geometry and theoretical physics. We apply some…