Related papers: SpectralFly: Ramanujan Graphs as Flexible and Effi…

Graph eigenvalues play a fundamental role in controlling structural properties, such as bisection bandwidth, diameter, and fault tolerance, which are critical considerations in the design of supercomputing interconnection networks. This…

We report on some recent developments in the search for optimal network topologies. First we review some basic concepts on spectral graph theory, including adjacency and Laplacian matrices, and paying special attention to the topological…

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…

We introduce a high-performance cost-effective network topology called Slim Fly that approaches the theoretically optimal network diameter. Slim Fly is based on graphs that approximate the solution to the degree-diameter problem. We analyze…

The question of finding expander graphs with strong vertex expansion properties such as unique neighbor expansion and lossless expansion is central to computer science. A barrier to constructing these is that strong notions of expansion…

Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high dimensional theory has emerged. In this paper these developments…

We propose two new spectral measures for graphs and networks which characterize the ratios between the width of the "bulk" part of the spectrum and the spectral gap, as well as the ratio between spectral length and the width of the "bulk"…

This paper introduces a new class of efficient inter connection networks called as M-graphs for large multi-processor systems.The concept of M-matrix and M-graph is an extension of Mn-matrices and Mn-graphs.We analyze these M-graphs…

In this paper, we present an algorithm for optimizing synchronizability of complex dynamical networks. Based on some network properties, rewirings, i.e. eliminating an edge and creating a new edge elsewhere, are performed iteratively…

We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…

Sparse neural networks are shown to give accurate predictions competitive to denser versions, while also minimizing the number of arithmetic operations performed. However current hardware like GPU's can only exploit structured sparsity…

We present a novel theoretical framework connecting k-component edge connectivity with spectral graph theory and homology theory to pro vide new insights into the resilience of real-world networks. By extending classical edge connectivity…

Communication latency has become one of the determining factors for the performance of parallel clusters. To design low-latency network topologies for high-performance computing clusters, we optimize the diameters, mean path lengths, and…

The recent line of research into topology design focuses on lowering network diameter. Many low-diameter topologies such as Slim Fly or Jellyfish that substantially reduce cost, power consumption, and latency have been proposed. A key…

Novel low-diameter network topologies such as Slim Fly (SF) offer significant cost and power advantages over the established Fat Tree, Clos, or Dragonfly. To spearhead the adoption of low-diameter networks, we design, implement, deploy, and…

Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…

We currently witness the emergence of interesting new network topologies optimized towards the traffic matrices they serve, such as demand-aware datacenter interconnects (e.g., ProjecToR) and demand-aware overlay networks (e.g., SplayNets).…

In their seminal paper, Lubotzky, Phillips and Sarnak (LPS) defined the notion of regular Ramanujan graphs and gave an explicit construction of infinite families of $(p+1)$-regular Ramanujan Cayley graphs, for infinitely many primes $p$. In…

Constantly growing demands of high productivity and security of computer systems and computer networks call the interest of specialists in the environment of construction of optimum topologies of computer mediums. In earliest phases of…

We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov…