Related papers: Spectral identification of networks with inputs
Dynamics on networks are often characterized by the second smallest eigenvalue of the Laplacian matrix of the network, which is called the spectral gap. Examples include the threshold coupling strength for synchronization and the relaxation…
Using methods from algebraic graph theory and convex optimization, we study the relationship between local structural features of a network and spectral properties of its Laplacian matrix. In particular, we derive expressions for the…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of…
Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…
Determining and analyzing the spectra of graphs is an important and exciting research topic in theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on…
Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this…
We examine numerically the three-way relationships among structure, Laplacian spectra and frequency synchronization dynamics on complex networks. We study the effects of clustering, degree distribution and a particular type of coupling…
We introduce a new methodology for model selection in the context of modeling network data. The statistical network analysis literature has developed many different classes of network data models, with notable model classes including…
A recent development in data-driven modelling addresses the problem of identifying dynamic models of interconnected systems, represented as linear dynamic networks. For these networks the notion network identifiability has been introduced…
In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system…
The identification of distribution network topology and parameters is a critical problem that lays the foundation for improving network efficiency, enhancing reliability, and increasing its capacity to host distributed energy resources.…
One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded…
Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of…
Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide…
The eigenvalues of the normalized Laplacian matrix of a network plays an important role in its structural and dynamical aspects associated with the network. In this paper, we study the spectra and their applications of normalized Laplacian…
We derive the determinant of the Laplacian for the Hanoi networks and use it to determine their number of spanning trees (or graph complexity) asymptotically. While spanning trees generally proliferate with increasing average degree, the…
Training of neural networks can be reformulated in spectral space, by allowing eigenvalues and eigenvectors of the network to act as target of the optimization instead of the individual weights. Working in this setting, we show that the…
In this work, we explore the state-space formulation of network processes to recover the underlying structure of the network (local connections). To do so, we employ subspace techniques borrowed from system identification literature and…
We introduce new geometric objects called spectral networks. Spectral networks are networks of trajectories on Riemann surfaces obeying certain local rules. Spectral networks arise naturally in four-dimensional N=2 theories coupled to…