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A network of coupled dynamical systems is represented by a graph whose vertices represent individual cells and whose edges represent couplings between cells. Motivated by the impact of synchronization results of the Kuramoto networks, we…
Representing graphs as quantum states is becoming an increasingly important approach to study entanglement of mixed states, alternate to the standard linear algebraic density matrix-based approach of study. In this paper, we propose a…
Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from…
Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…
In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…
We derive the spectral properties of adjacency matrix of complex networks and of their Laplacian by the replica method combined with a dynamical population algorithm. By assuming the order parameter to be a product of Gaussian…
This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity)…
Complex-valued Laplacians have been shown to be powerful tools in the study of distributed coordination of multi-agent systems in the plane including formation shape control problems and set surrounding control problems. In this paper, we…
Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the…
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…
Higher-order networks encode the many-body interactions existing in complex systems, such as the brain, protein complexes, and social interactions. Simplicial complexes are higher-order networks that allow a comprehensive investigation of…
Electrical grids are large-sized complex systems that require strong computing power for monitoring and analysis. Kron reduction is a general reduction method in graph theory and is often used for electrical circuit simplification. In this…
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…
Signed graphs encode positive (attractive) and negative (repulsive) relations between nodes. We extend spectral clustering to signed graphs via the one-parameter family of Signed Power Mean Laplacians, defined as the matrix power mean of…
The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…
Classical spectral graph theory relies on the symmetry of the adjacency and Laplacian operators, which guarantees orthogonal eigenbases and energy-preserving Fourier transforms. However, real-world networks are intrinsically directed and…
We introduce nonlocal dynamics on directed networks through the construction of a fractional version of a nonsymmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both…
The vertex-weighted Laplacian naturally extends the combinatorial Laplacian for simplicial complexes. Inspired by Lew's foundational techniques for vertex-weighted Laplacians, we present a comprehensive spectral analysis of this operator.…
The work done in this paper, proposes a complex Laplacian-based distributed control scheme for convergence in the multi-agent network. The proposed scheme has been designated as cascade formulation. The proposed technique exploits the…
Motivated by the relationship between the eigenvalue spectrum of the Laplacian matrix of a network and the behavior of dynamical processes evolving in it, we propose a distributed iterative algorithm in which a group of $n$ autonomous…