Related papers: Maximizing Algebraic Connectivity in Interconnecte…
In this paper a tight lower bound for algebraic connectivity of graphs (second smallest eigenvalue of the Laplacian matrix of the graph) based on connection-graph-stability method is introduced. The connection-graph-stability score for each…
The spectral graph theory provides an algebraical approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the…
We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in a graph. We prove that this lower bound implies a strengthening of the Laplacian Spread Conjecture. We…
We consider the problem on finding the edge weights that maximize the algebraic connectivity of a graph (smallest positive eigenvalue of the Laplacian), subject to the condition that the total effective resistance is kept constant. We…
We take a new perspective on the weighted sum-rate maximization in multiple-input multiple-output (MIMO) interference networks, by formulating an equivalent max-min problem. This seemingly trivial reformulation has significant implications:…
In this paper, we consider the robustness of a basic model of a dynamical distribution network. In the first problem, i.e., optimal weight allocation, we minimize the H-inf- norm of the dynamical distribution network subject to allocation…
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 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)…
This paper studies the problem of increasing the connectivity of an ad-hoc peer-to-peer network subject to cyber-attacks targeting the agents in the network. The adopted strategy involves the design of local interaction rules for the agents…
Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the…
Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected…
We establish that in distributed optimization, the prevalent strategy of minimizing the second-largest eigenvalue modulus (SLEM) of the averaging matrix for selecting communication weights, while optimal for existing theoretical performance…
For a graph $G$, let $\lambda_2(G)$ denote its second smallest Laplacian eigenvalue. It was conjectured that $\lambda_2(G) + \lambda_2(\overline G) \ge 1$, where $\overline G$ is the complement of $G$. In this paper, it is shown that…
The mathematical framework of multiplex networks has been increasingly realized as a more suitable framework for modelling real-world complex systems. In this work, we investigate the optimization of synchronizability in multiplex networks…
We formulate an optimization problem for maximizing the data rate of a common message transmitted from nodes within an airborne network broadcast to a central station receiver while maintaining a set of intra-network rate demands. Assuming…
Eigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics. In particular, it has been successfully used for proving a number of results about the relation between the (adjacency matrix or Laplacian)…
This paper studies an open consensus network design problem: identifying the optimal simple directed graphs, given a fixed number of vertices and arcs, that maximize the second smallest real part of all Laplacian eigenvalues, referred to as…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…
This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is…
The notion of network connectivity is used to characterize the robustness and failure tolerance of networks, with high connectivity being a desirable feature. In this paper, we develop a novel approach to the problem of identifying critical…