Related papers: Maximizing the algebraic connectivity in multilaye…
We introduce a measure of {\em greedy connectivity} for geographical networks (graphs embedded in space) and where the search for connecting paths relies only on local information, such as a node's location and that of its neighbors.…
We explore how to study dynamical interactions between brain regions using functional multilayer networks whose layers represent the different frequency bands at which a brain operates. Specifically, we investigate the consequences of…
The problem of connectivity assessment in an asymmetric network represented by a weighted directed graph is investigated in this article. A power iteration algorithm in a centralized implementation is developed first to compute the…
In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power…
The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, structure identification from…
The interference at a wireless node s can be modelled by the number of wireless nodes whose transmission ranges cover s. Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius…
The algebraic connectivity $a(G)$, defined as the second smallest eigenvalue of the Laplacian matrix $L(G)$, admits a well-known variational characterization involving the minimization of a quadratic form subject to an $\ell_{2}$-norm…
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…
Embedding the vertices of arbitrary graphs into trees while minimizing some measure of overlap is an important problem with applications in computer science and physics. In this work, we consider the problem of bijectively embedding the…
Denote the Laplacian of a graph $G$ by $L(G)$ and its second smallest Laplacian eigenvalue by $\lambda_2(G)$. If $G$ is a graph on $n\ge 2$ vertices, then it is shown that the second smallest eigenvalue of $L(G) + \frac{1}{n}…
Given a set of wireless links, a fundamental problem is to find the largest subset that can transmit simultaneously, within the SINR model of interference. Significant progress on this problem has been made in recent years. In this note, we…
We derive a number of upper and lower bounds for the first nontrivial eigenvalue of a finite quantum graph in terms of the edge connectivity of the graph, i.e., the minimal number of edges which need to be removed to make the graph…
The algebraic connectivity $a(G)$ of a graph $G$ is defined as the second smallest eigenvalue of its Laplacian matrix $L(G)$. It also admits a variational characterization as the minimum of a quadratic form associated with $L(G)$, subject…
In this paper we characterize the unique graph whose algebraic connectivity is minimum among all connected graphs with given order and fixed matching number or edge covering number, and present two lower bounds for the algebraic…
Motivated by its relevance to various types of dynamical behavior of network systems, the maximum eigenvalue $\lambda_Q$ of the adjacency matrix $A$ of a network has been considered, and mean-field-type approximations to $\lambda_Q$ have…
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…
We study the problem of maximizing sum rates in a Gaussian interference-limited channel that models multiuser communication in a CDMA wireless network or DSL cable binder. Using tools from nonnegative irreducible matrix theory, in…
We study the allocation of indivisible goods that form an undirected graph and quantify the loss of fairness when we impose a constraint that each agent must receive a connected subgraph. Our focus is on well-studied fairness notions…
The way the topological structure transforms from a decoupled to a coupled state in multiplex networks has been extensively studied through both analytical and numerical approaches, often utilizing models of artificial networks. These…
We study the multi-message broadcast problem using abstract MAC layer models of wireless networks. These models capture the key guarantees of existing MAC layers while abstracting away low-level details such as signal propagation and…