Related papers: Are networks with more edges easier to synchronize…
The spectral gap for Laplace operators on metric graphs is investigated in relation to graph's connectivity, in particular what happens if an edge is added to (or deleted from) a graph. It is shown that in contrast to discrete graphs…
We resolve a conjecture of Hegarty regarding the number of edges in the square of a regular graph. If $G$ is a connected $d$-regular graph with $n$ vertices, the graph square of $G$ is not complete, and $G$ is not a member of two narrow…
Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure…
Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the…
The problem of increasing the centrality of a network node arises in many practical applications. In this paper, we study the optimization problem of maximizing the information centrality $I_v$ of a given node $v$ in a network with $n$…
Reliability and determinism of Wi-Fi can be tangibly improved by means of seamless redundancy, to the point of making this technology suitable for industrial environments. As pointed out in recent papers, the most benefits can be achieved…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…
Replacing conventional power sources by renewable sources in current power grids drastically alters their structure and functionality. The resulting grid will be far more decentralized with an distinctly different topology. Here we analyze…
We study synchronization in heterogeneous FitzHugh-Nagumo networks. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. Here, we develop a controller to counteract the impact of these…
The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks call for an explanation of…
Recently a distributed algorithm has been proposed for multi-agent networks to solve a system of linear algebraic equations, by assuming each agent only knows part of the system and is able to communicate with nearest neighbors to update…
Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in an undirected graph, subject to edge insertions and deletions.…
Complex networks grow subject to structural constraints which affect their measurable properties. Assessing the effect that such constraints impose on their observables is thus a crucial aspect to be taken into account in their analysis. To…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree…
Recent studies have explored the addition of virtual edges to word co-occurrence networks using word embeddings to enhance graph representations, particularly for short texts. While these enriched networks have demonstrated some success,…
Localization is a fundamental task for sensor networks. Traditional network construction approaches allow to obtain localized networks requiring the nodes to be at least tri-connected (in 2D), i.e., the communication graph needs to be…
A very interesting matter of Network Science is assessing how complex a given network is. In other words, by how much does such a network departs from any general patterns which could be evoked for its description. Among other choices,…
We analyse signed networks from the perspective of balance theory which predicts structural balance as a global structure for signed social networks that represent groups of friends and enemies. The scarcity of balanced networks encouraged…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…