Related papers: Are networks with more edges easier to synchronize…
This brief paper further investigates the locally and globally adaptive synchronization of an uncertain complex dynamical network. Several network synchronization criteria are deduced. Especially, our hypotheses and designed adaptive…
A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a…
In the past few years, the discoveries of small-world and scale-free properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the…
This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying…
Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to…
In a cost sharing problem on a weighted undirected graph, all other nodes want to connect to the source node for some service. Each edge has a cost denoted by a weight and all the connected nodes should share the total cost for the…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
The random matrix theory is used to bridge the network structures and the dynamical processes defined on them. We propose a possible dynamical mechanism for the enhancement effect of network structures on synchronization processes, based…
In social network, a person located at the periphery region (marginal node) is likely to be treated unfairly when compared with the persons at the center. While existing fairness works on graphs mainly focus on protecting sensitive…
We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of…
The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is commonly focalised on edge processes, and a dual edge-centric perspective can…
We investigate the optimization of synchronizability in multiplex networks and demonstrate that the interlayer coupling strength is the deciding factor for the efficiency of optimization. The optimized networks have homogeneity in the…
This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this…
Synchronization is essential for proper functioning of the power grid. We investigate the synchronous state and its stability for a network with a cyclic topology and with the evolution of the states satisfying the swing equations. We…
Network centrality plays an important role in many applications. Central nodes in social networks can be influential, driving opinions and spreading news or rumors.In hyperlinked environments, such as the Web, where users navigate via…
We consider network structures that optimize the $\mathcal{H}_2$ norm of weighted, time scaled consensus networks, under a minimal representation of such consensus networks described by the edge Laplacian. We show that a greedy algorithm…
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by additionally making use of graph structure based on the relational inductive bias (edge bias), rather than treating the nodes as collections of independent and identically…
Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these…
In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average…
Networks describing the interaction of the elements that constitute a complex system grow and develop via a number of different mechanisms, such as the addition and deletion of nodes, the addition and deletion of edges, as well as the…