Related papers: Are networks with more edges easier to synchronize…
Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in…
The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of…
This paper investigates the impact of addition/removal of edges in a complex networked control system, for the purposes of improving its controllability, system performances or robustness to external disturbances. The transfer function…
Many, if not most network analysis algorithms have been designed specifically for single-relational networks; that is, networks in which all edges are of the same type. For example, edges may either represent "friendship," "kinship," or…
Communities often represent key structural and functional clusters in networks. To preserve such communities, it is important to understand their robustness under network perturbations. Previous work in community robustness analysis has…
Edges in a network can be divided into two kinds according to their different roles: some enhance the locality like the ones inside a cluster while others contribute to the global connectivity like the ones connecting two clusters. A recent…
Recent studies have shown that synchronizability of complex networks can be significantly improved by asymmetric couplings, and increase of coupling gradient is always in favor of network synchronization. Here we argue and demonstrate that,…
In order to conduct analyses of networked systems where connections between individuals take on a range of values - counts, continuous strengths or ordinal rankings - a common technique is to dichotomize the data according to their…
In this paper, we present an algorithm for optimizing synchronizability of complex dynamical networks. Based on some network properties, rewirings, i.e. eliminating an edge and creating a new edge elsewhere, are performed iteratively…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…
In this paper, we investigate the factors that affect the synchronization of coupled oscillators on networks. By using the edge-intercrossing method, we keep the degree distribution unchanged to see other statistical properties' effects on…
Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…
Previous research claimed or disclaimed the role of a small diameter in the synchronization of a network of coupled dynamical systems. We investigate this connection and show that it is two folds. We first construct two classes of networks,…
We investigate the effects of structural perturbations of both, undirected and directed diffusive networks on their ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We…
Graph Neural Networks (GNNs) as deep learning models working on graph-structure data have achieved advanced performance in many works. However, it has been proved repeatedly that, not all edges in a graph are necessary for the training of…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…
With the rapid growth of online social networks, strengthening their stability has emerged as a key research focus. This study aims to identify influential relationships that significantly impact community stability. In this paper, we…
Many real-world complex networks simultaneously exhibit topological features of scale-free behaviour and hierarchical organization. In this regard, deterministic scale-free [A.-L. Barab\'asi \etal, Physica A, 299, 3 (2001)] and…
Complex networks are made up of vertices and edges. The latter connect the vertices. There are several ways to measure the importance of the vertices, e.g., by counting the number of edges that start or end at each vertex, or by using the…