Related papers: Are networks with more edges easier to synchronize…

Heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators. Scale-free networks display a great deal of heterogeneity, containing a few nodes, termed hubs,…

Short cycles connectivity is a generalization of ordinary connectivity. Instead by a path (sequence of edges), two vertices have to be connected by a sequence of short cycles, in which two adjacent cycles have at least one common vertex. If…

Graph neural networks (GNNs) extend convolutional neural networks (CNNs) to graph-based data. A question that arises is how much performance improvement does the underlying graph structure in the GNN provide over the CNN (that ignores this…

In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…

We consider the impact of network connectivity on the dynamics of a population in a stream environment. The population is modeled using a graph theoretical framework, with habitats represented by isolated patches. We introduce a change in…

We investigate the transition to synchronization in a two-layer network with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the time-scale of topological changes. Initially, we observe a smooth…

The problem of worst case edge deletion from a network is considered. Suppose that you have a communication network and you can delete a single edge. Which edge deletion causes the largest disruption? More formally, given a graph, which…

This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…

In this paper the effects of external links on the synchronization performance of community networks, especially on the competition between individual community and the whole network, are studied in detail. The study is organized from two…

One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…

We study the robustness of complex networks subject to edge removal. Several network models and removing strategies are simulated. Rather than the existence of the giant component, we use total connectedness as the criterion of breakdown.…

A bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components. We calculate the fraction of bridges in a wide range of real-world networks and their randomized counterparts. We find that…

Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for…

Cycles are ubiquitous in various networks such as social, biological, and technological systems, where they play a significant functional and dynamical role. This paper proposes a node similarity measure based on minimal simple cycles,…

We study the impact of interaction of nodes in a layer of a multiplex network on the dynamical behavior and cluster synchronization of these nodes in other layers. We find that nodes interactions in one layer affects the cluster…

The width of a neural network matters since increasing the width will necessarily increase the model capacity. However, the performance of a network does not improve linearly with the width and soon gets saturated. In this case, we argue…

The propensity for synchronization is studied in a complex network of asymmetrically coupled units, where the asymmetry in a given link is determined by the relative age of the involved nodes. In growing scale-free networks synchronization…

Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous…

Graph modification problems with the goal of optimizing some measure of a given node's network position have a rich history in the algorithms literature. Less commonly explored are modification problems with the goal of equalizing…