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Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
The present paper studies local distributed graph problems in highly dynamic networks. Communication and changes of the graph happen in synchronous rounds and our algorithms always, i.e., in every round, satisfy non-trivial guarantees, no…
{\em Algorithms with predictions} incorporate machine learning predictions into algorithm design. A plethora of recent works incorporated predictions to improve on worst-case optimal bounds for online problems. In this paper, we initiate…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
The Capsule Network is widely believed to be more robust than Convolutional Networks. However, there are no comprehensive comparisons between these two networks, and it is also unknown which components in the CapsNet affect its robustness.…
We study the problem of resilient consensus of sampled-data multi-agent networks with double-integrator dynamics. The term resilient points to algorithms considering the presence of attacks by faulty/malicious agents in the network. Each…
Complex networks are ubiquitous: a cell, the human brain, a group of people and the Internet are all examples of interconnected many-body systems characterized by macroscopic properties that cannot be trivially deduced from those of their…
In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…
Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an…
Graphlet counting is an important problem as it has numerous applications in several fields, including social network analysis, biological network analysis, transaction network analysis, etc. Most of the practical networks are dynamic. A…
Spreading information through a network of devices is a core activity for most distributed systems. As such, self-stabilizing algorithms implementing information spreading are one of the key building blocks enabling aggregate computing to…
The $k$-core decomposition in a graph is a fundamental problem for social network analysis. The problem of $k$-core decomposition is to calculate the core number for every node in a graph. Previous studies mainly focus on $k$-core…
Time-evolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one…
We introduce a method that can be used to evolve the topology of a network in a way that preserves both the network's spectral as well as local structure. This method is quite versatile in the sense that it can be used to evolve a network's…
A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the…
This paper focuses on network resilience to perturbation of edge weight. Other than connectivity, many network applications nowadays rely upon some measure of network distance between a pair of connected nodes. In these systems, a metric…
We compare asynchronous vs. synchronous update of discrete dynamical networks and find that a simple time delay in the nodes may induce a reproducible deterministic dynamics even in the case of asynchronous update in random order. In…
With the rise of deep neural networks, the challenge of explaining the predictions of these networks has become increasingly recognized. While many methods for explaining the decisions of deep neural networks exist, there is currently no…
We suggest to simulate evolution of complex organisms constrained by the sole requirement of robustness in their expression patterns. This scenario is illustrated by evolving discrete logical networks with epigenetic properties. Evidence…