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In signed networks, each edge is labeled as either positive or negative. The edge sign captures the polarity of a relationship. Balance of signed networks is a well-studied property in graph theory. In a balanced (sub)graph, the vertices…
We study the problem of score and rank monotonicity for spectral ranking methods, such as eigenvector centrality and PageRank, in the case of undirected networks. Score monotonicity means that adding an edge increases the score at both ends…
Biological networks, such as cellular metabolic pathways or networks of corticocortical connections in the brain, are intricately organized, yet remarkably robust toward structural damage. Whereas many studies have investigated specific…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
Is it always beneficial to create a new relationship (have a new follower/friend) in a social network? This question can be formally stated as a property of the centrality measure that defines the importance of the actors of the network.…
Network visualization is essential for many scientific, societal, technological and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication and…
Knowledge graphs play a central role for linking different data which leads to multiple layers. Thus, they are widely used in big data integration, especially for connecting data from different domains. Few studies have investigated the…
Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In…
We study the effect of memory on synchronization of identical chaotic systems driven by common external noises. Our examples show that while in general synchronization transition becomes more difficult to meet when memory range increases,…
Network sparsification aims to reduce the number of edges of a network while maintaining its structural properties; such properties include shortest paths, cuts, spectral measures, or network modularity. Sparsification has multiple…
The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact…
Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional…
Controlling a complex network is of great importance in many applications. The network can be controlled by inputting external control signals through some selected nodes, which are called input nodes. Previous works found that the majority…
Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection…
This paper re-introduces the network reliability polynomial - introduced by Moore and Shannon in 1956 -- for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is…
Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
In this article, we study algorithms for dynamic networks with asynchronous start, i.e., each node may start running the algorithm in a different round. Inactive nodes transmit only heartbeats, which contain no information but can be…
We present a new, novel approach to obtaining a network's connectivity. More specifically, we show that there exists a relationship between a network's graph isoperimetric properties and its conditional connectivity. A network's…