Related papers: Offdiagonal complexity: A computationally quick ne…
A prominent tool in many problems involving metric spaces is a notion of randomized low-diameter decomposition. Loosely speaking, $\beta$-decomposition refers to a probability distribution over partitions of the metric into sets of low…
Networks are versatile representations of the interactions between entities in complex systems. Cycles on such networks represent feedback processes which play a central role in system dynamics. In this work, we introduce a measure of the…
Determining causal inference has become popular in physical and engineering applications. While the problem has immense challenges, it provides a way to model the complex networks by observing the time series. In this paper, we present the…
The use of graph centrality measures applied to biological networks, such as protein interaction networks, underpins much research into identifying key players within biological processes. This approach however is restricted to dyadic…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
The transmission of a vertex $v$ of a graph $G$ is the sum of distances from $v$ to all the other vertices in $G$. The Wiener complexity of $G$ is the number of different transmissions of its vertices. Similarly, the eccentric complexity of…
The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…
Event logs are widely used to record the status of high-tech systems, making log anomaly detection important for monitoring those systems. Most existing log anomaly detection methods take a log event count matrix or log event sequences as…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
Complex networks have become increasingly popular for modeling various real-world phenomena. Realistic generative network models are important in this context as they avoid privacy concerns of real data and simplify complex network research…
We study the widely used hierarchical agglomerative clustering (HAC) algorithm on edge-weighted graphs. We define an algorithmic framework for hierarchical agglomerative graph clustering that provides the first efficient $\tilde{O}(m)$ time…
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…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
While branching network structures abound in nature, their objective analysis is more difficult than expected because existing quantitative methods often rely on the subjective judgment of branch structures. This problem is particularly…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
The betweenness centrality (BC) is an important quantity for understanding the structure of complex large networks. However, its calculation is in general difficult and known in simple cases only. In particular, the BC has been exactly…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…
Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. In order to compute the various topological descriptors commonly used to characterize the structure of…