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Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on…
Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…
In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on…
This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity)…
Empirical contact networks or interaction networks demonstrate peculiar characteristics stemming from the fundamental social, psychological, physical mechanisms governing human interactions. Although these mechanisms are complex, we test…
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…
Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical…
Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the…
Motivated by the relationship between the eigenvalue spectrum of the Laplacian matrix of a network and the behavior of dynamical processes evolving in it, we propose a distributed iterative algorithm in which a group of $n$ autonomous…
Calculating a product of multiple graphs has been studied in mathematics, engineering, computer science, and more recently in network science, particularly in the context of multilayer networks. One of the important questions to be…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely…
While kernel methods and Graph Neural Networks offer complementary strengths, integrating the two has posed challenges in efficiency and scalability. The Graph Neural Tangent Kernel provides a theoretical bridge by interpreting GNNs through…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
We present a novel theoretical framework connecting k-component edge connectivity with spectral graph theory and homology theory to pro vide new insights into the resilience of real-world networks. By extending classical edge connectivity…
In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], Schneider et al. proposed a new measure for network robustness and investigated optimal networks with respect to this quantity. For networks with a power-law degree…
Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the…
Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections…
We introduce simplicial persistence, a measure of time evolution of network motifs in subsequent temporal layers. We observe long memory in the evolution of structures from correlation filtering, with a two regime power law decay in the…
Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties…