Networks are mathematical structures that are universally used to describe a large variety of
complex systems such as the brain or the Internet. Characterizing the geometrical properties …

Centrality metrics have been studied in the network science research. They have been used
in various networks, such as communication, social, biological, geographic, or contact …

In the near future, value streams associated with Industry 4.0 will be formed by
interconnected cyber–physical elements forming complex networks that generate huge …

Networks are topological and geometric structures used to describe systems as different as
the Internet, the brain, or the quantum structure of space-time. Here we define complex …

Connections between continuous and discrete worlds tend to be elusive. One example is
curvature. Even though there exist numerous nonequivalent definitions of graph curvature …

Cheeger inequalities for unbounded graph Laplacians Page 1 DOI 10.4171/JEMS/503 J. Eur.
Math. Soc. 17, 259–271 c European Mathematical Society 2015 Frank Bauer · Matthias Keller …

The main focus in this memoir is on Laplacians on both weighted graphs and weighted
metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not …

We apply Alexandrov geometry methods to study geometric analysis aspects of infinite
semiplanar graphs with nonnegative combinatorial curvature. We obtain the metric …

We study complex networks formed by triangulations and higher-dimensional simplicial
complexes representing closed evolving manifolds. In particular, for triangulations, the set of …

The goal of this work is to evaluate a deep learning algorithm that has been designed to
predict the topological evolution of dynamic complex non-Euclidean graphs in discrete–time …