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Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…

An ecological network is a formal representation of a specific type of interaction in a corresponding ecosystem. Such networks have traditionally been modelled as encoding exclusively pairwise interactions among the fundamental units of…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the…

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…

Simplicial complexes are increasingly used to study complex system structure and dynamics including diffusion, synchronization and epidemic spreading. The spectral dimension of the graph Laplacian is known to determine the diffusion…

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…

Real networks exhibit nontrivial topological features such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are…

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…

Recent studies have been using graph theoretical approaches to model complex networks (such as social, infrastructural or biological networks), and how their hardwired circuitry relates to their dynamic evolution in time. Understanding how…

Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…

Network synchronization is an emerging phenomenon in complex networks. The spectrum of Laplacian matrix will be immensely helpful for getting the network dynamics information. Especially, network synchronizability is characterized by the…

A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…

One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and…

Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years,…

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and…

For studying intrusion detection data we consider data points referring to individual IP addresses and their connections: We build networks associated with those data points, such that vertices in a graph are associated via the respective…

Despite the vast literature on network dynamics, we still lack basic insights into dynamics on higher-order structures (e.g., edges, triangles, and more generally, $k$-dimensional "simplices") and how they are influenced through…

Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behavior of complex systems under various…