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Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how…

Many real-world networks exhibit hierarchical, tree-like structure and heavy-tailed degree distributions, phenomena not readily captured by standard statistical models for network data. Extensions of the popular continuous latent space…

Real world networks have, for a long time, been modelled by scale-free networks, which have many sparsely connected nodes and a few highly connected ones (the hubs). However, both in society and in biology, a new structure must be…

Randomly connected neural networks have long served as a theoretical tool for studying collective dynamics in neural populations, yet quantitative comparisons to experiments remain limited. Recent technological advances have made it…

Empirical complex systems must differentially respond to external perturbations and, at the same time, internally distribute information to coordinate their components. While networked backbones help with the latter, they limit the…

Many real-world complex systems such as social, biological, information as well as technological systems results of a decentralized and unplanned evolution which leads to a common structuration. Irrespective of their origin, these so-called…

The latent space approach to complex networks has revealed fundamental principles and symmetries, enabling geometric methods. However, the conditions under which network topology implies geometricity remain unclear. We provide a…

Although the community structure organization is one of the most important characteristics of real-world networks, the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for…

One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…

Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has…

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…

We study typical distances in a geometric random graph on the hyperbolic plane. Introduced by Krioukov et al.~\cite{ar:Krioukov} as a model for complex networks, $N$ vertices are drawn randomly within a bounded subset of the hyperbolic…

We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an $m$-dimensional metric space with power-law distributed…

One of the defining features of complex networks is the connectivity properties that we observe emerging from local interactions. Recently, hypergraphs have emerged as a versatile tool to model networks with non-dyadic, higher-order…

Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…

Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic…

How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…

Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…

All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are…

Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…