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Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…

Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…

Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their…

We introduce a network growth model based on complete redirection: a new node randomly selects an existing target node, but attaches to a random neighbor of this target. For undirected networks, this simple growth rule generates unusual,…

While gradient descent has proven highly successful in learning connection weights for neural networks, the actual structure of these networks is usually determined by hand, or by other optimization algorithms. Here we describe a simple…

We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…

Resilience characterizes a system's ability to retain its original function when perturbations happen. In the past years our attention mainly focused on small-scale resilience, yet our understanding of resilience in large-scale network…

The minimal number of nodes required to multilaterate a network endowed with geodesic distance (i.e., to uniquely identify all nodes based on shortest path distances to the selected nodes) is called its metric dimension. This quantity is…

Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing…

Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex…

Bipartite networks appear in many real-world contexts, linking entities across two distinct sets. They are often analyzed via one-mode projections, but such projections can introduce artificial correlations and inflated clustering,…

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…

We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…

Network controllability is a powerful tool to study causal relationships in complex systems and identify the driver nodes for steering the network dynamics into desired states. However, due to ill-posed conditions, results become unreliable…

Many real world networks, such as social networks, are primarily formed through local interactions between agents. Additionally, in contrast with common network models, social and biological networks exhibit a high degree of clustering.…

Creating new ties in a social network facilitates knowledge exchange and affects positional advantage. In this paper, we study the process, which we call network building, of establishing ties between two existing social networks in order…

Experimentally observed complex networks are often scale-free, small-world and have unexpectedly large number of small cycles. Apollonian network is one notable example of a model network respecting simultaneously having all three of these…

Heteroclinic cycles and networks are structures in dynamical systems composed of invariant sets and connecting heteroclinic orbits, and can be robust in systems with invariant subspaces. The usual method for analysing the stability of…

In this article the generalized Lotka-Volterra model of ensemble of four excitory or inhibitory coupled elements are studied. It is shown that in the phase space of the model there exist heteroclinic network: a connected union of two or…

Multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features, which may vary across the networks. This paper introduces a class of models for…