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Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…

We present an analytic model specifically designed to address the long standing issue of small scale structure on cosmic string networks. The model is derived from the microscopic string equations, together with a few motivated assumptions.…

We build on recent work of Yeats, Courtiel, and others involving connected chord diagrams. We first derive from a Hopf-algebraic foundation a class of tree-like functional equations and prove that they are solved by weighted generating…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…

Network theory provides a rich toolbox consisting of methods, measures, and models for studying the structure and dynamics of complex systems found in nature, society, or technology. Recently, it has been pointed out that many real-world…

When dealing with evolving or multi-dimensional complex systems, network theory provides with elegant ways of describing their constituting components, through respectively time-varying and multi-layer complex networks. Nevertheless, the…

The study of networks has grown into a substantial interdisciplinary endeavour that encompasses myriad disciplines in the natural, social, and information sciences. Here we introduce a framework for constructing taxonomies of networks based…

Transformer architectures offer significant advantages regarding the generation of symbolic music; their capabilities for incorporating user preferences toward what they generate is being studied under many aspects. This paper studies the…

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…

Directed networks are ubiquitous and are necessary to represent complex systems with asymmetric interactions---from food webs to the World Wide Web. Despite the importance of edge direction for detecting local and community structure, it…

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…

It is known for decades that computer-based systems cannot be understood without a concept of modularization and decomposition. We suggest a universal, expressive, intuitively attractive composition operator for Petri nets, combined with a…

Motif counting plays a crucial role in understanding the structural properties of networks. By computing motif frequencies, researchers can draw key insights into the structural properties of the underlying network. As networks become…

In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random…

Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…

We employ the recently developed theory of isospectral network reductions to analyze multi-mode social networks. This procedure allows us to uncover the hierarchical structure of the networks we consider as well as the hierarchical…

Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…

We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…