Related papers: Emergent Hyperbolic Network Geometry
Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…
In recent years, there has been a growing recognition that higher-order structures are important features in real-world networks. A particular class of structures that has gained prominence is known as a simplicial complex. Despite their…
Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…
Simplicial complexes are gaining increasing scientific attention as they are generalized network structures that can represent the many-body interactions existing in complex systems raging from the brain to high-order social networks.…
Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…
Networks are fundamental for our understanding of complex systems. Interactions between individual nodes in networks generate network motifs - small recurrent patterns that can be considered the network's building-block components,…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…
We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure. Using a gravitationally motivated action with…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
We study when co-evolving (or adaptive) higher-order networks defined on directed hypergraphs admit a simplicial description. Binary and triadic couplings are modelled by time-dependent weight tensors. Using representation theory of the…
Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
Recent years have shown a promising progress in understanding geometric underpinnings behind the structure, function, and dynamics of many complex networks in nature and society. However these promises cannot be readily fulfilled and lead…
A complex system with many interacting individuals can be represented by a network consisting of nodes and links representing individuals and pairwise interactions, respectively. However, real-world systems grow with time and include many…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…
Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading,…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…