Related papers: Study of higher-order interactions in unweighted, …
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the…
As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural…
Persistent homology is a fundamental tool in topological data analysis; however, it lacks methods to quantify the fragility or fineness of cycles, anticipate their formation or disappearance, or evaluate their stability beyond persistence.…
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…
Complex systems consist of interacting units whose interactions may be pairwise, involving two units, or higher-order, involving more than two units simultaneously. Graphs capture pairwise interactions and represent such systems as…
Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…
Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
In brain network analysis using resting-state fMRI, there is growing interest in modeling higher-order interactions beyond simple pairwise connectivity via persistent homology. Despite the promise of these advanced topological tools, robust…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently…
A hypergraph is a generalization of an ordinary graph, and it naturally represents group interactions as hyperedges (i.e., arbitrary-sized subsets of nodes). Such group interactions are ubiquitous in many domains: the sender and receivers…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…