Related papers: Topological strata of weighted complex networks
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…
In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…
While branching network structures abound in nature, their objective analysis is more difficult than expected because existing quantitative methods often rely on the subjective judgment of branch structures. This problem is particularly…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
Granular materials exhibit intricate force networks, often concentrated in chains rather than being uniformly distributed. These meso-scale structures are complex to characterize, owing to their heterogeneous and anisotropic nature. We…
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…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Although two-dimensional periodic structures have functioned as the primary platform for exploring topological phenomena, recent advances have substantially expanded this research boundary to include more intricate, aperiodic structures:…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose…
In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this…