Related papers: Stable Homology-Based Cycle Centrality Measures

Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes…

Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best…

Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under…

In complex networks, each node has some unique characteristics that define the importance of the node based on the given application-specific context. These characteristics can be identified using various centrality metrics defined in the…

The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of the space of data, a persistence barcode tracks the evolution of its homological features. In this…

Persistent homology is a branch of computational algebraic topology that studies shapes and extracts features over multiple scales. In this paper, we present an unsupervised approach that uses persistent homology to study divergent behavior…

Finding the important nodes in complex networks by topological structure is of great significance to network invulnerability. Several centrality measures have been proposed recently to evaluate the performance of nodes based on their…

Topological Data Analysis (TDA) is a field that leverages tools and ideas from algebraic topology to provide robust methods for analysing geometric and topological aspects of data. One of the principal tools of TDA, persistent homology,…

A fundamental problem in the study of networks is the identification of important nodes. This is typically achieved using centrality metrics, which rank nodes in terms of their position in the network. This approach works well for static…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…

Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…

Interconnected networks of rigid struts are critical for application in lightweight, load-bearing structures. However, accurately modeling stress distribution in these strut lattices poses significant computational challenges due to its…

The problem of assigning centrality values to nodes and edges in graphs has been widely investigated during last years. Recently, a novel measure of node centrality has been proposed, called k-path centrality index, which is based on the…

In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…

Topological Data Analysis (TDA) provides powerful tools to explore the shape and structure of data through topological features such as clusters, loops, and voids. Persistence diagrams are a cornerstone of TDA, capturing the evolution of…

The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks the evolution of its homology groups. In this paper, we…

Modeling the associations between real world entities from their multivariate cross-sectional profiles can provide cues into the concerted working of these entities as a system. Several techniques have been proposed for deciphering these…

Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…

We propose a practical computational framework for detecting structural changes in parameter-dependent topological data. In many applications, such as time-series data analysis, anomaly detection, and monitoring of systems under changing…