Related papers: Computing the Homology of Hypergraphs
We generalize some homotopy calculation techniques such as splittings and matching trees that are introduced for the computations in the case of the independence complexes of graphs to arbitrary simplicial complexes, and exemplify their…
Directed graphs can be studied by their associated directed flag complex. The homology of this complex has been successful in applications as a topological invariant for digraphs. Through comparison with path homology theory, we derive a…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…
This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets, and to provide computational tools for multipath…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…
Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…
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…
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 propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
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…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for {\em graphs with semi-edges}. The notion of graph covering is a discretization of coverings between surfaces or topological…
In this paper tackle the problem of computing the ranks of certain eulerian magnitude homology groups of a graph G. First, we analyze the computational cost of our problem and prove that it is #W[1]-complete. Then we develop the first…
The entropy of a hierarchical network topology in an ensemble of sparse random networks with "hidden variables" associated to its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble.We obtain a…