Abstract Information networks are becoming increasingly popular to capture complex
relationships across various disciplines, such as social networks, citation networks, and …

Develo** sensitive and reliable methods to distinguish normal and abnormal brain states
is a key neuroscientific challenge. Topological Data Analysis, despite its relative novelty …

While standard persistent homology has been successful in extracting information from
metric datasets, its applicability to more general data, eg directed networks, is hindered by …

We study two methods for computing network features with topological underpinnings: the
Rips and Dowker persistent homology diagrams. Our formulations work for general …

A graph homomorphism is a map between two graphs that preserves adjacency relations.
We consider the problem of sampling a random graph homomorphism from a graph into a …

Persistent homology theory provides approaches for analyzing topological features, which is
now widely applied in graph comparison on social networks, biological networks, and co …

We provide a characterization of two types of directed homology for fully-connected,
feedforward neural network architectures. These exact characterizations of the directed …

Abstract We study Vietoris–Rips complexes of metric wedge sums and metric gluings. We
show that the Vietoris–Rips complex of a wedge sum, equipped with a natural metric, is …

Path homology is a powerful method for attaching algebraic invariants to digraphs. While
there have been growing theoretical developments on the algebro-topological framework …

Pattern detection in network models provides insights to both global structure and local node
interactions. In particular, studying patterns embedded within remittance and migration flow …