19 citations · 20 across the 6 of their papers we have counts for
8 papers
Geometric characterisation of structural and regular equivalences in undirected (hyper)graphs
Marzieh Eidi, Nina Otter
Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We gener…
From the discrete to the continuous, from simplicial complexes to Riemannian manifolds. Approximating flows and cuts on manifolds by discrete versions
Marzieh Eidi, Juergen Jost, Dong Zhang
Many fundamental structures of Riemannian geometry have found discrete counterparts for graphs or combinatorial ones for simplicial complexes. These include those discussed in this…
Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing
Diaaeldin Taha, James Chapman, Marzieh Eidi +2
Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data. However, phenomena such as oversquashing in topological me…
Higher Order Bipartiteness vs Bi-Partitioning in Simplicial Complexes
Marzieh Eidi, Sayan Mukherjee
Bipartite graphs are a fundamental concept in graph theory with diverse applications. A graph is bipartite iff it contains no odd cycles, a characteristic that has many implication…
Irreducibility of Markov Chains on simplicial complexes, the Spectrum of the Discrete Hodge Laplacian and Homology
Marzieh Eidi, Sayan Mukherjee
Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability,…
Floer Homology: From Generalized Morse-Smale Dynamical Systems to Forman's Combinatorial Vector Fields
Marzieh Eidi, Jürgen Jost
We construct a Floer type boundary operator for generalised Morse-Smale dynamical systems on compact smooth manifolds by counting the number of suitable flow lines between closed (…
Edge-based analysis of networks: Curvatures of graphs and hypergraphs
Marzieh Eidi, Amirhossein Farzam, Wilmer Leal +2
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergr…
Ollivier Ricci Curvature of Directed Hypergraphs
Marzieh Eidi, Jürgen Jost
We develop a definition of Ricci curvature on directed hypergraphs and explore the consequences of that definition. The definition generalizes Ollivier's definition for graphs. It…