4 papers
Effective Resistance in Simplicial Complexes as Bilinear Forms: Generalizations and Properties
Inés García-Redondo, Claudia Landi, Sarah Percival +3
The concept of effective resistance, originally introduced in electrical circuit theory, has been extended to the setting of graphs by interpreting each edge as a resistor. In this…
Finding the Cores of Higher Graphs Using Geometric and Topological Means: A Survey
Inés García-Redondo, Claudia Landi, Sarah Percival +3
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, al…
Towards an Optimal Bound for the Interleaving Distance on Mapper Graphs
Erin Wolf Chambers, Ishika Ghosh, Elizabeth Munch +2
Mapper graphs are widely used tools in topological data analysis and visualization. They can be understood as discrete approximations of Reeb graphs, providing insight into the sha…
A Distance for Geometric Graphs via the Labeled Merge Tree Interleaving Distance
Erin Wolf Chambers, Elizabeth Munch, Sarah Percival +1
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and prese…