5 papers
Sharp Low-Degree Thresholds for Planted-vs-Planted Testing
Anda Skeja, Daniel Gutiérrez Espinoza, Fiona Skerman +1
We establish the first sharp thresholds for low-degree polynomial tests in planted-vs-planted settings, where the goal is to determine with vanishing error which of two structured…
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…
Quantifying Multivariate Graph Dependencies: Theory and Estimation for Multiplex Graphs
Anda Skeja, Sofia C. Olhede
Multiplex graphs, characterised by their layered structure, exhibit informative interdependencies within layers that are crucial for understanding complex network dynamics. Quantif…
Entropy of Exchangeable Random Graphs
Anda Skeja, Sofia C. Olhede
Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative…