8 citations · 9 across the 3 of their papers we have counts for
7 papers
On the Bipartiteness Constant and Expansion of Cayley Graphs
Nina Moorman, Peter Ralli, Prasad Tetali
Let be a finite, undirected -regular graph and its normalized adjacency matrix, with eigenvalues . It is a classical fact that $λ…
An Alon-Boppana theorem for powered graphs and generalized Ramanujan graphs
Emmanuel Abbe, Peter Ralli
The r-th power of a graph modifies a graph by connecting every vertex pair within distance r. This paper gives a generalization of the Alon-Boppana Theorem for the r-th power of gr…
Graph powering and spectral robustness
Emmanuel Abbe, Enric Boix, Peter Ralli +1
Spectral algorithms, such as principal component analysis and spectral clustering, typically require careful data transformations to be effective: upon observing a matrix , one…
Volume growth, curvature, and Buser-type inequalities in graphs
Brian Benson, Peter Ralli, Prasad Tetali
We study the volume growth of metric balls as a function of the radius in discrete spaces, and focus on the relationship between volume growth and discrete curvature. We improve vo…
Bounds on curvature in regular graphs
Peter Ralli
We study the curvature-dimension inequality in regular graphs. We develop techniques for calculating the curvature of such graphs, and we give characterizations of classes of graph…
Discrete curvature and abelian groups
Bo'az Klartag, Gady Kozma, Peter Ralli +1
We study a natural discrete Bochner-type inequality on graphs, and explore its merit as a notion of curvature in discrete spaces. An appealing feature of this discrete version seem…
Inverse Expander Mixing for Hypergraphs
Emma Cohen, Dhruv Mubayi, Peter Ralli +1
We formulate and prove inverse mixing lemmas in the settings of simplicial complexes and k-uniform hypergraphs. In the hypergraph setting, we extend results of Bilu and Linial for…