118 citations · 689 across the 53 of their papers we have counts for
6 papers · 1 filter
The critical exponent: a novel graph invariant
Dominique Guillot, Apoorva Khare, Bala Rajaratnam
A surprising result of FitzGerald and Horn (1977) shows that is positive semidefinite (p.s.d.) for every entrywise nonnegative p.s.d. matri…
Model-free consistency of graph partitioning
Peter Diao, Dominique Guillot, Apoorva Khare +1
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Bo…
Critical exponents of graphs
Dominique Guillot, Apoorva Khare, Bala Rajaratnam
The study of entrywise powers of matrices was originated by Loewner in the pursuit of the Bieberbach conjecture. Since the work of FitzGerald and Horn (1977), it is known that $A^{…
Differential calculus on the space of countable labelled graphs
Apoorva Khare, Bala Rajaratnam
The study of very large graphs is a prominent theme in modern-day mathematics. In this paper we develop a rigorous foundation for studying the space of finite labelled graphs and t…
Differential Calculus on Graphon Space
Peter Diao, Dominique Guillot, Apoorva Khare +1
Recently, the theory of dense graph limits has received attention from multiple disciplines including graph theory, computer science, statistical physics, probability, statistics,…
Sparse Matrix Decompositions and Graph Characterizations
Kshitij Khare, Bala Rajaratnam
The question of when zeros (i.e., sparsity) in a positive definite matrix are preserved in its Cholesky decomposition, and vice versa, was addressed by Paulsen et al. in the Jo…