121 citations · 199 across the 7 of their papers we have counts for
7 papers
Exploring the space of graphs with fixed discrete curvatures
Michelle Roost, Karel Devriendt, Giulio Zucal +1
Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and th…
Lipschitz regularity of sub-elliptic harmonic maps into CAT(0) spaces
Renan Assimos, Yaoting Gui, Jürgen Jost
We prove the local Lipschitz continuity of sub-elliptic harmonic maps between certain singular spaces, more specifically from the -dimensional Heisenberg group into spa…
Petals and Books: The largest Laplacian spectral gap from 1
Jürgen Jost, Raffaella Mulas, Dong Zhang
We prove that, for any connected graph on vertices, the spectral gap from the value with respect to the normalized Laplacian is at most . Moreover, we show that…
Comparative analysis of two discretizations of Ricci curvature for complex networks
Areejit Samal, R. P. Sreejith, Jiao Gu +3
We have performed an empirical comparison of two distinct notions of discrete Ricci curvature for graphs or networks, namely, the Forman-Ricci curvature and Ollivier-Ricci curvatur…
Systematic evaluation of a new combinatorial curvature for complex networks
R. P. Sreejith, Jürgen Jost, Emil Saucan +1
We have recently introduced Forman's discretization of Ricci curvature to the realm of complex networks. Forman curvature is an edge-based measure whose mathematical definition ele…
Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
Frank Bauer, Jürgen Jost, Shiping Liu
We prove the following estimate for the spectrum of the normalized Laplace operator on a finite graph , \begin{equation*}1- (1- k[t])^{\frac{1}{t}}\leq λ_1 \leq \cdots \leq…
Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplacian
Frank Bauer, Jürgen Jost
We study the spectrum of the normalized Laplace operator of a connected graph . As is well known, the smallest nontrivial eigenvalue measures how difficult it is to decompose $Γ…