1 citations · 1 across the 10 of their papers we have counts for
10 papers
Graphon as a Bridge between Graphs and Manifolds
Dong Zhang
We show that there exist graphons that interpolate between Riemannian manifolds and weighted geometric graphs. Specifically, the graph-to-manifold approximation used in manifold le…
Choquet-type extensions of set-pair functions, and applications in graph limits, hypergraphs, and metric measure spaces
Dong Zhang
We propose Choquet-type extensions for set-pair functions, an -integration of a family of such extensions, and the associated min-max extension constants, and apply these to i…
From the discrete to the continuous, from simplicial complexes to Riemannian manifolds. Approximating flows and cuts on manifolds by discrete versions
Marzieh Eidi, Juergen Jost, Dong Zhang
Many fundamental structures of Riemannian geometry have found discrete counterparts for graphs or combinatorial ones for simplicial complexes. These include those discussed in this…
Combinatorial Courant-Fischer-Weyl Minimax Principle on Cheeger -constants of Weighted Forests
Zijun Meng, Dong Zhang
We present several max-min and minimax characterizations of Cheeger -constants in weighted forests, thereby providing the first combinatorial analogue of the Courant-\\Fischer-W…
Finite projective planes meet spectral gaps
Yuhan Guo, Dong Zhang
We show that for any connected graph with maximum degree , the spectral gap from with respect to the adjacency matrix is at most , with equality if and o…
Notes on suu Chern-Simons theory and Torsional Newton-Cartan gravity
Yang Lei, Dong Zhang
In this study, we investigate three-dimensional torsional Newton-Cartan (TNC) gravity by gauging the suu algebra and construct its action using the Chern-Simons t…
Nonlinear spectral graph theory
Piero Deidda, Francesco Tudisco, Dong Zhang
Nonlinear spectral graph theory is an extension of the traditional (linear) spectral graph theory and studies relationships between spectral properties of nonlinear operators defin…
Equivalent spectral theory for fundamental graph cut problems
Sihong Shao, Chuan Yang, Dong Zhang +1
We introduce and develop equivalent spectral graph theory for several fundamental graph cut problems including maxcut, mincut, Cheeger cut, anti-Cheeger cut, dual Cheeger problem a…
Introduction to graph theory and basic algorithms
Mikhail Tuzhilin, Dong Zhang
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. G…
New graph invariants based on -Laplacian eigenvalues
Chuanyuan Ge, Shiping Liu, Dong Zhang
We present monotonicity inequalities for certain functions involving eigenvalues of -Laplacians on signed graphs with respect to . Inspired by such monotonicity, we propose n…