Ricci curvature, graphs and eigenvalues

نویسندگان

چکیده

We express the discrete Ricci curvature of a graph as minimal eigenvalue family matrices, one for each vertex whose entries depend on local adjacency structure graph. Using this method we compute or bound Cayley graphs finite Coxeter groups and affine Weyl groups. As an application obtain isoperimetric inequality that holds all

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Ricci Curvature of Graphs

We modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the properties of the Ricci curvature of general graphs, Cartesian product of graphs, random graphs, and some special class of graphs.

متن کامل

Exact and asymptotic results on coarse Ricci curvature of graphs

Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has been studied extensively in the context of graphs in recent years. In this paper we obtain the exact formulas for Ollivier’s Ricci-curvature for bipartite graphs and for the graphs with girth at least 5. These are the first formulas for Ricci-curvature that hold for a wide class of graphs, and e...

متن کامل

Harnack inequalities for graphs with non-negative Ricci curvature

a r t i c l e i n f o a b s t r a c t Keywords: The Laplace operator for graphs The Harnack inequalities Eigenvalues Diameter We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results for Ricci flat graphs.

متن کامل

Lower Bounds of the First Closed and Neumann Eigenvalues of Compact Manifolds with Positive Ricci Curvature

We give new estimates on the lower bounds for the first closed and Neumann eigenvalues for the compact manifolds with positive Ricci curvature in terms of the diameter and the lower bound of Ricci curvature.

متن کامل

Positive Ricci Curvature

We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homotopy spheres Σ the moduli space of Sasakian structures has infinitely many positive components det...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Linear Algebra and its Applications

سال: 2021

ISSN: ['1873-1856', '0024-3795']

DOI: https://doi.org/10.1016/j.laa.2021.02.026