Generalized Ricci curvature and the geometry of graphs

Frank Bauer; Bobo Hua; Jürgen Jost; Shiping Liu

Actes des rencontres du CIRM (2013)

  • Volume: 3, Issue: 1, page 69-78
  • ISSN: 2105-0597

How to cite


Bauer, Frank, et al. "Generalized Ricci curvature and the geometry of graphs." Actes des rencontres du CIRM 3.1 (2013): 69-78. <>.

author = {Bauer, Frank, Hua, Bobo, Jost, Jürgen, Liu, Shiping},
journal = {Actes des rencontres du CIRM},
language = {eng},
month = {11},
number = {1},
pages = {69-78},
publisher = {CIRM},
title = {Generalized Ricci curvature and the geometry of graphs},
url = {},
volume = {3},
year = {2013},

AU - Bauer, Frank
AU - Hua, Bobo
AU - Jost, Jürgen
AU - Liu, Shiping
TI - Generalized Ricci curvature and the geometry of graphs
JO - Actes des rencontres du CIRM
DA - 2013/11//
VL - 3
IS - 1
SP - 69
EP - 78
LA - eng
UR -
ER -


  1. F. Bauer, F. M. Atay, J. Jost, Synchronized chaos in networks of simple units, EPL (Europhysics Letters) 89 (2010) 
  2. Frank Bauer, Normalized graph Laplacians for directed graphs., Linear Algebra Appl. 436 (2012), 4193-4222 Zbl1241.05066MR2915277
  3. Frank Bauer, Fatihcan M. Atay, Jürgen Jost, Synchronization in discrete-time networks with general pairwise coupling., Nonlinearity 22 (2009), 2333-2351 Zbl1171.05355MR2539756
  4. Frank Bauer, Jürgen Jost, Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplace operator., Commun. Anal. Geom. 21 (2013), 787-845 Zbl1290.05100MR3078942
  5. Frank Bauer, Jürgen Jost, Shiping Liu, Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator, Mathematical research letters 19 (2012), 1185-1205 Zbl1297.05143MR3091602
  6. V.N. Berestovskij, I.G. Nikolaev, Multidimensional generalized Riemannian spaces., Geometry IV. Non-regular Riemannian geometry. Transl. from the Russian by E. Primrose (1992), Berlin: Springer-Verlag Zbl0781.53049MR1263965
  7. D. Burago, Yu. Burago, S. Ivanov, A course in metric geometry., (2001), Providence, RI: American Mathematical Society (AMS) Zbl0981.51016MR1835418
  8. Fan R.K. Chung, Spectral graph theory., (1997), Providence, RI: AMS, American Mathematical Society Zbl0867.05046MR1421568
  9. Matt DeVos, Bojan Mohar, An analogue of the Descartes-Euler formula for infinite graphs and Higuchi’s conjecture, Transactions of the American Mathematical Society 359 (2007), 3287-3300 (electronic) Zbl1117.05026MR2299456
  10. C. Fr. Gauß, Allgemeine Flächentheorie. (Disquisitiones generales circa superficies curvas.) (1827.)., Deutsch herausgeg. von A. Wangerin. 5. Aufl. Leipzig: Akad. Verlagsges., 64 S. (1921). (Ostwalds Klassiker der exakten Wissenschaften, Nr. 5.) (1921). (1921) Zbl48.0008.01
  11. Bobo Hua, Jürgen Jost, Shiping Liu, Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature, (2011) Zbl1308.05033MR2775397
  12. Jürgen Jost, Riemannian geometry and geometric analysis. 6th ed., (2011), Berlin: Springer Zbl1227.53001MR2829653
  13. Jürgen Jost, Mathematical methods in biology and neurobiology., (2014), London: Springer Zbl1295.92002MR3157168
  14. Jürgen Jost, Shiping Liu, Ollivier’s Ricci curvature, local clustering and curvature dimension inequalities on graphs, Discrete and Computational Geometry 51 (2014), 300-322 Zbl1294.05061MR3164168
  15. Yong Lin, Shing-Tung Yau, Ricci curvature and eigenvalue estimate on locally finite graphs, Mathematical research letters 17 (2010), 343-356 Zbl1232.31003MR2644381
  16. Yann Ollivier, Ricci curvature of Markov chains on metric spaces, Journal of Functional Analysis 256 (2009), 810-864 Zbl1181.53015MR2484937
  17. Yann Ollivier, A survey of Ricci curvature for metric spaces and Markov chains., Probabilistic approach to geometry. Proceedings of the 1st international conference, Kyoto , Japan, 28th July – 8th August, 2008 (2010), 343-381, Tokyo: Mathematical Society of Japan (MSJ) Zbl1204.53035MR2648269
  18. Bernhard Riemann, Bernhard Riemann “Über die Hypothesen, welche der Geometrie zu Grunde liegen”. Historisch und mathematisch kommentiert von Jürgen Jost., (2013), Berlin: Springer Spektrum Zbl1272.01002
  19. Duncan J Watts, Steven H Strogatz, Collective dynamics of ‘small-world’ networks, nature 393 (1998), 440-442 

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.