Mersenne banner
no. 1
Generalized Ricci curvature and the geometry of graphs
Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 69-78.
Published online:
DOI: 10.5802/acirm.56 
@article{ACIRM_2013__3_1_69_0,
     author = {Frank Bauer and Bobo Hua and J\"urgen Jost and Shiping Liu},
     title = {Generalized {Ricci} curvature and the geometry of graphs},
     journal = {Actes des rencontres du CIRM},
     pages = {69--78},
     publisher = {CIRM},
     volume = {3},
     number = {1},
     year = {2013},
     doi = {10.5802/acirm.56},
     zbl = {06938604},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.56/}
}
TY  - JOUR
TI  - Generalized Ricci curvature and the geometry of graphs
JO  - Actes des rencontres du CIRM
PY  - 2013
DA  - 2013///
SP  - 69
EP  - 78
VL  - 3
IS  - 1
PB  - CIRM
UR  - https://acirm.centre-mersenne.org/articles/10.5802/acirm.56/
UR  - https://zbmath.org/?q=an%3A06938604
UR  - https://doi.org/10.5802/acirm.56
DO  - 10.5802/acirm.56
LA  - en
ID  - ACIRM_2013__3_1_69_0
ER  - 
%0 Journal Article
%T Generalized Ricci curvature and the geometry of graphs
%J Actes des rencontres du CIRM
%D 2013
%P 69-78
%V 3
%N 1
%I CIRM
%U https://doi.org/10.5802/acirm.56
%R 10.5802/acirm.56
%G en
%F ACIRM_2013__3_1_69_0
Frank Bauer; Bobo Hua; Jürgen Jost; Shiping Liu. Generalized Ricci curvature and the geometry of graphs. Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 69-78. doi : 10.5802/acirm.56. https://acirm.centre-mersenne.org/articles/10.5802/acirm.56/

[1] F. Bauer; F. M. Atay; J. Jost Synchronized chaos in networks of simple units, EPL (Europhysics Letters), Volume 89 (2010) no. 2, 20002 pages http://stacks.iop.org/0295-5075/89/i=2/a=20002 | Article

[2] Frank Bauer Normalized graph Laplacians for directed graphs., Linear Algebra Appl., Volume 436 (2012) no. 11, pp. 4193-4222 | Article | MR: 2915277 | Zbl: 1241.05066

[3] Frank Bauer; Fatihcan M. Atay; Jürgen Jost Synchronization in discrete-time networks with general pairwise coupling., Nonlinearity, Volume 22 (2009) no. 10, pp. 2333-2351 | Article | MR: 2539756 | Zbl: 1171.05355

[4] Frank Bauer; Jürgen Jost Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplace operator., Commun. Anal. Geom., Volume 21 (2013) no. 4, pp. 787-845 | Article | MR: 3078942 | Zbl: 1290.05100

[5] Frank Bauer; Jürgen Jost; Shiping Liu Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator, Mathematical research letters, Volume 19 (2012) no. 6, pp. 1185-1205 | Article | MR: 3091602 | Zbl: 1297.05143

[6] V.N. Berestovskij; I.G. Nikolaev Multidimensional generalized Riemannian spaces., Geometry IV. Non-regular Riemannian geometry. Transl. from the Russian by E. Primrose, Berlin: Springer-Verlag, 1992

[7] D. Burago; Yu. Burago; S. Ivanov A course in metric geometry., Providence, RI: American Mathematical Society (AMS), 2001, xiv + 415 pages | Article | Zbl: 0981.51016

[8] Fan R.K. Chung Spectral graph theory., Providence, RI: AMS, American Mathematical Society, 1997, xi + 207 pages

[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, Volume 359 (2007) no. 7, p. 3287-3300 (electronic) | Article | MR: 2299456 | Zbl: 1117.05026

[10] C. Fr. Gauß Allgemeine Flächentheorie. (Disquisitiones generales circa superficies curvas.) (1827.)., Deutsch herausgeg. von A. Wangerin. 5. Aufl. Leipzig: Akad. Verlagsges., 64 S. 8 ∘ (1921). (Ostwalds Klassiker der exakten Wissenschaften, Nr. 5.) (1921)., 1921 | Zbl: 48.0008.01

[11] Bobo Hua; Jürgen Jost; Shiping Liu Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature, arXiv.org (2011) | Zbl: 1308.05033

[12] Jürgen Jost Riemannian geometry and geometric analysis. 6th ed., Berlin: Springer, 2011, xiii + 611 pages | Article | Zbl: 1227.53001

[13] Jürgen Jost Mathematical methods in biology and neurobiology., London: Springer, 2014, x + 226 pages | Article | Zbl: 1295.92002

[14] Jürgen Jost; Shiping Liu Ollivier’s Ricci curvature, local clustering and curvature dimension inequalities on graphs, Discrete and Computational Geometry, Volume 51 (2014) no. 2, pp. 300-322 | Article | MR: 3164168 | Zbl: 1294.05061

[15] Yong Lin; Shing-Tung Yau Ricci curvature and eigenvalue estimate on locally finite graphs, Mathematical research letters, Volume 17 (2010) no. 2, pp. 343-356 | MR: 2644381 | Zbl: 1232.31003

[16] Yann Ollivier Ricci curvature of Markov chains on metric spaces, Journal of Functional Analysis, Volume 256 (2009) no. 3, pp. 810-864 | Article | MR: 2484937 | Zbl: 1181.53015

[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, Tokyo: Mathematical Society of Japan (MSJ), 2010, pp. 343-381 | MR: 2648269 | Zbl: 1204.53035

[18] Bernhard Riemann Bernhard Riemann “Über die Hypothesen, welche der Geometrie zu Grunde liegen”. Historisch und mathematisch kommentiert von Jürgen Jost., Berlin: Springer Spektrum, 2013, x + 156 pages | Article | Zbl: 1272.01002

[19] Duncan J Watts; Steven H Strogatz Collective dynamics of ‘small-world’ networks, nature, Volume 393 (1998) no. 6684, pp. 440-442 | Article | Zbl: 1368.05139

Cited by Sources: