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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 
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     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},
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     year = {2013},
     doi = {10.5802/acirm.56},
     zbl = {06938604},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.56/}
}
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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 | DOI

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

[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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

[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 | DOI | Zbl

[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) | DOI | MR | Zbl

[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

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

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

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

[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 | DOI | MR | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | DOI | Zbl

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

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