M. Abu-ata and F. F. Dragan, Metric tree-like structures in real-world networks: an empirical study, Networks, vol.18, issue.1, pp.49-69, 2016.
DOI : 10.1002/net.21631

R. Albert, B. Dasgupta, and N. Mobasheri, Topological implications of negative curvature for biological and social networks, Physical Review E, vol.20, issue.3, p.32811, 2014.
DOI : 10.1142/S0218195997000260

H. Alrasheed and F. F. Dragan, Core-periphery models for graphs based on their ?hyperbolicity: An example using biological networks, CompleNet VI, pp.65-77
DOI : 10.1007/978-3-319-16112-9_7

R. Anstee and M. Farber, On bridged graphs and cop-win graphs, Journal of Combinatorial Theory, Series B, vol.44, issue.1, pp.22-28, 1988.
DOI : 10.1016/0095-8956(88)90093-7
URL : http://doi.org/10.1016/0095-8956(88)90093-7

B. Baker, Approximation algorithms for NP-complete problems on planar graphs, Journal of the ACM, vol.41, issue.1, pp.153-180, 1994.
DOI : 10.1145/174644.174650

H. Bandelt and H. Mulder, Distance-hereditary graphs, Journal of Combinatorial Theory, Series B, vol.41, issue.2, pp.182-208, 1986.
DOI : 10.1016/0095-8956(86)90043-2

S. Bermudo, J. Rodríguez, J. Sigarreta, and J. Vilaire, Gromov hyperbolic graphs, Discrete Mathematics, vol.313, issue.15, pp.3131575-1585, 2013.
DOI : 10.1016/j.disc.2013.04.009

A. Berry, R. Pogorelcnik, and G. Simonet, Efficient clique decomposition of a graph into its atom graph, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00678702

A. Berry, R. Pogorelcnik, and G. Simonet, An Introduction to Clique Minimal Separator Decomposition, Algorithms, vol.84, issue.2, pp.197-215, 2010.
DOI : 10.1016/j.disc.2005.12.017
URL : https://hal.archives-ouvertes.fr/lirmm-00485851

A. Berry, R. Pogorelcnik, and G. Simonet, Organizing the atoms of the clique separator decomposition into an atom tree, Discrete Applied Mathematics, vol.177, pp.1-13, 2014.
DOI : 10.1016/j.dam.2014.05.030
URL : https://hal.archives-ouvertes.fr/hal-01375915

H. L. Bodlaender, Discovering Treewidth, 31st Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM), pp.1-16, 2005.
DOI : 10.1007/978-3-540-30577-4_1

M. Boguñá, F. Papadopoulos, and D. V. Krioukov, Sustaining the Internet with hyperbolic mapping, Nature Communications, vol.16, issue.6, pp.1-18, 2010.
DOI : 10.1038/ncomms1063

J. A. Bondy and U. Murty, Graph theory with applications, 1976.
DOI : 10.1007/978-1-349-03521-2

M. Borassi, A. Chessa, and G. Caldarelli, Hyperbolicity measures democracy in real-world networks, Physical Review E, vol.6, issue.3, p.32812, 2015.
DOI : 10.1103/PhysRevE.80.016118
URL : http://arxiv.org/abs/1503.03061

M. Borassi, D. Coudert, P. Crescenzi, and A. Marino, On Computing the Hyperbolicity of Real-World Graphs, 23rd Annual European Symposium on Algorithms (ESA), pp.215-226, 2015.
DOI : 10.1080/15326349.2013.838510
URL : https://hal.archives-ouvertes.fr/hal-01199860

M. Borassi, P. Crescenzi, and M. Habib, Into the Square: On the Complexity of Some Quadratic-time Solvable Problems, Electronic Notes in Theoretical Computer Science, vol.322, pp.51-67, 2016.
DOI : 10.1016/j.entcs.2016.03.005
URL : https://hal.archives-ouvertes.fr/hal-01390131

A. Brandstädt and C. T. Hò, On clique separators, nearly chordal graphs, and the Maximum Weight Stable Set Problem, Theoretical Computer Science, vol.389, issue.1-2, pp.295-306, 2007.
DOI : 10.1016/j.tcs.2007.09.031

G. Brinkmann, J. H. Koolen, and V. Moulton, On the Hyperbolicity of Chordal Graphs, Annals of Combinatorics, vol.5, issue.1, pp.61-69, 2001.
DOI : 10.1007/s00026-001-8007-7

W. Carballosa, D. Pestana, J. Rodríguez, and J. Sigarreta, Distortion of the hyperbolicity constant of a graph, the Electronic Journal of Combinatorics, vol.19, issue.1, p.67, 2012.

J. Chakerian and S. Holmes, Computational Tools for Evaluating Phylogenetic and Hierarchical Clustering Trees, Journal of Computational and Graphical Statistics, vol.14, issue.2, pp.581-599, 2012.
DOI : 10.1080/10618600.2012.640901
URL : http://arxiv.org/abs/1006.1015

A. Chatr-aryamontri, R. Oughtred, L. Boucher, J. Rust, C. Chang et al., The BioGRID interaction database: 2017 update, Nucleic Acids Research, vol.45, issue.D1, pp.45-369, 2017.
DOI : 10.1093/nar/gkw1102

V. Chepoi, F. F. Dragan, B. Estellon, M. Habib, and Y. Vaxès, Diameters, centers, and approximating trees of delta-hyperbolic geodesic spaces and graphs, 24th Symposium on Computational Geometry (SCG), pp.59-68, 2008.
DOI : 10.1145/1377676.1377687

V. Chepoi, F. F. Dragan, and Y. Vaxes, Core congestion is inherent in hyperbolic networks, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.2264-2279, 2017.
DOI : 10.1137/1.9781611974782.149
URL : http://arxiv.org/abs/1605.03059

E. Cho, S. A. Myers, and J. Leskovec, Friendship and mobility, Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining, KDD '11, pp.1082-1090, 2011.
DOI : 10.1145/2020408.2020579

N. Cohen, D. Coudert, and A. Lancin, Exact and approximate algorithms for computing the hyperbolicity of large-scale graphs, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00735481

N. Cohen, D. Coudert, and A. Lancin, On Computing the Gromov Hyperbolicity, Journal of Experimental Algorithmics, vol.20, issue.1, pp.1-6, 2015.
DOI : 10.1145/2780652
URL : https://hal.archives-ouvertes.fr/hal-01182890

D. Coudert and G. Ducoffe, Recognition of $C_4$-Free and 1/2-Hyperbolic Graphs, SIAM Journal on Discrete Mathematics, vol.28, issue.3, pp.1601-1617, 2014.
DOI : 10.1137/140954787
URL : https://hal.archives-ouvertes.fr/hal-01070768

W. H. Cunningham, Decomposition of Directed Graphs, SIAM Journal on Algebraic Discrete Methods, vol.3, issue.2, pp.214-228, 1982.
DOI : 10.1137/0603021

B. Dasgupta, M. Karpinski, N. Mobasheri, and F. Yahyanejad, Effect of gromovhyperbolicity parameter on cuts and expansions in graphs and some algorithmic implications, 2015.

P. De, L. Harpe, and E. Ghys, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics, vol.83, 1990.

M. D. Biha, B. Kaba, M. Meurs, and E. Sanjuan, Graph Decomposition Approaches for Terminology Graphs, MICAI 2007: Advances in Artificial Intelligence, pp.883-893, 2007.
DOI : 10.1007/978-3-540-76631-5_84
URL : https://hal.archives-ouvertes.fr/hal-01318619

Y. Dourisboure and C. Gavoille, Tree-decompositions with bags of small diameter, Discrete Mathematics, vol.307, issue.16, pp.2008-2029, 2007.
DOI : 10.1016/j.disc.2005.12.060
URL : https://hal.archives-ouvertes.fr/hal-00307800

F. Dragan, Tree-Like Structures in Graphs: A Metric Point of View, 39th International Workshop on Graph-Theoretic Concepts in Computer Science (WG), pp.1-4, 2013.
DOI : 10.1007/978-3-642-45043-3_1

A. Dress, K. Huber, J. Koolen, V. Moulton, and A. Spillner, Basic Phylogenetic Combinatorics, 2011.
DOI : 10.1017/CBO9781139019767

D. Epstein, M. S. Paterson, J. W. Cannon, D. F. Holt, S. V. Levy et al., Word processing in groups, 1992.

H. Fournier, A. Ismail, and A. Vigneron, Computing the Gromov hyperbolicity of a discrete metric space, Information Processing Letters, vol.115, issue.6-8, pp.576-579, 2015.
DOI : 10.1016/j.ipl.2015.02.002

J. Gagneur, R. Krause, T. Bouwmeester, and G. Casari, Modular decomposition of proteinprotein interaction networks, Genome Biology, vol.5, issue.8, p.57, 2004.
DOI : 10.1186/gb-2004-5-8-r57

T. Gallai, Transitiv orientierbare Graphen, Acta Mathematica Academiae Scientiarum Hungaricae, vol.51, issue.1-2, pp.25-66, 1967.
DOI : 10.1007/BF02020961

A. Goldman, Optimal Center Location in Simple Networks, Transportation Science, vol.5, issue.2, pp.212-221, 1971.
DOI : 10.1287/trsc.5.2.212

M. Gromov, Hyperbolic Groups, of Mathematical Sciences Research Institute Publications, pp.75-263, 1987.
DOI : 10.1007/978-1-4613-9586-7_3

M. Habib, C. Paul, and L. Viennot, PARTITION REFINEMENT TECHNIQUES: AN INTERESTING ALGORITHMIC TOOL KIT, International Journal of Foundations of Computer Science, vol.17, issue.02, pp.147-170, 1999.
DOI : 10.1145/321879.321884

E. Howorka, On metric properties of certain clique graphs, Journal of Combinatorial Theory, Series B, vol.27, issue.1, pp.67-74, 1979.
DOI : 10.1016/0095-8956(79)90069-8

R. Impagliazzo, R. Paturi, and F. Zane, Which problems have strongly exponential complexity? In Foundations of Computer Science, Proceedings. 39th Annual Symposium on, pp.653-662, 1998.

E. A. Jonckheere and P. Lohsoonthorn, Geometry of network security, American Control Conference, pp.976-981, 2004.

B. Kaba, N. Pinet, G. Lelandais, A. Sigayret, and A. Berry, Clustering gene expression data using graph separators, In Silico Biology, vol.7, issue.4, pp.433-452, 2007.

W. S. Kennedy, I. Saniee, and O. Narayan, On the hyperbolicity of large-scale networks and its estimation, 2016 IEEE International Conference on Big Data (Big Data), pp.3344-3351, 2016.
DOI : 10.1109/BigData.2016.7840994

J. H. Koolen and V. Moulton, Hyperbolic Bridged Graphs, European Journal of Combinatorics, vol.23, issue.6, pp.683-699, 2002.
DOI : 10.1006/eujc.2002.0591
URL : http://doi.org/10.1006/eujc.2002.0591

R. Krauthgamer and J. Lee, Algorithms on negatively curved spaces, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06), pp.119-132, 2006.
DOI : 10.1109/FOCS.2006.9

L. Gall, Faster Algorithms for Rectangular Matrix Multiplication, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, pp.514-523
DOI : 10.1109/FOCS.2012.80

H. Leimer, Optimal decomposition by clique separators, Discrete Mathematics, vol.113, issue.1-3, pp.99-123, 1993.
DOI : 10.1016/0012-365X(93)90510-Z
URL : http://doi.org/10.1016/0012-365x(93)90510-z

J. Leskovec, J. Kleinberg, and C. Faloutsos, Graph evolution, ACM Transactions on Knowledge Discovery from Data, vol.1, issue.1, pp.1-41, 2007.
DOI : 10.1145/1217299.1217301

S. Mccullough, 2 ??? Chordal Graphs, Contributions to Operator Theory and its Applications, pp.143-192, 1988.
DOI : 10.1007/978-3-0348-9284-1_7

S. Mccullough, Minimal separators of 2-chordal graphs. Linear algebra and its applications, pp.187-199, 1993.

K. Olesen and A. Madsen, Maximal prime subgraph decomposition of Bayesian networks, IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), vol.32, issue.1, pp.21-31, 2002.
DOI : 10.1109/3477.979956

R. Paige and R. Tarjan, Three Partition Refinement Algorithms, SIAM Journal on Computing, vol.16, issue.6, pp.973-989, 1987.
DOI : 10.1137/0216062

D. J. Rose, R. E. Tarjan, and G. S. Lueker, Algorithmic Aspects of Vertex Elimination on Graphs, SIAM Journal on Computing, vol.5, issue.2, pp.266-283, 1976.
DOI : 10.1137/0205021

L. Salwinski, C. S. Miller, A. J. Smith, F. K. Pettit, J. U. Bowie et al., The Database of Interacting Proteins: 2004 update, Nucleic Acids Research, vol.32, issue.90001, pp.449-51, 2004.
DOI : 10.1093/nar/gkh086

M. A. Soto-gómez, Quelques propriétés topologiques des graphes et applicationsàapplicationsà internet et aux réseaux, 2011.

J. P. Spinrad, Recognizing quasi-triangulated graphs, Discrete Applied Mathematics, vol.138, issue.1-2, pp.203-213, 2004.
DOI : 10.1016/S0166-218X(03)00295-6
URL : http://doi.org/10.1016/s0166-218x(03)00295-6

C. Stark, B. Breitkreutz, T. Reguly, L. Boucher, A. Breitkreutz et al., BioGRID: a general repository for interaction datasets, Nucleic Acids Research, vol.34, issue.90001, pp.535-539, 2006.
DOI : 10.1093/nar/gkj109
URL : http://doi.org/10.1093/nar/gkj109

M. Sys-lo, Characterizations of outerplanar graphs, Discrete Mathematics, vol.26, issue.1, pp.47-53, 1979.
DOI : 10.1016/0012-365X(79)90060-8

R. Tamassia and I. Tollis, Planar grid embedding in linear time, IEEE Transactions on Circuits and Systems, vol.36, issue.9, pp.1230-1234, 1989.
DOI : 10.1109/31.34669

R. E. Tarjan, Depth-First Search and Linear Graph Algorithms, SIAM Journal on Computing, vol.1, issue.2, pp.146-160, 1972.
DOI : 10.1137/0201010
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.327.8418

R. E. Tarjan, Decomposition by clique separators, Discrete Mathematics, vol.55, issue.2, pp.221-232, 1985.
DOI : 10.1016/0012-365X(85)90051-2
URL : http://doi.org/10.1016/0012-365x(85)90051-2

V. Vassilevska-williams, J. Wang, R. Williams, and H. Yu, Finding four-node subgraphs in triangle time, Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '15, pp.1671-1680, 2015.

K. Verbeek and S. Suri, Metric embedding, hyperbolic space, and social networks, Annual Symposium on Computational Geometry (SCG), pp.501-510, 2014.
DOI : 10.1016/j.comgeo.2016.08.003
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.640.9882

D. J. Watts and S. H. Strogatz, Collective dynamics of 'small-world' networks, Nature, vol.393, issue.6684, pp.440-442, 1998.
DOI : 10.1038/30918

Y. Wu and C. Zhang, Hyperbolicity and chordality of a graph, The Electronic Journal of Combinatorics, vol.18, issue.1, p.43, 2011.

M. Yancey, An investigation into graph curvature's ability to measure congestion in network flow, 2015.