, Center for applied Internet data analysis

, Center for applied Internet data analysis

, Openflights network dataset -KONECT, 2016.

, University of oregon route-views project

A. Abboud, J. Wang, and V. Williams, Approximation and fixed parameter subquadratic algorithms for radius and diameter in sparse Graphs, SODA, pp.377-391, 2016.

A. Abboud, F. Grandoni, and V. Williams, Subcubic equivalences between graph centrality problems, APSP and diameter, pp.1681-1697, 2015.

M. Abu-ata and F. F. Dragan, Metric tree-like structures in real-world networks: an empirical study, Networks, vol.67, pp.49-68, 2016.

A. B. Adcock, B. D. Sullivan, and M. W. Mahoney, Tree-like structure in large social and information networks, ICDM 2013, pp.1-10

D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani, Fast estimation of diameter and shortest paths (without matrix multiplication), SIAM J. Comput, vol.28, pp.1167-1181, 1999.

R. Albert, H. Jeong, and A. Barabási, Internet: Diameter of the world-wide web, Nature, vol.401, pp.130-131, 1999.

J. M. Alonso, T. Brady, D. Cooper, V. Ferlini, M. Lustig et al., Notes on word hyperbolic groups, Group Theory from a Geometrical Viewpoint, pp.3-63, 1990.

H. Al-rasheed, Structural Properties in ?-Hyperbolic Networks: Algorithmic Analysis and Implications, Proceedings of the 25th International Conference Companion on World Wide Web (WWW 2016 Companion), pp.299-303

H. Al-rasheed and F. F. Dragan, Core-periphery models for graphs based on their d-hyperbolicity, Journal of Algorithms & Computational Technology, vol.11, pp.40-57, 2015.

V. Batagelj and A. Mrvar, , 2006.

B. Ben-moshe, B. K. Bhattacharya, Q. Shi, and A. Tamir, Efficient algorithms for center problems in cactus networks, Theor. Comput. Sci, vol.378, pp.237-252, 2007.

P. Berman and S. P. Kasiviswanathan, Faster approximation of distances in graphs, pp.541-552, 2007.

M. Borassi, D. Coudert, P. Crescenzi, and A. Marino, On computing the hyperbolicity of real-world graphs, pp.215-226, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01199860

M. Borassi, P. Crescenzi, and M. Habib, Into the square -on the complexity of quadratic-time solvable problems, Electr. Notes Theor. Comput. Sci, vol.322, pp.51-67, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01274008

M. Borassi, P. Crescenzi, M. Habib, W. A. Kosters, A. Marino et al., Takes: Fast diameter and radius BFS-based computation in (weakly connected) real-world graphs: With an application to the six degrees of separation games, Theor. Comput. Sci, vol.586, pp.59-80, 2015.

M. Borassi, P. Crescenzi, and L. Trevisan, An Axiomatic and an Average-Case Analysis of Algorithms and Heuristics for Metric Properties of Graphs, SODA, vol.2017, pp.920-939
URL : https://hal.archives-ouvertes.fr/hal-01525752

M. Cairo, R. Grossi, and R. Rizzi, New Bounds for Approximating Extremal Distances in Undirected Graphs, SODA, vol.2016, pp.363-376
URL : https://hal.archives-ouvertes.fr/hal-01526665

A. Brandstädt, V. Chepoi, and F. F. Dragan, The algorithmic use of hypertree structure and maximum neighbourhood orderings, Discr. Appl. Math, vol.82, pp.43-77, 1998.

A. Brandstädt, V. Chepoi, and F. F. Dragan, Distance approximating trees for chordal and dually chordal graphs, J. Algorithms, vol.30, pp.166-184, 1999.

A. Brandstädt, F. F. Dragan, and F. Nicolai, LexBFS-orderings and powers of chordal graphs, Discr. Math, vol.171, pp.27-42, 1997.

M. R. Bridson and A. Haefiger, Metric Spaces of Non-Positive Curvature, Grundlehren der Mathematischen Wissenschaften, vol.319, 1999.

D. Bu, Y. Zhao, and L. Cai, Topological structure analysis of the protein-protein interaction network in budding yeast, Nucleic Acids Research, vol.31, pp.2443-2450, 2003.

S. Cabello, Subquadratic algorithms for the diameter and the sum of pairwise distances in planar graphs, pp.2143-2152, 2017.

S. Chechik, D. Larkin, L. Roditty, G. Schoenebeck, R. E. Tarjan et al., Better approximation algorithms for the graph diameter, pp.1041-1052

J. Chalopin, V. Chepoi, F. F. Dragan, G. Ducoffe, A. Mohammed et al., Fast approximation and exact computation of negative curvature parameters of graphs, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01836063

V. Chepoi and F. F. Dragan, A linear-time algorithm for finding a central vertex of a chordal graph, pp.159-170, 1994.

V. D. Chepoi and F. F. Dragan, Finding a central vertex in HHD-free graphs, Discr. Appl. Math, vol.131, pp.93-111, 2003.

V. D. Chepoi, F. F. Dragan, B. Estellon, M. Habib, and Y. Vaxès, Diameters, centers, and approximating trees of ?-hyperbolic geodesic spaces and graphs, pp.59-68, 2008.

V. D. Chepoi, F. F. Dragan, B. Estellon, M. Habib, and Y. Vaxès, Notes on diameters, centers, and approximating trees of delta-hyperbolic geodesic spaces and graphs, Electronic Notes in Discrete Mathematics, vol.31, pp.231-234, 2008.

V. Chepoi, F. F. Dragan, B. Estellon, M. Habib, Y. Vaxès et al., Additive spanners and distance and routing labeling schemes for hyperbolic graphs, Algorithmica, pp.713-732, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01194836

V. Chepoi, F. F. Dragan, and Y. Vaxès, Center and diameter problems in plane triangulations and quadrangulations, SODA, pp.346-355, 2002.

V. Chepoi, F. F. Dragan, and Y. Vaxès, Core congestion is inherent in hyperbolic networks, pp.2264-2279, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02065777

V. Chepoi and B. Estellon, Packing and covering ?-hyperbolic spaces by balls, APPROX-RANDOM, pp.59-73, 2007.

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

D. G. Corneil, F. F. Dragan, M. Habib, and C. Paul, Diameter determination on restricted graph families, Discr. Appl. Math, vol.113, pp.143-166, 2001.
URL : https://hal.archives-ouvertes.fr/lirmm-00090363

D. G. Corneil, F. F. Dragan, and E. Köhler, On the power of BFS to determine a graph's diameter, Networks, vol.42, pp.209-222, 2003.

B. Dasgupta, M. Karpinski, N. Mobasheri, and F. Yahyanejad, Node expansions and cuts in Gromov-hyperbolic graphs, CoRR, 2015.

M. D. Choudhury, Y. Lin, H. Sundaram, K. Selçuk-candan, L. Xie et al., How does the data sampling strategy impact the discovery of information diffusion in social media? ICWSM, pp.34-41, 2010.

D. Dor, S. Halperin, and U. Zwick, All-pairs almost shortest paths, SIAM J. Comput, vol.29, pp.1740-1759, 2000.

Y. Dourisboure and C. Gavoille, Tree-decompositions with bags of small diameter, Discr. Math, vol.307, pp.208-229, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00307800

F. F. Dragan, Centers of graphs and the Helly property, 1989.

F. F. Dragan, Estimating All Pairs Shortest Paths in Restricted Graph Families: A, Unified Approach J. Algorithms, vol.57, pp.1-21, 2005.

F. F. Dragan, Almost diameter of a house-hole-free graph in linear time via LexBFS, Discr. Appl. Math, vol.95, pp.223-239, 1999.

F. F. Dragan, E. Köhler, and H. Alrasheed, Eccentricity approximating trees, Discr. Appl. Math, vol.232, pp.142-156, 2017.

F. F. Dragan, M. Habib, and L. Viennot, Revisiting Radius, Diameter, and all Eccentricity Computation in Graphs through Certificates, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01729748

F. F. Dragan and F. Nicolai, LexBFS-orderings of distance-hereditary graphs with application to the diametral pair problem, Discr. Appl. Math, vol.98, pp.191-207, 2000.

F. F. Dragan, F. Nicolai, and A. Brandstädt, LexBFS-orderings and powers of graphs, pp.166-180, 1996.

J. Duch and A. Arenas, Community detection in complex networks using extremal optimization, Physical Review, vol.72, p.27104, 2005.

D. Dvir and G. Handler, , pp.109-118, 2004.

K. Edwards, W. S. Kennedy, and I. Saniee, Fast approximation algorithms for p-centres in large delta-hyperbolic graphs, CoRR, 2016.

M. Elkin, Computing almost shortest paths, ACM Trans. Algorithms, vol.1, pp.283-323, 2005.

, Les groupes hyperboliques d'après M. Gromov, vol.83, 1990.

M. Gromov, Essays in group theory, Hyperbolic groups, vol.8, pp.75-263, 1987.

R. Guimera, L. Danon, A. Diaz-guilera, F. Giralt, and A. Arenas, Self-similar community structure in a network of human interactions, Physical Review E, vol.68, p.65103, 2003.

S. L. Hakimi, Optimum location of switching centers and absolute centers and medians of a graph, Oper. Res, vol.12, pp.450-459, 1964.

R. Impagliazzo and R. Paturi, On the complexity of k-SAT, J. Comput. Syst. Sci, vol.62, pp.367-375, 2001.

R. Impagliazzo, R. Paturi, and F. Zane, Which problems have strongly exponential complexity?, J. Comput. Syst. Sci, vol.63, pp.512-530, 2001.

H. Jeong, S. P. Mason, A. Barabasi, and Z. N. Oltvai, Lethality and centrality in protein networks, Nature, vol.411, pp.41-42, 2001.

C. Jordan, Sur les assemblages des lignes, J. für reine und angewandte Math, vol.70, pp.185-190, 1869.

W. S. Kennedy, I. Saniee, and O. Narayan, On the hyperbolicity of large-scale networks and its estimation, Big Data, pp.3344-3351, 2016.

B. Klimmt and Y. Yang, , 2004.

D. Koschützski, K. A. Lehmann, L. Peeters, S. Richter, D. Tenfelde-podehl et al., Centrality Indices, Network Analysis (U. Brandes and T, pp.17-61, 2005.

D. Kratsch, H. Le, H. Müller, E. Prisner, and D. Wagner, Additive tree spanners, SIAM J. Discrete Math, vol.17, pp.332-340, 2003.

J. Kunegis, Prosper loans, KONECT, the Koblenz Network Collection, 2016.

J. Leskovec, J. Kleinberg, and C. Faloutsos, Graph evolution: densification and shrinking diameters, 2007.

J. Leskovec, K. Lang, A. Dasgupta, and M. Mahoney, Community structure in large networks: natural cluster sizes and the absence of large well-defined clusters, Internet Math, vol.6, pp.29-123, 2009.

J. Leskovec and J. Mcauley, Learning to discover social circles in ego networks, pp.548-556, 2012.

M. S. Madanlal, G. Vankatesan, and C. Pandu-rangan, Tree 3-spanners on interval, permutation and regularbipartite graphs, Inform. Process. Lett, vol.59, pp.97-102, 1996.

A. Mohammed, , 2017.

O. Narayan and I. Saniee, Large-scale curvature of networks, Physical Review E, vol.84, p.66108, 2011.

L. Négyessy, T. Nepusz, L. Kocsis, and F. Bazsó, Prediction of the main cortical areas and connections involved in the tactile function of the visual cortex by network analysis, Europ. J. Neuroscience, vol.23, pp.1919-1930, 2006.

S. Olariu, A simple linear-time algorithm for computing the center of an interval graph, Int. J. Comput. Math, vol.34, pp.121-128, 1990.

E. Prisner, Distance approximating spanning trees, Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS'97), vol.1200, pp.499-510, 1997.

E. Prisner, Eccentricity-approximating trees in chordal graphs, Discr. Math, vol.220, pp.263-269, 2000.

M. Ripeanu, I. Foster, and A. Iamnitchi, Mapping the gnutella network: Macroscopic properties of large-scale peer-to-peer systems, Int. Workshop on Peer, pp.85-93, 2002.

L. Roditty, V. , and V. Williams, Fast approximation algorithms for the diameter and radius of sparse graphs, pp.515-524, 2013.

L. Roditty and U. Zwick, On dynamic shortest paths problems, Algorithmica, pp.389-401, 2011.

Y. Shavitt and T. Tankel, Hyperbolic embedding of internet graph for distance estimation and overlay construction, IEEE/ACM Trans. Netw, vol.16, pp.25-36, 2008.

C. Stark, B. Breitkreutz, T. Reguly, L. Boucher, A. Breitkreutz et al., Biogrid: a general repository for interaction datasets, Nucleic Acids Research, 2006.

J. Sun, J. Kunegis, and S. Staab, Predicting user roles in social networks using transfer learning with feature transformation, Proc. ICDM Workshop on Data Mining in Networks, 2016.

L. Subelj and M. Bajec, Robust network community detection using balanced propagation, Eur. Phys. J. B, vol.81, pp.353-362, 2011.

M. Thorup, Compact oracles for reachability and approximate distances in planar digraphs, J. ACM, vol.51, pp.993-1024, 2004.

V. Williams and R. Williams, Subcubic equivalences between path, matrix and triangle problems, FOCS 2010, pp.645-654

V. Williams, Hardness of easy problems: basing hardness on popular conjectures such as the strong exponential time hypothesis, pp.17-29, 2015.

K. Verbeek and S. Suri, Metric embedding, hyperbolic space, and social networks, pp.501-510, 2014.

D. Watts and S. Strogatz, Collective dynamics of small-world networks, Nature, vol.393, pp.440-442, 1998.

O. Weimann and R. Yuster, Approximating the diameter of planar Graphs in near linear time, ACM Trans. Algorithms, vol.12, 2016.

R. Williams, A new algorithm for optimal constraint satisfaction and its implications, pp.1227-1237, 2004.

J. Yang and J. Leskovec, Defining and Evaluating Network Communities based on Ground-truth, Knowledge and Information Systems, vol.42, pp.181-213, 2015.