On Computing the Hyperbolicity of Real-World Graphs

  • Michele Borassi
  • David Coudert
  • Pierluigi Crescenzi
  • Andrea Marino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)


The (Gromov) hyperbolicity is a topological property of a graph, which has been recently applied in several different contexts, such as the design of routing schemes, network security, computational biology, the analysis of graph algorithms, and the classification of complex networks. Computing the hyperbolicity of a graph can be very time consuming: indeed, the best available algorithm has running-time \(\mathcal{O}(n^{3.69})\), which is clearly prohibitive for big graphs. In this paper, we provide a new and more efficient algorithm: although its worst-case complexity is \(\mathcal{O}(n^4)\), in practice it is much faster, allowing, for the first time, the computation of the hyperbolicity of graphs with up to 200,000 nodes. We experimentally show that our new algorithm drastically outperforms the best previously available algorithms, by analyzing a big dataset of real-world networks. Finally, we apply the new algorithm to compute the hyperbolicity of random graphs generated with the Erdös-Renyi model, the Chung-Lu model, and the Configuration Model.


Complex Network Random Graph Input Graph Exact Asymptotics Greedy Forwarding 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Michele Borassi
    • 1
  • David Coudert
    • 2
  • Pierluigi Crescenzi
    • 3
  • Andrea Marino
    • 4
  1. 1.IMT Institute for Advanced Studies LuccaLuccaItaly
  2. 2.InriaSophia AntipolisFrance
  3. 3.Dipartimento di Ingegneria dell’InformazioneUniversità di FirenzeFirenzeItaly
  4. 4.Dipartimento di InformaticaUniversità di PisaPisaItaly

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