Abstract
The average shortest path length is one of the most important and frequent-invoked characteristics of real-world complex networks. However, the high time complexity of the algorithms prevents us to apply them to calculate the average shortest path lengths in real-world massive networks. In this paper, we present an empirical study of the vertex-vertex distance distributions in more than 30 artificial and real-world networks. To best of our knowledge, we are the first to find out the vertex-vertex distance distributions in these networks conform well to the normal distributions with different means and variations. We also investigate how to use the sampling algorithms to estimate the average shortest path lengths in these networks. Comparing our average shortest path estimating algorithm with other three different sampling strategies, the results show that we can estimate the average shortest path length quickly by just sampling a small number of vertices in both of real-world and artificial networks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Latora, V., Marchiori, M.: Efficient Behavior of Small-World Networks. Phys. Rev. Lett. 87, 198701 (2001)
Zwick, U.: Exact and approximate distances in graphs—a survey. In: Proceeding of the 9th Annual European Symposium on Algorithms, pp. 33–48 (2001)
Newman, M.E.J.: The Structure and Function of Complex Networks. SIAM REVIEW 45, 167–256 (2003)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT, Cambridge (2001)
Potamias, M., Bonchi, F., Castillo, C., Gionis, A.: Fast Shortest Path Distance Estimation in Large Networks. In: Proceeding of CIKM, pp. 867–876 (2009)
Kleinberg, J., Slivkins, A., Wexler, T.: Triangulation and embedding using small sets of beacons. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 444–453. IEEE Computer Society, Washington (2004)
Albert, R., Jeong, H., Barabási, A.-L.: Diameter of the world wide web. Nature 401, 130–131 (1999)
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the Internet topology. In: Proceedings of the Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 251–262. ACM, New York (1999)
Lee, S.H., Kim, P.J., Jeong, H.: Statistical properties of sampled networks. Phys. Rev. E. 73, 16102 (2006)
Airoldi, E.M., Carley, K.M.: Sampling algorithms for pure network topologies: stability and separability of metric embeddings. SIGKDD Explorations 7, 13–22 (2005)
Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Barabási, A.L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509–512 (1999)
Leskovec, J., Horvitz, E.: Planetary-scale views on a large instant-messaging network. In: Proceeding of the 17th International Conference on World Wide Web, pp. 915–924 (2008)
Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E. 78, 46110 (2008)
Ye, Q., Zhu, T., Hu, D., et al.: Cell Phone Mini Challenge Award: Exploring Temporal Communication in Mobile Call Graphs. In: 3rd IEEE Symposium on Visual Analytics Science and Technology, pp. 207–208. IEEE Press, Columbus (2008)
Ye, Q., Wu, B., et al.: TeleComVis: Exploring Temporal Communities in Telecom Networks. In: Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, pp. 755–758. Springer, Bled Slovenia (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ye, Q., Wu, B., Wang, B. (2010). Distance Distribution and Average Shortest Path Length Estimation in Real-World Networks. In: Cao, L., Feng, Y., Zhong, J. (eds) Advanced Data Mining and Applications. ADMA 2010. Lecture Notes in Computer Science(), vol 6440. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17316-5_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-17316-5_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17315-8
Online ISBN: 978-3-642-17316-5
eBook Packages: Computer ScienceComputer Science (R0)