Jure Leskovec
Christos Faloutsos
ABSTRACT
Given a huge real graph, how can we derive a representative sample? There are many known algorithms to compute interesting measures (shortest paths, centrality, betweenness, etc.), but several of them become impractical for large graphs. Thus graph sampling is essential.The natural questions to ask are (a) which sampling method to use, (b) how small can the sample size be, and (c) how to scale up the measurements of the sample (e.g., the diameter), to get estimates for the large graph. The deeper, underlying question is subtle: how do we measure success?.We answer the above questions, and test our answers by thorough experiments on several, diverse datasets, spanning thousands nodes and edges. We consider several sampling methods, propose novel methods to check the goodness of sampling, and develop a set of scaling laws that describe relations between the properties of the original and the sample.In addition to the theoretical contributions, the practical conclusions from our work are: Sampling strategies based on edge selection do not perform well; simple uniform random node selection performs surprisingly well. Overall, best performing methods are the ones based on random-walks and "forest fire"; they match very accurately both static as well as evolutionary graph patterns, with sample sizes down to about 15% of the original graph.
- M. Adler and M. Mitzenmacher. Towards compressing web graphs. In Data Compression Conference, 2001. Google Scholar
Digital Library
- E. M. Airoldi and K. M. Carley. Sampling algorithms for pure network topologies. SIGKDD Explor., 2005. Google ScholarDigital Library
- D. Chakrabarti, Y. Zhan, and C. Faloutsos. R-mat: A recursive model for graph mining. In SDM, 2004.Google ScholarCross Ref
- X. A. Dimitropoulos and G. F. Riley. Creating realistic BGP models. IEEE/ACM MASCOTS, 2003.Google ScholarCross Ref
- M. Faloutsos, P. Faloutsos, and C. Faloutsos. On power-law relationships of the internet topology. In SIGCOMM, pages 251--262, 1999. Google ScholarDigital Library
- T. Feder and R. Motwani. Clique partitions, graph compression and speeding-up algorithms. In Journal of Computer And System Sciences, volume 51, 1995. Google ScholarDigital Library
- A. C. Gilbert and K. Levchenko. Compressing network graphs. In LinkKDD, 2004.Google Scholar
- V. Krishnamurthy, M. Faloutsos, M. Chrobak, L. Lao, J.-H. Cui, and A. G. Percus. Reducing large internet topologies for faster simulations. In Networking, 2005. Google ScholarDigital Library
- J. Leskovec, J. Kleinberg, and C. Faloutsos. Graphs over time: Densification laws, shrinking diamaters and possible explanations. In ACM SIGKDD, 2005. Google ScholarDigital Library
- U. of Oregon. Route views project.Google Scholar
- C. R. Palmer, P. B. Gibbons, and C. Faloutsos. Anf: A fast and scalable tool for data mining in massive graphs. In SIGKDD, Edmonton, AB, Canada, 2002. Google ScholarDigital Library
- D. Rafiei and S. Curial. Effectively visualizing large networks through sampling. In Visualization, 2005.Google Scholar
- M. Richardson, R. Agrawal, and P. Domingos. Trust management for the semantic web. In Second International Semantic Web Conference, 2003.Google ScholarDigital Library
- M. P. H. Stumpf, C. Wiuf, and R. M. May. Subnets of scale-free networks are not scale-free: Sampling properties of networks. In PNAS, volume 102, 2005.Google ScholarCross Ref
- D. Stutzbach, R. Rejaie, N. Duffield, S. Sen, and W. Willinger. Sampling techniques for large, dynamics graphs. In CIS-TR-06-01, University of Oregon, 2006.Google Scholar
- D. J. Watts and S. H. Strogatz. Collective dynamics of 'small-world'networks. Nature , 393:440--442, 1998.Google Scholar
Index Terms
- Sampling from large graphs
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