Graft: An Efficient Graphlet Counting Method for Large Graph Analysis

IEEE Transactions on Knowledge and Data Engineering

Volumn 26, Issue 10, 2014, Pages 2466-2478

  Rahman, Mahmudur ^a   Bhuiyan, Mansurul Alam ^a   Al Hasan, Mohammad ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

GFD; Graph mining; graphlet counting

Indexed keywords

TOPOLOGY;

COMPUTATION COSTS; EXISTING PROBLEMS; FREQUENCY DISTRIBUTIONS; GRAPH MINING; GRAPHLET COUNTING; POWER LAW EXPONENT; REAL-LIFE NETWORKS; TOPOLOGICAL STRUCTURE;

GRAFTING (CHEMICAL);

EID: 84906656572     PISSN: 10414347     EISSN: None     Source Type: Journal    
DOI: 10.1109/TKDE.2013.2297929     Document Type: Article

References (35)

1. S.P. Borgatti, A. Mehra, D.J. Brass, and G. Labianca, "Network Analysis in the Social Sciences," Science, vol. 323, pp. 892-895, 2009.
2. M. Faloutsos, P. Faloutsos, and C. Faloutsos, "On Power-Law Relationships of the Internet Topology," Proc. ACM Conf. Applications, Technologies, Architectures, and Protocols for Computer Comm. (SIGCOMM'99), pp. 251-262, 1999.
3. N. Przulj, "Biological Network Comparison Using Graphlet Degree Distribution," Bioinformatics, vol. 23, no. 2, pp. e177-e183, 2007.
4. A.-L. Barabasi and R. Albert, "Emergence of Scaling in Random Networks," Science, vol. 286, pp. 509-512, Oct. 1999.
5. D.J. Watts and S.H. Strogatz, "Collective Dynamics of 'Small- World' Networks," Nature, vol. 393, pp. 440-442, June 1998.
6. J. Leskovec, J. Kleinberg, and C. Faloutsos, "Graphs Over Time: Densification Laws, Shrinking Diameters and Possible Explanations," Proc. 11th ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining, 2005.
7. V. Preciado and A. Jadbabaie, "Moment-Based Spectral Analysis of Large-Scale Networks Using Local Structural Information," IEEE/ACM Trans. Networking, vol. 21, no. 2, pp. 373-382, Apr. 2013.
8. T. Milenkovic and N. Przulj, "Uncovering Biological Network Function via Graphlet Degree Signatures," Cancer Informatics, vol. 6, pp. 257-273, 2008.
9. H.A. Soufiani and E.M. Airoldi, "Graphlet Decomposition of a Weighted Network," ArXiv e-prints, 2012.
10. O. Kuchaiev, A. Stevanovic, W. Hayes, and N. Przulj, "Graphcrunch 2: Software Tool for Network Modeling, Alignment and Clustering," BMC Bioinformatics, vol. 12, no. 1, 2011.
11. P. Ribeiro and F. Silva, "Querying Subgraph Sets with g-Tries," Proc. Second ACM SIGMOD Workshop Databases and Social Networks (DBSocial'12), 2012.
12. C.E. Tsourakakis, U. Kang, G.L. Miller, and C. Faloutsos, "Doulion: Counting Triangles in Massive Graphs with a Coin," Proc. 15th ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining (KDD), pp. 837-846, 2009.
13. H. Avron, "Counting Triangles in Large Graphs Using Randomized Matrix Trace Estimation," Proc. KDD-LDMTA'10, 2010.
14. E.C.E. Tsourakakis, "Counting Triangles in Real-World Networks Using Projections," Knowledge and Information Systems, vol. 26, pp. 501-520, 2011.
15. N. Pržulj, D.G. Corneil, and I. Jurisica, "Efficient Estimation of Graphlet Frequency Distributions in Protein-Protein Interaction Networks," Bioinformatics, vol. 22, no. 8, pp. 974-980, 2006.
16. D. Johnson, "Finding all the Elementary Circuits of a Directed Graph," SIAM J. Computing, vol. 4, pp. 77-84, 1975.
17. N. Alon, R. Yuster, and U. Zwick, "Finding and Counting Given Length Cycles," Algorithmica, vol. 17, pp. 209-223, 1997.
18. E. Akkoyunlu, "The Enumeration of Maximal Cliques of Large Graphs," SIAM J. Computing, vol. 2, pp. 1-6, 1973.
19. M. Latapy, "Main-Memory Triangle Computations for Very Large (Sparse (Power-Law)) Graphs," Theoretical Computer Science, vol. 407, pp. 458-473, 2008.
20. N. Przulj, D.G. Corneil, and I. Jurisica, "Modeling Interactome: Scale-Free or Geometric?" Bioinformatics, vol. 20, no. 18, pp. 3508- 3515, 2004.
21. D. Marcus and Y. Shavitt, "Rage-a Rapid Graphlet Enumerator for Large Networks," Computer Networks: The Int'l J. Computer and Telecomm., vol. 56, no. 2, pp. 810-819, 2012.
22. S. Wernicke, Efficient Detection of Network Motifs, vol. 3, no. 4, pp. 347-359, 2006.
23. S. Wernicke and F. Rasche, "Fanmod: A Tool for Fast Network Motif Detection," Bioinformatics, vol. 22, no. 9, pp. 1152-1153, 2006.
24. N. Shervashidzea, S. Vishwanathan, T. Petri, K. Mehlhorn, and K. Borgwardt, "Efficient Graphlet Kernels for Large Graph Comparison," Proc. 12th Int'l Conf. Artificial Intelligence and Statistics (AISTATS), 2009.
25. J. Janssen, M. Hurshman, and N. Kalyaniwalla, "Model Selection for Social Networks Using Graphlets," Internet Math., vol. 8, no. 4, pp. 338-363, 2012.
26. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, "Network Motifs: Simple Building Blocks of Complex Networks," Science, vol. 298, pp. 824-827, 2002.
27. N. Kashtan, S. Itzkovitz, R. Milo, and U. Alon, "Efficient Sampling Algorithm for Estimating Subgraph Concentrations and Detecting Network Motifs," Bioinformatics, vol. 20, no. 11, pp. 1746-1758, 2004.
28. R. Duke, H. Lefmann, and V. Rdl, "A Fast Approximation Algorithm for Computing the Frequencies of Subgraphs in a Given Graph," SIAM J. Computing, vol. 24, no. 3, pp. 598-620, 1995.
29. R. Itzhack, Y. Mogilevski, and Y. Louzoun, "An Optimal Algorithm for Counting Network Motifs," Physica D, vol. 381, pp. 482- 490, 2007.
30. M. Gonen and Y. Shavitt, "Approximating the Number of Network Motifs," Proc. Sixth Int'l Workshop Algorithms and Models for the Web-Graph, pp. 13-24, 2009.
31. M. Gonen, D. Ron, and Y. Shavitt, "Counting Stars and other Small Subgraphs in Sublinear Time," SIAM J. Discrete Math., vol. 25, no. 2, pp. 1365-1411, 2011.
32. E.C.E. Tsourakakis, "Fast Counting of Triangles in Large Real Networks without Counting: Algorithms and Laws," Proc. Eighth IEEE Int'l Conf. Data Mining, pp. 608-617, 2008.
33. M. Kolountzakis, G. Miller, R. Peng, and C. Tsourakakis, "Efficient Triangle Counting in Large Graphs via Degree-Based Vertex Partitioning," Internet Math., vol. 8, no. 1/2, pp. 161-185, 2012.
34. R. Pagh and C. Tsourakakis, "Colorful Triangle Counting and a Mapreduce Implementation," Information Processing Letters, vol. 112, no. 7, pp. 277-281, 2012.
35. J. Leskovec and C. Faloutsos, "Sampling from Large Graphs," Proc. 12th ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining (KDD'06), pp. 631-636, 2006.