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2017 | OriginalPaper | Chapter

Counting Edges and Triangles in Online Social Networks via Random Walk

Authors : Yang Wu, Cheng Long, Ada Wai-Chee Fu, Zitong Chen

Published in: Web and Big Data

Publisher: Springer International Publishing

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Abstract

Online social network (OSN) analysis has attracted much attention in recent years. Edge and triangle counts are both fundamental properties in OSNs. However, for many OSNs, one can only access parts of the network using the application programming interfaces (APIs). In such cases, conventional algorithms become infeasible. In this paper, we introduce efficient algorithms for estimating the number of edges and triangles in OSNs based on random walk sampling on OSNs. We also derive a theoretical bound on the sample size and number of APIs calls needed in our algorithms for a probabilistic accuracy guarantee. We ran experiments on several publicly available real-world networks and the results demonstrate the effectiveness of our algorithms.

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Appendix
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Literature
1.
go back to reference Katzir, L., Liberty, E., Somekh, O.: Estimating sizes of social networks via biased sampling. In: WWW, pp. 597–606 (2011) Katzir, L., Liberty, E., Somekh, O.: Estimating sizes of social networks via biased sampling. In: WWW, pp. 597–606 (2011)
2.
go back to reference Hardiman, S.J., Katzir, L.: Estimating clustering coefficients and size of social networks via random walk. In: WWW, pp. 539–550 (2013) Hardiman, S.J., Katzir, L.: Estimating clustering coefficients and size of social networks via random walk. In: WWW, pp. 539–550 (2013)
3.
go back to reference Jha, M., Seshadhri, C., Pinar, A.: Path sampling: a fast and provable method for estimating 4-vertex subgraph counts. In: WWW, pp. 495–505 (2015) Jha, M., Seshadhri, C., Pinar, A.: Path sampling: a fast and provable method for estimating 4-vertex subgraph counts. In: WWW, pp. 495–505 (2015)
4.
go back to reference Lee, C.-H., Xu, X., Eun, D.Y.: Beyond random walk and metropolis-hastings samplers: why you should not backtrack for unbiased graph sampling. In: SIGMETRICS, pp. 319–330 (2012) Lee, C.-H., Xu, X., Eun, D.Y.: Beyond random walk and metropolis-hastings samplers: why you should not backtrack for unbiased graph sampling. In: SIGMETRICS, pp. 319–330 (2012)
5.
go back to reference Li, R.-H., Yu, J., Qin, L., Mao, R., Jin, T.: On random walk based graph sampling. In: ICDE, pp. 927–938 (2015) Li, R.-H., Yu, J., Qin, L., Mao, R., Jin, T.: On random walk based graph sampling. In: ICDE, pp. 927–938 (2015)
6.
go back to reference Wang, P., Lui, J.C.S., Ribeiro, B., Towsley, D., Zhao, J., Guan, X.: Efficiently estimating motif statistics of large networks. In: ICDE, pp. 8:1–8:27 (2014) Wang, P., Lui, J.C.S., Ribeiro, B., Towsley, D., Zhao, J., Guan, X.: Efficiently estimating motif statistics of large networks. In: ICDE, pp. 8:1–8:27 (2014)
7.
go back to reference Bhuiyan, M., Rahman, M., Al Hasan, M.: Guise: uniform sampling of graphlets for large graph analysis. In: ICDM, pp. 91–100 (2012) Bhuiyan, M., Rahman, M., Al Hasan, M.: Guise: uniform sampling of graphlets for large graph analysis. In: ICDM, pp. 91–100 (2012)
8.
go back to reference Seshadhri, C., Pinar, A., KoldaWedge, T.G.: Sampling for computing clustering coefficients and triangle counts on large graphs. Stat. Anal. Data Mining 7(4), 233–235 (2014)MathSciNetCrossRef Seshadhri, C., Pinar, A., KoldaWedge, T.G.: Sampling for computing clustering coefficients and triangle counts on large graphs. Stat. Anal. Data Mining 7(4), 233–235 (2014)MathSciNetCrossRef
9.
go back to reference Gjoka, M., Kurant, M., Butts, C.T.: Walking in Facebook: a case study of unbiased sampling of OSNs. In: INFOCOM, pp. 1–9 (2010) Gjoka, M., Kurant, M., Butts, C.T.: Walking in Facebook: a case study of unbiased sampling of OSNs. In: INFOCOM, pp. 1–9 (2010)
10.
go back to reference Becchetti, L., Boldi, P., Castillo, C., Gionis, A.: Efficient semi-streaming algorithms for local triangle counting in massive graphs. In: KDD, pp. 16–24 (2008) Becchetti, L., Boldi, P., Castillo, C., Gionis, A.: Efficient semi-streaming algorithms for local triangle counting in massive graphs. In: KDD, pp. 16–24 (2008)
11.
go back to reference Eckmann, J.-P., Moses, E.: Curvature of co-links uncovers hidden thematic layers in the World Wide Web. In: PNAS, pp. 5825–5829 (2002) Eckmann, J.-P., Moses, E.: Curvature of co-links uncovers hidden thematic layers in the World Wide Web. In: PNAS, pp. 5825–5829 (2002)
13.
go back to reference Berry, J.W., Fosvedt, L., Nordman, D., Phillips, C.A., Wilson, A.G.: Listing triangles in expected linear time on power law graphs with exponent at least 7/3. Technical report SAND 2010–4474C (2011) Berry, J.W., Fosvedt, L., Nordman, D., Phillips, C.A., Wilson, A.G.: Listing triangles in expected linear time on power law graphs with exponent at least 7/3. Technical report SAND 2010–4474C (2011)
14.
go back to reference Chu, S., Cheng, J.: Triangle listing in massive networks and its applications. In: KDD, pp. 672–680 (2011) Chu, S., Cheng, J.: Triangle listing in massive networks and its applications. In: KDD, pp. 672–680 (2011)
15.
go back to reference Latapy, M.: Main-memory triangle computations for very large (sparse (power-law)) graphs. Theoret. Comput. Sci. 407, 458–473 (2008)MathSciNetCrossRefMATH Latapy, M.: Main-memory triangle computations for very large (sparse (power-law)) graphs. Theoret. Comput. Sci. 407, 458–473 (2008)MathSciNetCrossRefMATH
16.
go back to reference Tsourakakis, C.E., Kang, U., Miller, G.L., Faloutsos, C.: Doulion: counting triangles in massive graphs with a coin. In: KDD, pp. 837–846 (2009) Tsourakakis, C.E., Kang, U., Miller, G.L., Faloutsos, C.: Doulion: counting triangles in massive graphs with a coin. In: KDD, pp. 837–846 (2009)
17.
go back to reference Chen, X., Li, Y., Wang, G.P., Lui, J.C.S.: A general framework for estimating graphlet statistics via random walk. CoRR abs/1603.07504 (2016) Chen, X., Li, Y., Wang, G.P., Lui, J.C.S.: A general framework for estimating graphlet statistics via random walk. CoRR abs/1603.07504 (2016)
18.
go back to reference Park, H.-M., Silvestri, F., Kang, U., Pagh, R.: MapReduce triangle enumeration with guarantees. In: ACM Conference Information Knowledge Manage, pp. 1739–1748 (2014) Park, H.-M., Silvestri, F., Kang, U., Pagh, R.: MapReduce triangle enumeration with guarantees. In: ACM Conference Information Knowledge Manage, pp. 1739–1748 (2014)
19.
go back to reference Suri, S., Vassilvitskii, S.: Counting triangles and the curse of the last reducer. In: WWW, pp. 607–614 (2011) Suri, S., Vassilvitskii, S.: Counting triangles and the curse of the last reducer. In: WWW, pp. 607–614 (2011)
20.
21.
go back to reference Hu, X., Tao, Y., Chung, C.-W.: Massive graph triangulation. In: SIGMOD, pp. 325–336 (2013) Hu, X., Tao, Y., Chung, C.-W.: Massive graph triangulation. In: SIGMOD, pp. 325–336 (2013)
22.
go back to reference Chu, S., Cheng, J.: Triangle listing in massive networks. ACM Trans. Knowl. Discov. Data 6(4), 17 (2012)CrossRef Chu, S., Cheng, J.: Triangle listing in massive networks. ACM Trans. Knowl. Discov. Data 6(4), 17 (2012)CrossRef
23.
go back to reference Pagh, R., Silvestri, F.: The input/output complexity of triangle enumeration. In: ACM Symposium Principles Database System, pp. 224–233 (2014) Pagh, R., Silvestri, F.: The input/output complexity of triangle enumeration. In: ACM Symposium Principles Database System, pp. 224–233 (2014)
24.
go back to reference Seshadhri, C., Pinar, A., Kold, T.G.: Triadic measures on graphs: the power of wedge sampling. In: SDM (2013) Seshadhri, C., Pinar, A., Kold, T.G.: Triadic measures on graphs: the power of wedge sampling. In: SDM (2013)
25.
go back to reference Berry, J.W., Hendrickson, B., LaViolette, R.A., Phillips, C.A.: Tolerating the community detection resolutionlimit with edge weighting. Phys. Rev. E 83, 056119 (2011)CrossRef Berry, J.W., Hendrickson, B., LaViolette, R.A., Phillips, C.A.: Tolerating the community detection resolutionlimit with edge weighting. Phys. Rev. E 83, 056119 (2011)CrossRef
Metadata
Title
Counting Edges and Triangles in Online Social Networks via Random Walk
Authors
Yang Wu
Cheng Long
Ada Wai-Chee Fu
Zitong Chen
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-63579-8_27

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