Webgraph

The webgraph describes the directed links between pages of the World Wide Web. A graph, in general, consists of several vertices, some pairs connected by edges. In a directed graph, edges are directed lines or arcs. The webgraph is a directed graph, whose vertices correspond to the pages of the WWW, and a directed edge connects page X to page Y if there exists a hyperlink on page X, referring to page Y.

Properties

The degree distribution of the webgraph strongly differs from the degree distribution of the classical random graph model, the Erdős–Rényi model:^[1] in the Erdős–Rényi model, there are very few large degree nodes, relative to the webgraph's degree distribution. The precise distribution is unclear,^[2] however: it is relatively well described by a lognormal distribution, as well as the Barabási–Albert model for power laws.^[3]^[4]
The webgraph is an example of a scale-free network.

Applications

The webgraph is used for:

computing the PageRank^[5] of the WWW-pages;
computing the personalized PageRank;^[6]
detecting webpages of similar topics, through graph-theoretical properties only, like co-citation;^[7]
and identifying hubs and authorities in the web for HITS algorithm.

References

^ P. Erdős, A. Renyi, Publ. Math. Inst. Hung. Acad. Sci. 5 (1960)
^ Meusel, R.; Vigna, S.; Lehmberg, O.; Bizer, C. (2015). "The Graph Structure in the Web - Analyzed on Different Aggregation Levels" (PDF). Journal of Web Science. 1 (1): 33–47. doi:10.1561/106.00000003. hdl:2434/372411.
^ Clauset, A.; Shalizi, C. R.; Newman, M. E. J. (2009). "Power-law distributions in empirical data". SIAM Rev. 51 (4): 661–703. arXiv:0706.1062. Bibcode:2009SIAMR..51..661C. doi:10.1137/070710111. S2CID 9155618.
^ Barabási, Albert-László; Albert, Réka (October 1999). "Emergence of scaling in random networks" (PDF). Science. 286 (5439): 509–512. arXiv:cond-mat/9910332. Bibcode:1999Sci...286..509B. doi:10.1126/science.286.5439.509. PMID 10521342. S2CID 524106..
^ S. Brin, L. Page, Computer Networks and ISDN Systems 30, 107 (1998)
^ Glen Jeh and Jennifer Widom. 2003. Scaling personalized web search. In Proceedings of the 12th international conference on World Wide Web (WWW '03). ACM, New York, NY, USA, 271–279. doi:10.1145/775152.775191
^ Kumar, Ravi; Raghavan, Prabhakar; Rajagopalan, Sridhar; Tomkins, Andrew (1999). "Trawling the Web for emerging cyber-communities". Computer Networks. 31 (11–16): 1481–1493. CiteSeerX 10.1.1.89.4025. doi:10.1016/S1389-1286(99)00040-7. S2CID 7069190.

External links

[1] P. Erdős, A. Renyi, Publ. Math. Inst. Hung. Acad. Sci. 5 (1960)

[2] Meusel, R.; Vigna, S.; Lehmberg, O.; Bizer, C. (2015). "The Graph Structure in the Web - Analyzed on Different Aggregation Levels" (PDF). Journal of Web Science. 1 (1): 33–47. doi:10.1561/106.00000003. hdl:2434/372411.

[3] Clauset, A.; Shalizi, C. R.; Newman, M. E. J. (2009). "Power-law distributions in empirical data". SIAM Rev. 51 (4): 661–703. arXiv:0706.1062. Bibcode:2009SIAMR..51..661C. doi:10.1137/070710111. S2CID 9155618.

[4] Barabási, Albert-László; Albert, Réka (October 1999). "Emergence of scaling in random networks" (PDF). Science. 286 (5439): 509–512. arXiv:cond-mat/9910332. Bibcode:1999Sci...286..509B. doi:10.1126/science.286.5439.509. PMID 10521342. S2CID 524106..

[5] S. Brin, L. Page, Computer Networks and ISDN Systems 30, 107 (1998)

[6] Glen Jeh and Jennifer Widom. 2003. Scaling personalized web search. In Proceedings of the 12th international conference on World Wide Web (WWW '03). ACM, New York, NY, USA, 271–279. doi:10.1145/775152.775191

[7] Kumar, Ravi; Raghavan, Prabhakar; Rajagopalan, Sridhar; Tomkins, Andrew (1999). "Trawling the Web for emerging cyber-communities". Computer Networks. 31 (11–16): 1481–1493. CiteSeerX 10.1.1.89.4025. doi:10.1016/S1389-1286(99)00040-7. S2CID 7069190.

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