Web graph Source: en.wikipedia.org/wiki/Web_graph

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.^[1]

Properties

The degree distribution of the webgraph strongly differs from the degree distribution of the classical random graph model, the Erdős–Rényi model:^[2] in the Erdős–Rényi model, there are very few large degree nodes, relative to the webgraph's degree distribution. The precise distribution is unclear,^[3] however: it is relatively well described by a lognormal distribution, as well as the Barabási–Albert model for power laws.^[4]^[5]
The webgraph is an example of a scale-free network.

Applications

The webgraph is used for:

computing the PageRank^[6] of the world wide web's pages;
computing the personalized PageRank;^[7]
detecting webpages of similar topics, through graph-theoretical properties only, like co-citation;^[8]
and identifying hubs and authorities in the web for HITS algorithm.

References

^ Manning, Christopher D.; Raghavan, Prabhakar; Schütze, Hinrich (2008). "The web graph". Introduction to Information Retrieval. Cambridge University Press.
^ Erdős, Paul; Rényi, Alfréd (1960). "On the evolution of random graphs" (PDF). Publication of the Mathematical Institute of the Hungarian Academy of Sciences. 5: 17–61.
^ 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..
^ Brin, Sergey; Page, Lawrence (1998-04-01). "The anatomy of a large-scale hypertextual Web search engine". Computer Networks and ISDN Systems. Proceedings of the Seventh International World Wide Web Conference. 30 (1): 107–117. doi:10.1016/S0169-7552(98)00110-X. ISSN 0169-7552.
^ 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] Manning, Christopher D.; Raghavan, Prabhakar; Schütze, Hinrich (2008). "The web graph". Introduction to Information Retrieval. Cambridge University Press.

[2] Erdős, Paul; Rényi, Alfréd (1960). "On the evolution of random graphs" (PDF). Publication of the Mathematical Institute of the Hungarian Academy of Sciences. 5: 17–61.

[3] 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.

[4] 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.

[5] 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..

[6] Brin, Sergey; Page, Lawrence (1998-04-01). "The anatomy of a large-scale hypertextual Web search engine". Computer Networks and ISDN Systems. Proceedings of the Seventh International World Wide Web Conference. 30 (1): 107–117. doi:10.1016/S0169-7552(98)00110-X. ISSN 0169-7552.

[7] 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

[8] 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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