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Diameter of the World-Wide Web
Open accessAbstract
Despite its increasing role in communication, the World-Wide Web remains uncontrolled: any individual or institution can create a website with any number of documents and links. This unregulated growth leads to a huge and complex web, which becomes a large directed graph whose vertices are documents and whose edges are links (URLs) that point from one document to another. The topology of this graph determines the web's connectivity and consequently how effectively we can locate information on it. But its enormous size (estimated to be at least 8×108 documents) and the continual changing of documents and links make it impossible to catalogue all the vertices and edges.
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Citations
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Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
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Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2008/10/p10008 · Cited by 21,424
Statistical mechanics of complex networks
Albert, R., & Barabási, A.-L. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.47 · Cited by 20,471
Self-citationThe Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
Community structure in social and biological networks
Girvan, M., & Newman, M. E. J. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.122653799 · Cited by 15,502
Finding and evaluating community structure in networks
Newman, M. E. J., & Girvan, M. (2004) · Physical Review E · doi:10.1103/physreve.69.026113 · Cited by 13,931
Fortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293
Complex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010
Error and attack tolerance of complex networks
Albert, R., Jeong, H., & Barabási, A.-L. (2000) · Nature · doi:10.1038/35019019 · Cited by 7,534
Self-citationFinding community structure in very large networks
Clauset, A., Newman, M. E. J., & Moore, C. (2004) · Physical Review E · doi:10.1103/physreve.70.066111 · Cited by 7,390
Efficient behavior of small-world networks
Latora, V., & Marchiori, M. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.198701 · Cited by 5,119
The Large-Scale Organization of Metabolic Networks
Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N., & Barabási, A.-L. (2000) · Nature · doi:10.1038/35036627 · Cited by 4,972
Self-citationMeasurement and analysis of online social networks
Mislove, A., Marcon, M., Gummadi, K. P., Druschel, P., & Bhattacharjee, B. (2007) · Proceedings of the 7th ACM SIGCOMM conference on Internet measurement · doi:10.1145/1298306.1298311 · Cited by 3,057
Classes of small-world networks
Amaral, L. A. N., Scala, A., Barthélémy, M., & Stanley, H. E. (2000) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.200327197 · Cited by 3,051
Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., & Wiener, J. (2000) · Computer Networks · doi:10.1016/s1389-1286(00)00083-9 · Cited by 2,810
Barthélemy, M. (2011) · Physics Reports · doi:10.1016/j.physrep.2010.11.002 · Cited by 2,469
Defining and identifying communities in networks
Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., & Parisi, D. (2004) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0400054101 · Cited by 2,450
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Critical phenomena in complex networks
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Farrell, H., & Newman, A. L. (2019) · International Security · doi:10.1162/isec_a_00351 · Cited by 1,879
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Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence
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Mitzenmacher, M. (2004) · Internet Mathematics · doi:10.1080/15427951.2004.10129088 · Cited by 1,188
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Noh, J. D., & Rieger, H. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.118701 · Cited by 1,148
Competition and multiscaling in evolving networks
Bianconi, G., & Barabási, A.-L. (2001) · Europhysics Letters (EPL) · doi:10.1209/epl/i2001-00260-6 · Cited by 1,067
Self-citationBroido, A. D., & Clauset, A. (2019) · Nature Communications · doi:10.1038/s41467-019-08746-5 · Cited by 875
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Bianconi, G., & Barabási, A.-L. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5632 · Cited by 808
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Barthélemy, M. (2004) · The European Physical Journal B · doi:10.1140/epjb/e2004-00111-4 · Cited by 804
Scale-Free Networks from Varying Vertex Intrinsic Fitness
Caldarelli, G., Capocci, A., De Los Rios, P., & Muñoz, M. A. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.258702 · Cited by 794
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Power, J. D., Fair, D. A., Schlaggar, B. L., & Petersen, S. E. (2010) · Neuron · doi:10.1016/j.neuron.2010.08.017 · Cited by 751
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Power, J. D., Schlaggar, B. L., Lessov-Schlaggar, C. N., & Petersen, S. E. (2013) · Neuron · doi:10.1016/j.neuron.2013.07.035 · Cited by 716
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Barabási, A.-L. (2012) · Nature Physics · doi:10.1038/nphys2188 · Cited by 502
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Modular networks and cumulative impact of lateral transfer in prokaryote genome evolution
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Dyhrfjeld-Johnsen, J., Santhakumar, V., Morgan, R. J., Huerta, R., Tsimring, L., & Soltesz, I. (2007) · Journal of Neurophysiology · doi:10.1152/jn.00950.2006 · Cited by 230
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(2002)
Metadata
- Authors
- Albert, R., Jeong, H., & Barabási, A.-L.
- Venue
- Nature
- Published
- 1999-09
- Volume
- 401
- Issue
- 6749
- Pages
- 130-131
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W2769133055
- Cited by
- 4,260
- References
- 0
- FWCI
- 70.42
- Type
- journal article
- Language
- en
- Open access
- green
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