{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T00:05:29Z","timestamp":1725494729191},"publisher-location":"Berlin, Heidelberg","reference-count":42,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540770039"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-77004-6_4","type":"book-chapter","created":{"date-parts":[[2007,11,14]],"date-time":"2007-11-14T01:40:36Z","timestamp":1195004436000},"page":"41-55","source":"Crossref","is-referenced-by-count":8,"title":["A Geometric Preferential Attachment Model of Networks II"],"prefix":"10.1007","author":[{"given":"Abraham D.","family":"Flaxman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alan M.","family":"Frieze","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan","family":"Vera","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"4_CR1","doi-asserted-by":"crossref","unstructured":"Aiello, W., Chung, F.R.K., Lu, L.: A random graph model for massive graphs. In: Proc. of the 32nd Annual ACM Symposium on the Theory of Computing, pp. 171\u2013180 (2000)","DOI":"10.1145\/335305.335326"},{"key":"4_CR2","doi-asserted-by":"crossref","unstructured":"Aiello, W., Chung, F.R.K., Lu, L.: Random Evolution in Massive Graphs. In: Proc. of IEEE Symposium on Foundations of Computer Science, pp. 510\u2013519 (2001)","DOI":"10.1109\/SFCS.2001.959927"},{"key":"4_CR3","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1038\/43601","volume":"401","author":"R. Albert","year":"1999","unstructured":"Albert, R., Barab\u00e1si, A., Jeong, H.: Diameter of the world wide web. Nature\u00a0401, 103\u2013131 (1999)","journal-title":"Nature"},{"key":"4_CR4","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1126\/science.286.5439.509","volume":"286","author":"A. Barabasi","year":"1999","unstructured":"Barabasi, A., Albert, R.: Emergence of scaling in random networks. Science\u00a0286, 509\u2013512 (1999)","journal-title":"Science"},{"key":"4_CR5","doi-asserted-by":"crossref","unstructured":"Berger, N., Bollobas, B., Borgs, C., Chayes, J., Riordan, O.: Degree distribution of the FKP network model. In: Proc. of the 30th International Colloquium of Automata, Languages and Programming, pp. 725\u2013738 (2003)","DOI":"10.1007\/3-540-45061-0_57"},{"key":"4_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1007\/978-3-540-27836-8_20","volume-title":"Automata, Languages and Programming","author":"N. Berger","year":"2004","unstructured":"Berger, N., Borgs, C., Chayes, J., D\u2019Souza, R., Kleinberg, R.D.: Competition-induced preferential attachment. In: D\u00edaz, J., Karhum\u00e4ki, J., Lepist\u00f6, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol.\u00a03142, pp. 208\u2013221. Springer, Heidelberg (2004)"},{"key":"4_CR7","unstructured":"Blandford, D., Blelloch, G.E., Kash, I.: Compact Representations of Separable Graphs. In: Proc. of ACM\/SIAM Symposium on Discrete Algorithms, pp. 679\u2013688 (2003)"},{"key":"4_CR8","volume-title":"Handbook of Graphs and Networks","author":"B. Bollob\u00e1s","year":"2002","unstructured":"Bollob\u00e1s, B., Riordan, O.: Mathematical Results on Scale-free Random Graphs. In: Handbook of Graphs and Networks, Wiley-VCH, Berlin (2002)"},{"key":"4_CR9","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s00493-004-0002-2","volume":"4","author":"B. Bollob\u00e1s","year":"2004","unstructured":"Bollob\u00e1s, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica\u00a04, 5\u201334 (2004)","journal-title":"Combinatorica"},{"issue":"2","key":"4_CR10","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1080\/15427951.2004.10129084","volume":"1","author":"B. Bollob\u00e1s","year":"2004","unstructured":"Bollob\u00e1s, B., Riordan, O.: Coupling scale free and classical random graphs. Internet Mathematics\u00a01(2), 215\u2013225 (2004)","journal-title":"Internet Mathematics"},{"key":"4_CR11","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1002\/rsa.1009","volume":"18","author":"B. Bollob\u00e1s","year":"2001","unstructured":"Bollob\u00e1s, B., Riordan, O., Spencer, J., Tusan\u00e1dy, G.: The degree sequence of a scale-free random graph process. Random Structures and Algorithms\u00a018, 279\u2013290 (2001)","journal-title":"Random Structures and Algorithms"},{"key":"4_CR12","doi-asserted-by":"crossref","unstructured":"Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph structure in the web. In: Proc. of the 9th Intl. World Wide Web Conference, pp. 309\u2013320 (2002)","DOI":"10.1016\/S1389-1286(00)00083-9"},{"key":"4_CR13","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.disc.2003.10.020","volume":"282","author":"G. Buckley","year":"2004","unstructured":"Buckley, G., Osthus, D.: Popularity based random graph models leading to a scale-free degree distribution. Discrete Mathematics\u00a0282, 53\u201368 (2004)","journal-title":"Discrete Mathematics"},{"key":"4_CR14","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s00026-003-0178-y","volume":"7","author":"F.R.K. Chung","year":"2003","unstructured":"Chung, F.R.K., Lu, L., Vu, V.: Eigenvalues of random power law graphs. Annals of Combinatorics\u00a07, 21\u201333 (2003)","journal-title":"Annals of Combinatorics"},{"key":"4_CR15","doi-asserted-by":"publisher","first-page":"6313","DOI":"10.1073\/pnas.0937490100","volume":"100","author":"F.R.K. Chung","year":"2003","unstructured":"Chung, F.R.K., Lu, L., Vu, V.: The spectra of random graphs with expected degrees. Proceedings of national Academy of Sciences\u00a0100, 6313\u20136318 (2003)","journal-title":"Proceedings of national Academy of Sciences"},{"key":"4_CR16","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1002\/rsa.10084","volume":"22","author":"C. Cooper","year":"2003","unstructured":"Cooper, C., Frieze, A.M.: A General Model of Undirected Web Graphs. Random Structures and Algorithms\u00a022, 311\u2013335 (2003)","journal-title":"Random Structures and Algorithms"},{"key":"4_CR17","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1080\/15427951.2004.10129095","volume":"1","author":"C. Cooper","year":"2004","unstructured":"Cooper, C., Frieze, A.M., Vera, J.: Random deletions in a scale free random graph process. Internet Mathematics\u00a01, 463\u2013483 (2004)","journal-title":"Internet Mathematics"},{"key":"4_CR18","unstructured":"Drinea, E., Enachescu, M., Mitzenmacher, M.: Variations on Random Graph Models for the Web, Harvard Technical Report TR-06-01 (2001)"},{"issue":"4","key":"4_CR19","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1209\/epl\/i2005-10441-3","volume":"73","author":"E. Estrada","year":"2006","unstructured":"Estrada, E.: Spectral scaling and good expansion properties in complex networks. Europhysics Letters\u00a073(4), 649\u2013655 (2006)","journal-title":"Europhysics Letters"},{"key":"4_CR20","doi-asserted-by":"crossref","first-page":"290","DOI":"10.5486\/PMD.1959.6.3-4.12","volume":"6","author":"P. Erd\u00f6s","year":"1959","unstructured":"Erd\u00f6s, P., R\u00e9nyi, A.: On random graphs I. Publicationes Mathematicae Debrecen\u00a06, 290\u2013297 (1959)","journal-title":"Publicationes Mathematicae Debrecen"},{"key":"4_CR21","doi-asserted-by":"crossref","unstructured":"Fabrikant, A., Koutsoupias, E., Papadimitriou, C.H.: Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet. In: Proc. of 29th International Colloquium of Automata, Languages and Programming (2002)","DOI":"10.1007\/3-540-45465-9_11"},{"key":"4_CR22","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1145\/316194.316229","volume":"29","author":"M. Faloutsos","year":"1999","unstructured":"Faloutsos, M., Faloutsos, P., Faloutsos, C.: On Power-law Relationships of the Internet Topology. ACM SIGCOMM Computer Communication Review\u00a029, 251\u2013262 (1999)","journal-title":"ACM SIGCOMM Computer Communication Review"},{"key":"4_CR23","unstructured":"Flaxman, A.: Expansion and lack thereof in randomly perturbed graphs. In: Proc. of the Web Algorithms Workshop (to appear, 2006)"},{"key":"4_CR24","unstructured":"Flaxman, A., Frieze, A.M., Vera, J.: A Geometric Preferential Attachment Model of Networks, Internet Mathematics (to appear)"},{"key":"4_CR25","doi-asserted-by":"crossref","first-page":"037103","DOI":"10.1103\/PhysRevE.69.037103","volume":"69","author":"J. G\u00f3mez-Garde\u00f1es","year":"2004","unstructured":"G\u00f3mez-Garde\u00f1es, J., Moreno, Y.: Local versus global knowledge in the Barab\u00e1si-Albert scale-free network model. Physical Review E\u00a069, 037103 (2004)","journal-title":"Physical Review E"},{"key":"4_CR26","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1511\/2000.2.104","volume":"88","author":"B. Hayes","year":"2000","unstructured":"Hayes, B.: Graph theory in practice: Part II. American Scientist\u00a088, 104\u2013109 (2000)","journal-title":"American Scientist"},{"key":"4_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48686-0_1","volume-title":"Computing and Combinatorics","author":"J.M. Kleinberg","year":"1999","unstructured":"Kleinberg, J.M., Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A.S.: The Web as a Graph: Measurements, Models and Methods. In: Asano, T., Imai, H., Lee, D.T., Nakano, S.-i., Tokuyama, T. (eds.) COCOON 1999. LNCS, vol.\u00a01627, Springer, Heidelberg (1999)"},{"key":"4_CR28","doi-asserted-by":"crossref","unstructured":"Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: Stochastic Models for the Web Graph. In: Proc. IEEE Symposium on Foundations of Computer Science, p. 57 (2000)","DOI":"10.1109\/SFCS.2000.892065"},{"key":"4_CR29","doi-asserted-by":"crossref","unstructured":"Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: The Web as a Graph. In: PODS 2000. Proc. 19th ACM SIGACT-SIGMOD-AIGART Symp. Principles of Database Systems, pp. 1\u201310 (2000)","DOI":"10.1145\/335168.335170"},{"key":"4_CR30","doi-asserted-by":"crossref","unstructured":"Li, L., Alderson, D., Doyle, J.C., Willinger, W.: Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications. Internet Mathematics\u00a02(4), 431\u2013523","DOI":"10.1080\/15427951.2005.10129111"},{"key":"4_CR31","unstructured":"Mihail, M.: private communication"},{"key":"4_CR32","doi-asserted-by":"publisher","first-page":"1481","DOI":"10.1016\/S1389-1286(99)00040-7","volume":"31","author":"R. Kumar","year":"1999","unstructured":"Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A.: Trawling the Web for emerging cyber-communities. Computer Networks\u00a031, 1481\u20131493 (1999)","journal-title":"Computer Networks"},{"key":"4_CR33","doi-asserted-by":"crossref","unstructured":"McDiarmid, C.J.H.: Concentration. Probabilistic methods in algorithmic discrete mathematics, 195\u2013248 (1998)","DOI":"10.1007\/978-3-662-12788-9_6"},{"key":"4_CR34","doi-asserted-by":"crossref","unstructured":"Mihail, M., Papadimitriou, C.H.: On the Eigenvalue Power Law. In: Proc. of the 6th International Workshop on Randomization and Approximation Techniques, pp. 254\u2013262 (2002)","DOI":"10.1007\/3-540-45726-7_20"},{"key":"4_CR35","doi-asserted-by":"crossref","unstructured":"Mihail, M., Papadimitriou, C.H., Saberi, A.: On Certain Connectivity Properties of the Internet Topology. In: Proc. IEEE Symposium on Foundations of Computer Science, p. 28 (2003)","DOI":"10.1109\/SFCS.2003.1238178"},{"issue":"2","key":"4_CR36","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1080\/15427951.2004.10129088","volume":"1","author":"M. Mitzenmacher","year":"2004","unstructured":"Mitzenmacher, M.: A brief history of generative models for power law and lognormal distributions. Internet Mathematics\u00a01(2), 226\u2013251 (2004)","journal-title":"Internet Mathematics"},{"key":"4_CR37","unstructured":"Newman, M., Barab\u00e1si, A.-L., Watts, D.J.: The Structure and Dynamics of Networks, Princeton University Press (2006)"},{"key":"4_CR38","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198506263.001.0001","volume-title":"Random Geometric Graphs","author":"M.D. Penrose","year":"2003","unstructured":"Penrose, M.D.: Random Geometric Graphs. Oxford University Press, Oxford (2003)"},{"key":"4_CR39","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1093\/biomet\/42.3-4.425","volume":"42","author":"H.A. Simon","year":"1955","unstructured":"Simon, H.A.: On a class of skew distribution functions. Biometrika\u00a042, 425\u2013440 (1955)","journal-title":"Biometrika"},{"key":"4_CR40","unstructured":"van der Hofstad, R.: Random Graphs and Complex Networks, unpublished manuscript (2007)"},{"key":"4_CR41","doi-asserted-by":"crossref","DOI":"10.1515\/9780691188331","volume-title":"Small Worlds: The Dynamics of Networks between Order and Randomness","author":"D.J. Watts","year":"1999","unstructured":"Watts, D.J.: Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton (1999)"},{"key":"4_CR42","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1098\/rstb.1925.0002","volume":"213","author":"G. Yule","year":"1925","unstructured":"Yule, G.: A mathematical theory of evolution based on the conclusions of Dr. J.C. Willis. Philosophical Transactions of the Royal Society of London (Series B)\u00a0213, 21\u201387 (1925)","journal-title":"Philosophical Transactions of the Royal Society of London (Series B)"}],"container-title":["Lecture Notes in Computer Science","Algorithms and Models for the Web-Graph"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-77004-6_4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,14]],"date-time":"2023-05-14T14:30:37Z","timestamp":1684074637000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-77004-6_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540770039"],"references-count":42,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-77004-6_4","relation":{},"subject":[]}}