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On the spread of viruses on the internet
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The changing face of web search: algorithms, auctions and advertising
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Evolution of page popularity under random web graph models
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Using a room metaphor for e-forensic working environments
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Protean graphs with a variety of ranking schemes
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Evolution of two-sided markets
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Rank-Based Attachment Leads to Power Law Graphs
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Rank-based models of network structure and the discovery of content
WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
Random hyperbolic graphs: degree sequence and clustering
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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The design of algorithms on complex networks, such as routing, ranking or recommendation algorithms, requires a detailed understanding of the growth characteristics of the networks of interest, such as the Internet,the web graph, social networks or online communities. To this end, preferential attachment, in which the popularity (or relevance) of a node is determined by its degree, is a well-known and appealing random graph model, whose predictions are in accordance with experiments on the web graph and several social networks. However, its central assumption, that the popularity of the nodes dependsonly on their degree, is not a realistic one, since every node has potentially some intrinsic quality which can differentiate its attractiveness from other nodes with similar degrees. In this paper, we provide a rigorous analysis of preferential attachment with fitness, suggested by Bianconi and Barabási and studied by Motwani and Xu, in which the degree of a vertex is scaled by its quality to determine its attractiveness. Including quality considerations in the classical preferential attachment model provides a much more realistic description of many complex networks, such as the web graph, and allows toobserve a much richer behavior in the growth dynamics of these networks. Specifically, depending on the shape of the distributionfrom which the qualities of the vertices are drawn, we observe three distinct phases, namely a first-mover-advantage phase, afit-get-richer phase and an innovation-pays-offphase. We precisely characterize the properties of the quality distribution that result in each of these phases and we computethe exact growth dynamics for each phase. The dynamics provide rich information about the quality of the vertices, which can bevery useful in many practical contexts, including ranking algorithms for the web, recommendation algorithms, as well as thestudy of social networks.