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...ibit high clustering. Studies have shown that the Web [5,12], scientific collaboration on research papers [41], film actors [6], and general social networks [3] have small-world properties. Kleinberg =-=[23]-=- proposes a model to explain the small-world phenomenon in offline social networks, and also examines navigability in these networks [22]. The online social networks examined in this paper have small-...

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... chain, then (106) 1 − λ2(P ∗ ) ≤ dmax(1 − λ2(Pmd)). (107) Thus the averaging times for both random walks are of the same order, and differ by a factor of atmost dmax. For example, the social network =-=[Kle00]-=- is a regular graph with dmax = 5, which is the degree of each node in the graph. For the social network, therefore, the natural random walk (which is the same as the maximum degree chain) leads to an...

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...selves to a pre-existing node with probability proportional to the degree of the latter. This “rich get richer” principle can be analytically shown to induce power-law degree distributions. Kleinberg =-=[17, 15]-=- proposed a model to explain the small-world phenomenon and navigability in social networks; see also [30]. Leskovec et al [22] proposed a forest-fire graph model to explain the decreasing diameter ph...

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...ay that a key is mapped to its successor on the ring. Routing on Viceroy networks uses links between successorssand predecessors on the ring for short distances. Borrowing from the ideas of Kleinberg =-=[6]-=- and Barriere et al. [2], we augment the ring construction with a constant number of long range contacts chosen appropriately so that a localized routing strategy produces short paths. The inspiration...

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...). Since inter-hub routing can take at most one hop, the number of hops taken for routing4 is at most O( 1 k log2 n) as well. This guarantee is based upon Kleinberg’s analysis of small-world networks =-=[14]-=-. Unfortunately, the “uniform node ranges” assumption can be easily violated for many reasons. For example, explicit load-balancing would cause nodes to cluster closely in parts of the ring which are ...

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... Those that are publicly available [2, 1] are quite small, which prevents a thorough evaluation of probabilistic guarantees. Thus we use the widely accepted Kleinberg’s synthetic social network model =-=[12]-=- in our evaluation, which generalizes from the Watts-Strogatz model [25]. We use the model to instantiate three different graphs: a million-node graph with average node degree of 24, a 10000-node grap...

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...ure that is an approximation to a butterfly network [38], as shown in Figure 6 (adapted from diagram in [15]), and uses links between successors and predecessors - ideas that were based on Kleingberg =-=[39]-=- and Barrière et al. [40] — on the ring (a key is mapped to its successor on the ring) for short distances. Its diameter of the overlay is better than CAN and its degree is better than Chord, Tapestry...

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...consider, among them being Tapestry [28] (though our discussion of PRR should mostly apply to Tapestry as well), a recent de Bruijn inspired algorithm [6], and a randomized algorithm due to Kleinberg =-=[11]-=-. 1 Our simulation results, presented later in the paper, do not assume dense identifier space. However, they all use base 2 to allow us to work with reasonable path lengths (typically 6-8 hops); clea...