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Small Worlds as Navigable Augmented Networks — Model, Analysis, and Validation —
"... Abstract. The small world phenomenon, a.k.a. the six degree of separation between individuals, was identified by Stanley Milgram at the end of the 60s. Milgram experiment demonstrated that letters from arbitrary sources and bound to an arbitrary target can be transmitted along short chains of closel ..."
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Abstract. The small world phenomenon, a.k.a. the six degree of separation between individuals, was identified by Stanley Milgram at the end of the 60s. Milgram experiment demonstrated that letters from arbitrary sources and bound to an arbitrary target can be transmitted along short chains of closely related individuals, based solely on some characteristics of the target (professional occupation, state of leaving, etc.). In his paper on small world navigability, Jon Kleinberg modeled this phenomenon in the framework of augmented networks, and analyzed the performances of greedy routing in augmented multidimensional meshes. This paper objective is to survey the results that followed up Kleinberg seminal work, including results about: – extensions of the augmented network model, and variants of greedy routing, – designs of polylognavigable graph classes, – the quest for universal augmentation schemes, and
Recovering the long range links in Augmented graphs
 n o RR6197, Institut National de Recherche en Informatique et Automatique (INRIA), 2007, https:// hal.inria.fr/inria00147536. References in notes
"... Abstract. The augmented graph model, as introduced by Kleinberg (STOC 2000), is an appealing model for analyzing navigability in social networks. Informally, this model is defined by a pair (H, ϕ), where H is a graph in which internode distances are supposed to be easy to compute or at least easy t ..."
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Abstract. The augmented graph model, as introduced by Kleinberg (STOC 2000), is an appealing model for analyzing navigability in social networks. Informally, this model is defined by a pair (H, ϕ), where H is a graph in which internode distances are supposed to be easy to compute or at least easy to estimate. This graph is ”augmented ” by links, called longrange links, which are selected according to the probability distribution ϕ. The augmented graph model enables the analysis of greedy routing in augmented graphs G ∈ (H, ϕ). In greedy routing, each intermediate node handling a message for a target t selects among all its neighbors in G the one that is the closest to t in H and forwards the message to it. This paper addresses the problem of checking whether a given graph G is an augmented graph. It answers part of the questions raised by Kleinberg in his Problem 9 (Int. Congress of Math. 2006). More precisely, given G ∈ (H, ϕ), we aim at extracting the base graph H and
WWW Graphs Call Graphs Collaboration Graphs Gene Regulatory Graphs
"... A graph consists of two sets V and E. V is the set of vertices (or nodes). E is the set of edges, where each edge is a pair of vertices. ..."
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A graph consists of two sets V and E. V is the set of vertices (or nodes). E is the set of edges, where each edge is a pair of vertices.