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111
Structure and evolution of online social networks
 In Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
, 2006
"... In this paper, we consider the evolution of structure within large online social networks. We present a series of measurements of two such networks, together comprising in excess of five million people and ten million friendship links, annotated with metadata capturing the time of every event in the ..."
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Cited by 400 (4 self)
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In this paper, we consider the evolution of structure within large online social networks. We present a series of measurements of two such networks, together comprising in excess of five million people and ten million friendship links, annotated with metadata capturing the time of every event in the life of the network. Our measurements expose a surprising segmentation of these networks into three regions: singletons who do not participate in the network; isolated communities which overwhelmingly display star structure; and a giant component anchored by a wellconnected core region which persists even in the absence of stars. We present a simple model of network growth which captures these aspects of component structure. The model follows our experimental results, characterizing users as either passive members of the network; inviters who encourage offline friends and acquaintances to migrate online; and linkers who fully participate in the social evolution of the network.
Distance Estimation and Object Location via Rings of Neighbors
 In 24 th Annual ACM Symposium on Principles of Distributed Computing (PODC
, 2005
"... We consider four problems on distance estimation and object location which share the common flavor of capturing global information via informative node labels: lowstretch routing schemes [47], distance labeling [24], searchable small worlds [30], and triangulationbased distance estimation [33]. Fo ..."
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Cited by 77 (7 self)
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We consider four problems on distance estimation and object location which share the common flavor of capturing global information via informative node labels: lowstretch routing schemes [47], distance labeling [24], searchable small worlds [30], and triangulationbased distance estimation [33]. Focusing on metrics of low doubling dimension, we approach these problems with a common technique called rings of neighbors, which refers to a sparse distributed data structure that underlies all our constructions. Apart from improving the previously known bounds for these problems, our contributions include extending Kleinberg’s small world model to doubling metrics, and a short proof of the main result in Chan et al. [14]. Doubling dimension is a notion of dimensionality for general metrics that has recently become a useful algorithmic concept in the theoretical computer science literature. 1
Object Location Using Path Separators
, 2006
"... We study a novel separator property called kpath separable. Roughly speaking, a kpath separable graph can be recursively separated into smaller components by sequentially removing k shortest paths. Our main result is that every minor free weighted graph is kpath separable. We then show that kpat ..."
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Cited by 41 (11 self)
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We study a novel separator property called kpath separable. Roughly speaking, a kpath separable graph can be recursively separated into smaller components by sequentially removing k shortest paths. Our main result is that every minor free weighted graph is kpath separable. We then show that kpath separable graphs can be used to solve several object location problems: (1) a smallworldization with an average polylogarithmic number of hops; (2) an (1 + ε)approximate distance labeling scheme with O(log n) space labels; (3) a stretch(1 + ε) compact routing scheme with tables of polylogarithmic space; (4) an (1+ε)approximate distance oracle with O(n log n) space and O(log n) query time. Our results generalizes to much wider classes of weighted graphs, namely to boundeddimension isometric sparable graphs.
Dynamics of conversations
 In Proc. KDD
, 2010
"... How do online conversations build? Is there a common model that is followed in human communication? In this work we explore these questions in detail. By considering three different social datasets, namely, Usenet groups, Yahoo! Groups, and Twitter, we analyze the structure of conversations in each ..."
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Cited by 30 (1 self)
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How do online conversations build? Is there a common model that is followed in human communication? In this work we explore these questions in detail. By considering three different social datasets, namely, Usenet groups, Yahoo! Groups, and Twitter, we analyze the structure of conversations in each of these datasets. We propose simple mathematical models for the generation of basic conversation structures and then refine this model to take into account the identities of each member of the conversation. 1.
Stochastic kronecker graphs
 Proceedings of the 5th Workshop on Algorithms and Models for the WebGraph
, 2007
"... A random graph model based on Kronecker products of probability matrices has been recently proposed as a generative model for largescale realworld networks such as the web. This model simultaneously captures several wellknown properties of realworld networks; in particular, it gives rise to a he ..."
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Cited by 27 (2 self)
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A random graph model based on Kronecker products of probability matrices has been recently proposed as a generative model for largescale realworld networks such as the web. This model simultaneously captures several wellknown properties of realworld networks; in particular, it gives rise to a heavytailed degree distribution, has a low diameter, and obeys the densification power law. Most properties of Kronecker products of graphs (such as connectivity and diameter) are only rigorously analyzed in the deterministic case. In this paper, we study the basic properties of stochastic Kronecker products based on an initiator matrix of size two (which is the case that is shown to provide the best fit to many realworld networks). We will show a phase transition for the emergence of the giant component and another phase transition for connectivity, and prove that such graphs have constant diameters beyond the connectivity threshold, but are not searchable using a decentralized algorithm. 1
Greedy Forwarding in Dynamic ScaleFree Networks Embedded in Hyperbolic Metric Spaces
"... Abstract—We show that complex (scalefree) network topologies naturally emerge from hyperbolic metric spaces. Hyperbolic geometry facilitates maximally efficient greedy forwarding in these networks. Greedy forwarding is topologyoblivious. Nevertheless, greedy packets find their destinations with 10 ..."
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Cited by 25 (1 self)
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Abstract—We show that complex (scalefree) network topologies naturally emerge from hyperbolic metric spaces. Hyperbolic geometry facilitates maximally efficient greedy forwarding in these networks. Greedy forwarding is topologyoblivious. Nevertheless, greedy packets find their destinations with 100 % probability following almost optimal shortest paths. This remarkable efficiency sustains even in highly dynamic networks. Our findings suggest that forwarding information through complex networks, such as the Internet, is possible without the overhead of existing routing protocols, and may also find practical applications in overlay networks for tasks such as applicationlevel routing, information sharing, and data distribution. I.
On the Windfall of Friendship: Inoculation Strategies on Social Networks
 EC'08
, 2008
"... This paper studies a virus inoculation game on social networks. A framework is presented which allows the measuring of the windfall of friendship, i.e., how much players benefit if they care about the welfare of their direct neighbors in the social network graph compared to purely selfish environmen ..."
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Cited by 23 (2 self)
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This paper studies a virus inoculation game on social networks. A framework is presented which allows the measuring of the windfall of friendship, i.e., how much players benefit if they care about the welfare of their direct neighbors in the social network graph compared to purely selfish environments. We analyze the corresponding equilibria and show that the computation of the worst and best Nash equilibrium is N Phard. Intriguingly, even though the windfall of friendship can never be negative, the social welfare does not increase monotonically with the extent to which players care for each other. While these phenomena are known on an anecdotal level, our framework allows us to quantify these effects analytically.
A Social Network Based Approach to Personalized Recommendation
 of Participatory Media Content,” ICWS
, 2008
"... Given the rapid growth of participatory media content such as blogs, there is a need to design personalized recommender systems to recommend only useful content to users. We believe that in addition to producing useful recommendations, certain insights from media research such as simplification and ..."
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Cited by 23 (8 self)
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Given the rapid growth of participatory media content such as blogs, there is a need to design personalized recommender systems to recommend only useful content to users. We believe that in addition to producing useful recommendations, certain insights from media research such as simplification and opinion diversity in recommendations should form the foundations of such recommender systems, so that the behavior of the systems can be understood more closely, and modified if necessary. We propose and evaluate such a system based on a Bayesian usermodel. We use the underlying social network of blog authors and readers to model the preference features for individual users. The initial results of our proposed solution are encouraging, and set the agenda for future research.
Benefits of bias: Towards better characterization of network sampling
 In SIGKDD
, 2011
"... From social networks to P2P systems, network sampling arises in many settings. We present a detailed study on the nature of biases in network sampling strategies to shed light on how best to sample from networks. We investigate connections between specific biases and various measures of structural r ..."
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Cited by 19 (0 self)
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From social networks to P2P systems, network sampling arises in many settings. We present a detailed study on the nature of biases in network sampling strategies to shed light on how best to sample from networks. We investigate connections between specific biases and various measures of structural representativeness. We show that certain biases are, in fact, beneficial for many applications, as they “push” the sampling process towards inclusion of desired properties. Finally, we describe how these sampling biases can be exploited in several, realworld applications including disease outbreak detection and market research.
Smallworld Datacenters
 In SOCC
, 2011
"... In this paper, we propose an unorthodox topology for datacenters that eliminates all hierarchical switches in favor of connecting nodes at random according to a smallworldinspired distribution. Specifically, we examine topologies where the underlying nodes are connected at the small scale in a regu ..."
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Cited by 18 (1 self)
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In this paper, we propose an unorthodox topology for datacenters that eliminates all hierarchical switches in favor of connecting nodes at random according to a smallworldinspired distribution. Specifically, we examine topologies where the underlying nodes are connected at the small scale in a regular pattern, such as a ring, torus or cube, such that every node can route efficiently to nodes in its immediate vicinity, and amended by the addition of random links to nodes throughout the datacenter, such that a greedy algorithm can route packets to far away locations efficiently. Coupled with geographical address assignment, the resulting network can provide content routing in addition to traditional routing, and thus efficiently implement keyvalue stores. The irregular but selfsimilar nature of the network facilitates constructing large networks easily using prewired, commodity racks. We show that SmallWorld Datacenters can achieve higher bandwidth and fault tolerance compared to both conventional hierarchical datacenters as well as the recently proposed CamCube topology. Coupled withhardware acceleration for packetswitching, smallworld datacenters can achieve an order of magnitude higher bandwidth than a conventional datacenter, dependingon the network traffic.