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3,069
The dynamics of viral marketing
 ACM Trans. Web
, 2007
"... 3 The research was done while at HP Labs. ..."
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A Random Graph Model for Massive Graphs
 STOC 2000
, 2000
"... We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and loglog growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from t ..."
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Cited by 406 (26 self)
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We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and loglog growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from these parameters, various properties of the graph can be derived. For example, for certain ranges of the parameters, we will compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We will illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We will also discuss the threshold function, the giant component, and the evolution of random graphs in this model.
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.
On the Minimum Node Degree and Connectivity of a Wireless Multihop Network
 ACM MobiHoc
, 2002
"... This paper investigates two fundamental characteristics of a wireless multihop network: its minimum node degree and its k–connectivity. Both topology attributes depend on the spatial distribution of the nodes and their transmission range. Using typical modeling assumptions — a random uniform distri ..."
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Cited by 318 (4 self)
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This paper investigates two fundamental characteristics of a wireless multihop network: its minimum node degree and its k–connectivity. Both topology attributes depend on the spatial distribution of the nodes and their transmission range. Using typical modeling assumptions — a random uniform distribution of the nodes and a simple link model — we derive an analytical expression that enables the determination of the required range r0 that creates, for a given node density ρ, an almost surely k–connected network. Equivalently, if the maximum r0 of the nodes is given, we can find out how many nodes are needed to cover a certain area with a k–connected network. We also investigate these questions by various simulations and thereby verify our analytical expressions. Finally, the impact of mobility is discussed. The results of this paper are of practical value for researchers in this area, e.g., if they set the parameters in a network–level simulation of a mobile ad hoc network or if they design a wireless sensor network. Categories and Subject Descriptors C.2 [Computercommunication networks]: Network architecture and design—wireless communication, network communications, network topology; G.2.2 [Discrete mathematics]: Graph theory; F.2.2 [Probability and statistics]: Stochastic processes
Random graph models of social networks
"... We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predic ..."
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Cited by 252 (1 self)
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We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predictions of our models to data for a number of realworld social networks and find that in some cases the models are in remarkable agreement with the data, while in others the agreement is poorer, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
The degree sequence of a scalefree random graph process
, 2001
"... Recently, Barabási and Albert [2] suggested modeling complex realworld networks such as the worldwide web as follows: consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional ..."
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Cited by 243 (2 self)
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Recently, Barabási and Albert [2] suggested modeling complex realworld networks such as the worldwide web as follows: consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. In [2] and, with Jeong, in [3], Barabási and Albert suggested that after many steps the proportion Pd of vertices with degree d should obey a power law Pdαd−γ. They obtained γ = 29 ± 01 by experiment and gave a simple heuristic argument suggesting that γ = 3. Here we obtain Pd asymptotically for all d ≤ n1/15, where n is the number of vertices, proving as a consequence that γ = 3.
Deterministic and Stochastic Models for Coalescence (Aggregation, Coagulation): a Review of the MeanField Theory for Probabilists
 Bernoulli
, 1997
"... Consider N particles, which merge into clusters according to the rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K(x; y)=N , where K is a specified rate kernel. This MarcusLushnikov model of stochastic coalescence, and the underlying deterministic approximation given by ..."
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Cited by 222 (13 self)
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Consider N particles, which merge into clusters according to the rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K(x; y)=N , where K is a specified rate kernel. This MarcusLushnikov model of stochastic coalescence, and the underlying deterministic approximation given by the Smoluchowski coagulation equations, have an extensive scientific literature. Some mathematical literature (Kingman's coalescent in population genetics; component sizes in random graphs) implicitly studies the special cases K(x; y) = 1 and K(x; y) = xy. We attempt a wideranging survey. General kernels are only now starting to be studied rigorously, so many interesting open problems appear. Keywords. branching process, coalescence, continuum tree, densitydependent Markov process, gelation, random graph, random tree, Smoluchowski coagulation equation Research supported by N.S.F. Grant DMS9622859 1 Introduction Models, implicitly or explicitly stochastic, of coalescence (= coagulati...
Peertopeer membership management for gossipbased protocols
 IEEE TRANSACTIONS ON COMPUTERS
, 2003
"... Gossipbased protocols for group communication have attractive scalability and reliability properties. The probabilistic gossip schemes studied so far typically assume that each group member has full knowledge of the global membership and chooses gossip targets uniformly at random. The requirement ..."
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Cited by 222 (23 self)
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Gossipbased protocols for group communication have attractive scalability and reliability properties. The probabilistic gossip schemes studied so far typically assume that each group member has full knowledge of the global membership and chooses gossip targets uniformly at random. The requirement of global knowledge impairs their applicability to very largescale groups. In this paper, we present SCAMP (Scalable Membership protocol), a novel peertopeer membership protocol which operates in a fully decentralized manner and provides each member with a partial view of the group membership. Our protocol is selforganizing in the sense that the size of partial views naturally converges to the value required to support a gossip algorithm reliably. This value is a function of the group size, but is achieved without any node knowing the group size. We propose additional mechanisms to achieve balanced view sizes even with highly unbalanced subscription patterns. We present the design, theoretical analysis, and a detailed evaluation of the basic protocol and its refinements. Simulation results show that the reliability guarantees provided by SCAMP are comparable to previous schemes based on global knowledge. The scale of the experiments attests to the scalability of the protocol.