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Graph Densification
, 2011
"... We initiate a principled study of graph densification. Given a graph G the goal of graph densification is to come up with another graph H that has significantly more edges than G but nevertheless approximates G well with respect to some set of test functions. In this paper we focus on the case of cu ..."
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We initiate a principled study of graph densification. Given a graph G the goal of graph densification is to come up with another graph H that has significantly more edges than G but nevertheless approximates G well with respect to some set of test functions. In this paper we focus on the case
Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 534 (48 self)
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How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include
Graph evolution: Densification and shrinking diameters
 ACM TKDD
, 2007
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 263 (16 self)
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that are densifying. Graphs with decreasing distance between the nodes are generated around this transition point. Last, we analyze the connection between the temporal evolution of the degree distribution and densification of a graph. We find that the two are fundamentally related. We also observe that real networks
DENSIFICATION
"... Several biomass samples of soybean straw, dry corn stalks, wet corn stalks, and dry alfalfa hay were compression tested. The objectives of this experiment were to (1) define a relationship between bulk density and applied pressure for several samples of corn stalks, soybean straw, and alfalfa hay, a ..."
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, and curve fit the results using Equation 1 that models biomass densification, and (2) observe similarities or differences in the values for the constants k and n due to differences in moisture or type of biomass. ()npk=γ (1) where: γ = bulk density, kg/m3 k = constant p = pressure, kPa n = exponential
The dynamics of viral marketing
 ACM Trans. Web
, 2007
"... 3 The research was done while at HP Labs. ..."
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.
ABSTRACT Densification Arising from Sampling Fixed Graphs
"... During the past decade, a number of different studies have identified several peculiar properties of networks that arise from a diverse universe, ranging from social to computer networks. A recently observed feature is known as network densification, which occurs when the number of edges grows much ..."
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Cited by 3 (1 self)
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, we propose a new model called Edge Sampling to explain how densification can arise. Our model is innovative, as we consider a fixed underlying graph and a process that discovers this graph by probabilistically sampling its edges. We show that this model possesses several interesting features
Graphs over time: Densification and shrinking diameters
 ACM Transactions on Knowledge Discovery from Data (ACM TKDD
"... How do real graphs evolve over time? What are “normal ” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include he ..."
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Cited by 1 (0 self)
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that are densifying. Graphs with decreasing distance between the nodes are generated around this transition point. Last, we analyze the connection between the temporal evolution of the degree distribution and densification of a graph. We find that the two are fundamentally related. We also observe that real networks
Stochastic Geometry and Wireless Networks, Volume
 II — Applications. Foundations and Trends in Networking. NoW Publishers
"... i Preface A wireless communication network can be viewed as a collection of nodes, located in some domain, which can in turn be transmitters or receivers (depending on the network considered, nodes may be mobile users, base stations in a cellular network, access points of a WiFi mesh etc.). At a giv ..."
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Cited by 257 (37 self)
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i Preface A wireless communication network can be viewed as a collection of nodes, located in some domain, which can in turn be transmitters or receivers (depending on the network considered, nodes may be mobile users, base stations in a cellular network, access points of a WiFi mesh etc.). At a given time, several nodes transmit simultaneously, each toward its own receiver. Each transmitter–receiver pair requires its own wireless link. The signal received from the link transmitter may be jammed by the signals received from the other transmitters. Even in the simplest model where the signal power radiated from a point decays in an isotropic way with Euclidean distance, the geometry of the locations of the nodes plays a key role since it determines the signal to interference and noise ratio (SINR) at each receiver and hence the possibility of establishing simultaneously this collection of links at a given bit rate. The interference seen by a receiver is the sum of the signal powers received from all transmitters, except its own transmitter. Stochastic geometry provides a natural way of defining and computing macroscopic properties of such networks, by averaging over all potential geometrical patterns for the nodes, in the same way as queuing theory provides response times or congestion, averaged over all potential arrival patterns within a given parametric class.
Improved Densification of One Permutation Hashing
"... The existing work on densification of one permutation hashing [24] reduces the query processing cost of the (K,L)parameterized Locality Sensitive Hashing (LSH) algorithm with minwise hashing, from O(dKL) to merely O(d + KL), where d is the number of nonzeros of the data vector, K is the number of ..."
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Cited by 1 (1 self)
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The existing work on densification of one permutation hashing [24] reduces the query processing cost of the (K,L)parameterized Locality Sensitive Hashing (LSH) algorithm with minwise hashing, from O(dKL) to merely O(d + KL), where d is the number of nonzeros of the data vector, K is the number
Results 1  10
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