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508
Measurement and Analysis of Online Social Networks
 In Proceedings of the 5th ACM/USENIX Internet Measurement Conference (IMC’07
, 2007
"... Online social networking sites like Orkut, YouTube, and Flickr are among the most popular sites on the Internet. Users of these sites form a social network, which provides a powerful means of sharing, organizing, and finding content and contacts. The popularity of these sites provides an opportunity ..."
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Cited by 698 (14 self)
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and 328 million links. We believe that this is the first study to examine multiple online social networks at scale. Our results confirm the powerlaw, smallworld, and scalefree properties of online social networks. We observe that the indegree of user nodes tends to match the outdegree; that the networks
Evolution of networks
 Adv. Phys
, 2002
"... We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence rece ..."
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Cited by 419 (3 self)
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recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scalefree and show striking resilience against random breakdowns. In spite of large sizes of these networks
Scalefree networks in cell biology
 JOURNAL OF CELL SCIENCE
"... A cell’s behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond to and adapt to an everchanging environ ..."
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Cited by 203 (6 self)
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changing environment. The large number of components, the degree of interconnectivity and the complex control of cellular networks are becoming evident in the integrated genomic and proteomic analyses that are emerging. It is increasingly recognized that the understanding of properties that arise from whole
Mathematical results on scalefree random graphs
 Handbook of Graphs and Networks
, 2003
"... Recently there has been much interest in studying largescale realworld networks and attempting to model their properties using random graphs. Although the study of realworld networks as graphs goes back some time, recent activity perhaps started with the paper of Watts and Strogatz [55] about the ..."
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Cited by 147 (3 self)
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Recently there has been much interest in studying largescale realworld networks and attempting to model their properties using random graphs. Although the study of realworld networks as graphs goes back some time, recent activity perhaps started with the paper of Watts and Strogatz [55] about
Directed scalefree graphs.
 In SODA’03,
, 2003
"... Abstract We introduce a model for directed scalefree graphs that grow with preferential attachment depending in a natural way on the inand outdegrees. We show that the resulting inand outdegree distributions are power laws with different exponents, reproducing observed properties of the worldw ..."
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Cited by 76 (5 self)
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Abstract We introduce a model for directed scalefree graphs that grow with preferential attachment depending in a natural way on the inand outdegrees. We show that the resulting inand outdegree distributions are power laws with different exponents, reproducing observed properties
Towards a theory of scalefree graphs: Definition, properties, and implications
 Internet Mathematics
, 2005
"... Abstract. There is a large, popular, and growing literature on “scalefree ” networks with the Internet along with metabolic networks representing perhaps the canonical examples. While this has in many ways reinvigorated graph theory, there is unfortunately no consistent, precise definition of scale ..."
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Cited by 137 (12 self)
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of scalefree graphs and few rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and that the most celebrated claims regarding the Internet and biology are verifiably false. In this paper, we introduce a structural
Structural properties of scalefree networks
 IN HANDBOOK OF GRAPHS AND NETWORKS
, 2003
"... Many networks have been reported recently to follow a scalefree degree distribution in which the fraction of sites having ¥¤§¦©¨ � ���� connections follows a ¡£¢ power law:. In this chapter we study the structural properties of such networks. We show that the average distance between sites in s ..."
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Cited by 18 (0 self)
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Many networks have been reported recently to follow a scalefree degree distribution in which the fraction of sites having ¥¤§¦©¨ � ���� connections follows a ¡£¢ power law:. In this chapter we study the structural properties of such networks. We show that the average distance between sites
Structural Properties of ScaleFree Networks
 In Handbook of Graphs and Networks
, 2002
"... Many networks have been reported recently to follow a scalefree degree distribution in which the fraction of sites having k connections follows a power law: P (k) = ck . In this chapter we study the structural properties of such networks. We show that the average distance between sites in scale ..."
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Many networks have been reported recently to follow a scalefree degree distribution in which the fraction of sites having k connections follows a power law: P (k) = ck . In this chapter we study the structural properties of such networks. We show that the average distance between sites in scalefree
Lensing Properties of ScaleFree Galaxies
, 2001
"... The multiple images of lensed quasars provide evidence on the mass distribution of the lensing galaxy. The lensing invariants are constructed from the positions of the images, their parities and their fluxes. They depend only on the structure of the lensing potential. The simplest is the magnificati ..."
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Cited by 2 (0 self)
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The multiple images of lensed quasars provide evidence on the mass distribution of the lensing galaxy. The lensing invariants are constructed from the positions of the images, their parities and their fluxes. They depend only on the structure of the lensing potential. The simplest is the magnification invariant, which is the sum of the signed magnifications of the images. Higher order configuration invariants are the sums of products of the signed magnifications with positive or negative powers of the position coordinates of the images. We consider the case of the four and five image systems produced by elliptical powerlaw galaxies with ψ ∝ (x 2 +y 2 q −2) β/2. This paper provides simple contour integrals for evaluating all their lensing invariants. For practical evaluation, this offers considerable advantages over the algebraic methods used previously. The magnification invariant is exactly B = 2/(2 − β) for the special cases β = 0, 1 and 4/3; for other values of β, this remains an approximation, but an excellent one at small source offset. Similarly, the sums of the first and second powers of the image positions (or their reciprocals), when weighted with the signed magnifications, are just proportional to the same powers of the source offset, with a constant of proportionality B. To illustrate the power of the contour integral method, we calculate full expansions in the source offset for all lensing invariants in the presence of arbitrary external shear. As an example, we use the elliptical powerlaw galaxies to fit to the data on the four images of the Einstein Cross (G2237+030). The lensing invariants play a role by reducing the dimensionality of the parameter space in which the χ 2 minimisation proceeds with consequent gains in accuracy and speed. Subject headings: gravitational lensing – galaxies: structure – quasars individual: G2237+030 – 2 – 1.
Results 1  10
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508