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Percolation on random recursive trees
, 2014
"... We study Bernoulli bond percolation on a random recursive tree of size n with percolation parameter p(n) converging to 1 as n tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove convergence in distribution of this tree to the genealogical tree of a cont ..."
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Cited by 1 (1 self)
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We study Bernoulli bond percolation on a random recursive tree of size n with percolation parameter p(n) converging to 1 as n tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove convergence in distribution of this tree to the genealogical tree of a
Profiles of random trees: planeoriented recursive trees
, 2005
"... We derive several limit results for the profile of random planeoriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximation to the expected width and the correlation coefficients of two level sizes. Most of ..."
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Cited by 19 (5 self)
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We derive several limit results for the profile of random planeoriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximation to the expected width and the correlation coefficients of two level sizes. Most
Random tree growth by vertex splitting
 Journal of Statistical Mechanics: Theory and Experiment
"... Abstract. We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. We develop a mean field theory for the vertex degree distribution, pr ..."
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Cited by 5 (1 self)
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Abstract. We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. We develop a mean field theory for the vertex degree distribution
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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as random graphs, it is increasingly recognized that the topology and evolution of real
Network Coding for Large Scale Content Distribution
"... We propose a new scheme for content distribution of large files that is based on network coding. With network coding, each node of the distribution network is able to generate and transmit encoded blocks of information. The randomization introduced by the coding process eases the scheduling of bloc ..."
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Cited by 497 (6 self)
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We propose a new scheme for content distribution of large files that is based on network coding. With network coding, each node of the distribution network is able to generate and transmit encoded blocks of information. The randomization introduced by the coding process eases the scheduling
Overcast: Reliable Multicasting with an Overlay Network
, 2000
"... Overcast is an applicationlevel multicasting system that can be incrementally deployed using today's Internet infrastructure. These properties stem from Overcast's implementation as an overlay network. An overlay network consists of a collection of nodes placed at strategic locations in a ..."
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Cited by 563 (10 self)
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Overcast is an applicationlevel multicasting system that can be incrementally deployed using today's Internet infrastructure. These properties stem from Overcast's implementation as an overlay network. An overlay network consists of a collection of nodes placed at strategic locations in an existing network fabric. These nodes implement a network abstraction on top of the network provided by the underlying substrate network. Overcast provides
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 heavy tails for in and outdegree distributions, communities, smallworld phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) orO(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification, requires very few parameters (like the “flammability” of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
Spectra of large random trees
 ArXiv
"... Abstract. We analyze the eigenvalues of the adjacency matrices of a wide variety of random trees. Using general, broadly applicable arguments based on the interlacing inequalities for the eigenvalues of a principal submatrix of a Hermitian matrix and a suitable notion of local weak convergence for a ..."
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Cited by 5 (1 self)
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spectral distributions to individual points also converge in distribution to constants. We conclude for ensembles such as the linear preferential attachment models, random recursive trees, and the uniform random trees that the limiting spectral distribution has a set of atoms that is dense in the real line
Focused crawling: a new approach to topicspecific Web resource discovery
, 1999
"... The rapid growth of the WorldWide Web poses unprecedented scaling challenges for generalpurpose crawlers and search engines. In this paper we describe a new hypertext resource discovery system called a Focused Crawler. The goal of a focused crawler is to selectively seek out pages that are relevan ..."
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Cited by 628 (10 self)
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The rapid growth of the WorldWide Web poses unprecedented scaling challenges for generalpurpose crawlers and search engines. In this paper we describe a new hypertext resource discovery system called a Focused Crawler. The goal of a focused crawler is to selectively seek out pages that are relevant to a predefined set of topics. The topics are specified not using keywords, but using exemplary documents. Rather than collecting and indexing all accessible Web documents to be able to answer all possible adhoc queries, a focused crawler analyzes its crawl boundary to find the links that are likely to be most relevant for the crawl, and avoids irrelevant regions of the Web. This leads to significant savings in hardware and network resources, and helps keep the crawl more uptodate. To achieve such goaldirected crawling, we designed two hypertext mining programs that guide our crawler: a classifier that evaluates the relevance of a hypertext document with respect to the focus topics, ...
Results 1  10
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