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Tracking the Empirical Distribution of a Markov-modulated Duplication-Deletion Random Graph
[article]

2013
*
arXiv
*
pre-print

The paper comprises

arXiv:1303.0050v1
fatcat:bct27m7z5je23ptekctj4iipfm
*of*2 results. First, motivated by social network applications, we analyze the asymptotic behavior*of*the degree distribution*of*the Markov-modulated*random**graph*. ... This paper considers a Markov-modulated duplication-deletion*random**graph*where at each time instant, one node can either join or leave the network; the probabilities*of*joining or leaving evolve according ... The*power**law*component for the*non*-Markovian*random**graph*generated according to Algorithm 1 obtained by , the*power**law*component is increasing in q and decreasing in p. V. ...##
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Stochastic kronecker graphs

2010
*
Random structures & algorithms (Print)
*

*power*

*law*. ... A

*random*

*graph*model based on Kronecker products

*of*probability matrices has been recently proposed as a generative model for large-scale real-world networks such as the web. ... bounded by a constant (the so-called densification

*power*

*law*[12] ). ...

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Non-searchability of random scale-free graphs

2007
*
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing - PODC '07
*

The degree distribution

doi:10.1145/1281100.1281183
dblp:conf/podc/DuchonEH07
fatcat:o55solos2ng4vh3dyrekacz4im
*of*the vertices tends to follow a*power*-*law*distribution, that is the number*of*vertices*of*degree δ is proportional to n 1 δ k for an n-vertex*graph*and k a constant strictly greater ... On the other hand, in a seminal paper, Kleinberg [Kle00] focuses on the ability*of*a user or a mobile agent to route along shorts paths within a class*of**random*small-world*graphs*, the navigable small-worlds ... However, the pure*random**graph*models do not explain how a*graph*comes to have a*power**law*degree sequence. The evolving models attempt to explain this emergence*of*the*power**law*distribution. ...##
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The navigability of strong ties: Small worlds, tie strength, and network topology

2002
*
Complexity
*

Doug White is indebted to John Padgett for the invitation to join the Working Group on the Co-Evolution

doi:10.1002/cplx.10053
fatcat:2h2wn33am5dj5lo7eolegvyuni
*of*States and Markets at SFI, and to the editors*of*the Encyclopaedia*of*Community, who permitted ... some*of*the literature review presented here to be reused. ... Firms show a*power*-*law*distribution*of*degree connectivity. ...##
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Generalizing Kronecker graphs in order to model searchable networks

2009
*
2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
*

can find very short paths

doi:10.1109/allerton.2009.5394816
fatcat:axjvz5fttvdb7dunek255dxley
*of*length O((log log n) 2 ) for*graphs*with n nodes. ... This paper describes an extension to stochastic Kronecker*graphs*that provides the special structure required for*searchability*, by defining a "distance"-dependent Kronecker operator. ... The resulting binary*random*matrix is the adjacency matrix*of*the generated*graph*. ...##
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Searchability of Central Nodes in Networks

2013
*
Journal of statistical physics
*

*Searchability*

*of*the strongest spreaders in epidemic dynamics tends to be substantially larger for supercritical than for subcritical spreading. ... Social networks are discrete systems with a large amount

*of*heterogeneity among nodes (individuals). Measures

*of*centrality aim at a quantification

*of*nodes' importance for structure and function. ...

*law*P (k) ∼ k −γ with γ ≈ 3. ...

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Pragmatic evaluation of folksonomies

2011
*
Proceedings of the 20th international conference on World wide web - WWW '11
*

We model exploratory navigation

doi:10.1145/1963405.1963465
dblp:conf/www/HelicSTML11
fatcat:yjeyjc66azhlbflfaq4wf2ufwi
*of*a tagging system as decentralized search on a network*of*tags. ... Evaluation is based on the fact that the performance*of*a decentralized search algorithm depends on the quality*of*the background knowledge used. ... Although such an algorithm makes a*random**power**law*network theoretically*searchable*[19] , within the scope*of*our framework we consider such a network to be less practical due to a lack*of*semantic ...##
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Modeling Transitivity in Complex Networks
[article]

2015
*
arXiv
*
pre-print

However, existing approaches for modeling transitivity suffer from at least one

arXiv:1411.0958v5
fatcat:fxpl6cfluzgr3o54v52priyrca
*of*the following problems: i) they produce*graphs*from a specific class like bipartite*graphs*, ii) they do not give an analytical ... In particular, we calculate a lower bound on the clustering coefficient*of*the model which is independent*of*the network size, as seen in real-world networks. ... Related work In Aiello et al. (2000) , a*power*-*law**random**graph*model P (α, β) is proposed as follows: let y be the number*of*vertices with degree x. ...##
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The anatomy of urban social networks and its implications in the searchability problem
[article]

2015
*
arXiv
*
pre-print

By exhaustive simulation

arXiv:1506.00770v1
fatcat:rjhi6ylelrfepeec5ffxco5t74
*of*decentralized search strategies we conclude that urban networks are*searchable*not through geographical proximity as their country-wide counterparts, but through an homophily-driven ... These two findings shed new light on the widely-studied*searchability*in self-organized networks. ... All logarithmic and*power*-*law*functions are guides to the eye. ...##
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The anatomy of urban social networks and its implications in the searchability problem

2015
*
Scientific Reports
*

These two findings shed new light on the widely-studied

doi:10.1038/srep10265
pmid:26035529
pmcid:PMC4451794
fatcat:45zc4nfgs5dizcllc3mpb27nym
*searchability*in self-organized networks. ... By exhaustive simulation*of*decentralized search strategies we conclude that urban networks are*searchable*not through geographical proximity as their country-wide counterparts, but through an homophily-driven ... All logarithmic and*power*-*law*functions are guides to the eye. ...##
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The "New" Science of Networks

2004
*
Annual Review of Sociology
*

A distinguishing feature

doi:10.1146/annurev.soc.30.020404.104342
fatcat:hpp2borqcjcbhok7z26odmgfca
*of**power*-*law*distributions is that when plotted on a double logarithmic scale, a*power**law*appears as a straight line with negative slope α. ... Pastor-Satorris & Vespignani (2001) have extended Kretschmar & Morris's notion*of*concurrency by investigating disease spreading on*random*networks with*power*-*law*distributions*of*degree. ...##
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Discover hidden web properties by random walk on bipartite graph

2013
*
Information retrieval (Boston)
*

This paper proposes to use

doi:10.1007/s10791-013-9230-7
fatcat:iqq4dtqjwfgrrfhwsbnvdjxcu4
*random*walk to discover the properties*of*the deep web data sources that are hidden behind*searchable*interfaces. ... Reuters corpus is used to demonstrate that the term degrees resemble*power**law*distribution, thus RW is better than UR sampling. ... The work is supported by NSERC (Natural Sciences and Engineering Research Council*of*Canada) and State Key Laboratory for Novel Software Technology at Nanjing University. ...##
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Tracking a Markov-Modulated Stationary Degree Distribution of a Dynamic Random Graph

2014
*
IEEE Transactions on Information Theory
*

This paper considers a Markov-modulated duplication-deletion

doi:10.1109/tit.2014.2346183
fatcat:htwyf4ffyreqphlkhvmh52iqqm
*random**graph*where at each time instant, one node can either join or leave the network; the probabilities*of*joining or leaving evolve according ... to the realization*of*a finite state Markov chain. ...*random**graphs*. 7 There is a difference between "*power**law*" and "*power**law*distribution". ...##
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Modeling Traffic of Information Packets on Graphs with Complex Topology
[chapter]

2003
*
Lecture Notes in Computer Science
*

We determine the statistics

doi:10.1007/3-540-44860-8_14
fatcat:ofpgk32w2fez5jkvigcz5bd2gq
*of*transit times*of*packets from posting until their arrival to given destinations on the*graph*when creation rate is varied. ... We then implement the algorithm*of*simultaneous transport*of*information packets that are created with a given rate and navigated on that*graph*by local up-to-next-neighbour search algorithm. ... The*power*-*law*behavior*of*the transit time distribution (cf. Fig. 3 ) agree with measured distribution*of*the round-trip-time [9] . ...##
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Networks: Structure and Dynamics
[chapter]

2009
*
Encyclopedia of Complexity and Systems Science
*

(k) ∼ k −γ , however, it is often used for networks where the tail

doi:10.1007/978-0-387-30440-3_356
fatcat:f2zg2yyyavaonfz4m5mwjr6rcu
*of*the distribution follows a*power*-*law*). • Degree exponent γ: the*power**law*exponent*of*the (tail*of*the) degree distribution • Scale-free ... Elegans worm, the*power*grid and the network*of*movie actors connected by feature films have a topology somewhere between regular lattices and*random**graphs*. ...
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