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

Maziyar Hamdi, Vikram Krishnamurthy, George Yin
2013 arXiv   pre-print
The paper comprises 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.  ... 
arXiv:1303.0050v1 fatcat:bct27m7z5je23ptekctj4iipfm

Stochastic kronecker graphs

Mohammad Mahdian, Ying Xu
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] ).  ... 
doi:10.1002/rsa.20335 fatcat:d7g22tloxfhghc2jvnlnnufd7u

Non-searchability of random scale-free graphs

Philippe Duchon, Nicole Eggemann, Nicolas Hanusse
2007 Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing - PODC '07  
The degree distribution 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.  ... 
doi:10.1145/1281100.1281183 dblp:conf/podc/DuchonEH07 fatcat:o55solos2ng4vh3dyrekacz4im

The navigability of strong ties: Small worlds, tie strength, and network topology

Douglas R. White, Michael Houseman
2002 Complexity  
Doug White is indebted to John Padgett for the invitation to join the Working Group on the Co-Evolution 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.  ... 
doi:10.1002/cplx.10053 fatcat:2h2wn33am5dj5lo7eolegvyuni

Generalizing Kronecker graphs in order to model searchable networks

Elizabeth Bodine, Babak Hassibi, Adam Wierman
2009 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
can find very short paths 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.  ... 
doi:10.1109/allerton.2009.5394816 fatcat:axjvz5fttvdb7dunek255dxley

Searchability of Central Nodes in Networks

Konstantin Klemm
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.  ... 
doi:10.1007/s10955-013-0727-7 fatcat:aptyzbh2abd75m7yi75dvdarly

Pragmatic evaluation of folksonomies

Denis Helic, Markus Strohmaier, Christoph Trattner, Markus Muhr, Kristina Lerman
2011 Proceedings of the 20th international conference on World wide web - WWW '11  
We model exploratory navigation 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  ... 
doi:10.1145/1963405.1963465 dblp:conf/www/HelicSTML11 fatcat:yjeyjc66azhlbflfaq4wf2ufwi

Modeling Transitivity in Complex Networks [article]

Morteza Haghir Chehreghani, Mostafa Haghir Chehreghani
2015 arXiv   pre-print
However, existing approaches for modeling transitivity suffer from at least one 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.  ... 
arXiv:1411.0958v5 fatcat:fxpl6cfluzgr3o54v52priyrca

The anatomy of urban social networks and its implications in the searchability problem [article]

C. Herrera-Yagüe, C.M. Schneider, T. Couronné, Z. Smoreda, R.M. Benito, P.J. Zufiria, M.C. González
2015 arXiv   pre-print
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  ...  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.  ... 
arXiv:1506.00770v1 fatcat:rjhi6ylelrfepeec5ffxco5t74

The anatomy of urban social networks and its implications in the searchability problem

C. Herrera-Yagüe, C. M. Schneider, T. Couronné, Z. Smoreda, R. M. Benito, P. J. Zufiria, M. C. González
2015 Scientific Reports  
These two findings shed new light on the widely-studied 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.  ... 
doi:10.1038/srep10265 pmid:26035529 pmcid:PMC4451794 fatcat:45zc4nfgs5dizcllc3mpb27nym

The "New" Science of Networks

Duncan J. Watts
2004 Annual Review of Sociology  
A distinguishing feature 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.  ... 
doi:10.1146/annurev.soc.30.020404.104342 fatcat:hpp2borqcjcbhok7z26odmgfca

Discover hidden web properties by random walk on bipartite graph

Yan Wang, Jie Liang, Jianguo Lu
2013 Information retrieval (Boston)  
This paper proposes to use 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.  ... 
doi:10.1007/s10791-013-9230-7 fatcat:iqq4dtqjwfgrrfhwsbnvdjxcu4

Tracking a Markov-Modulated Stationary Degree Distribution of a Dynamic Random Graph

Maziyar Hamdi, Vikram Krishnamurthy, George Yin
2014 IEEE Transactions on Information Theory  
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  ...  to the realization of a finite state Markov chain.  ...  random graphs. 7 There is a difference between "power law" and "power law distribution".  ... 
doi:10.1109/tit.2014.2346183 fatcat:htwyf4ffyreqphlkhvmh52iqqm

Modeling Traffic of Information Packets on Graphs with Complex Topology [chapter]

Bosiljka Tadić
2003 Lecture Notes in Computer Science  
We determine the statistics 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] .  ... 
doi:10.1007/3-540-44860-8_14 fatcat:ofpgk32w2fez5jkvigcz5bd2gq

Networks: Structure and Dynamics [chapter]

Erzsébet Ravasz Regan
2009 Encyclopedia of Complexity and Systems Science  
(k) ∼ k −γ , however, it is often used for networks where the tail 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.  ... 
doi:10.1007/978-0-387-30440-3_356 fatcat:f2zg2yyyavaonfz4m5mwjr6rcu
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