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PageRank in Scale-Free Random Graphs [chapter]

Ningyuan Chen, Nelly Litvak, Mariana Olvera-Cravioto
2014 Lecture Notes in Computer Science  
We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an  ...  This tree approximation is in turn related to the solution of a linear stochastic fixed point equation that has been thoroughly studied in the recent literature.  ...  In this paper we analyze the power law behavior of PageRank scores in scale-free directed random graphs.  ... 
doi:10.1007/978-3-319-13123-8_10 fatcat:mnsu6r6ixneulh7pynlazxfvky

PageRank in scale-free random graphs [article]

Ningyuan Chen, Nelly Litvak, Mariana Olvera-Cravioto
2014 arXiv   pre-print
We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an  ...  This tree approximation is in turn related to the solution of a linear stochastic fixed point equation that has been thoroughly studied in the recent literature.  ...  In this paper we analyze the power law behavior of PageRank scores in scale-free directed random graphs.  ... 
arXiv:1408.3610v1 fatcat:q7dvmmqqabhbrmss7sgrqt6fr4

Quantum Google in a Complex Network

Giuseppe Davide Paparo, Markus Müller, Francesc Comellas, Miguel Angel Martin-Delgado
2013 Scientific Reports  
Finally, we study to which extent the increased sensitivity of the quantum algorithm persists under coordinated attacks of the most important nodes in scale-free and Erdős-Rényi random graphs.  ...  order the most relevant nodes (hubs) of the graph according to their importance in the network structure.  ...  Moreover, the study of random and hierarchical networks results to be useful to confront its features with scale-free networks. Random scale-free graphs 24, 25 are ubiquitous in nature.  ... 
doi:10.1038/srep02773 pmid:24091980 pmcid:PMC3790229 fatcat:zfqkwqtxi5aabdu5d5cmifbopy

Comparing classical and quantum PageRanks [article]

T. Loke, J. W. Tang, J. Rodriguez, M. Small, J. B. Wang
2015 arXiv   pre-print
We affirm that all three quantum PageRank measures considered here distinguish clearly between outerplanar hierarchical, scale-free, and Erd\"os-R\'enyi network types.  ...  Following recent developments in quantum PageRanking, we present a comparative analysis of discrete-time and continuous-time quantum-walk-based PageRank algorithms.  ...  In [7] , Paparo et al. performed further analysis of their proposed quantum PageRank on complex networks, specifically on hierarchical graphs, directed scale-free graphs, and Erdös-Rényi random graphs  ... 
arXiv:1511.04823v1 fatcat:2poelsnnw5hfbdkuhfm2j7djga

Quantum Google algorithm

G. D. Paparo, M. Müller, F. Comellas, M. A. Martin-Delgado
2014 The European Physical Journal Plus  
a class known as small-world scale-free networks.  ...  In this paper we review the Quantum PageRank algorithm [1, 2] and illustrate the main findings when applied to complex networks of different sizes and topologies, like the scale-free and hierarchical ones  ...  Scale-free Networks Random scale-free graphs [52, 53] are networks that display a small fraction of hubs, i.e. nodes with a high connectivity.  ... 
doi:10.1140/epjp/i2014-14150-y fatcat:jal2skylxvb67nogsigbedetkq

Quantum Google Algorithm: Construction and Application to Complex Networks [article]

G.D. Paparo, M. Müller, F. Comellas, M.A. Martin-Delgado
2014 arXiv   pre-print
Examples of applications include real-world instances from the WWW, which typically display a scale-free network structure and models of hierarchical networks.  ...  We review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci.  ...  Scale-free Networks Random scale-free graphs [52, 53] are networks that display a small fraction of hubs, i.e. nodes with a high connectivity.  ... 
arXiv:1409.3793v1 fatcat:g6z6lm6q2naalhkuld3k3niiiu

Ranking spaces for predicting human movement in an urban environment

Bin Jiang
2009 International Journal of Geographical Information Science  
Keywords: Space syntax, topological analysis of networks, small world, scale free, human movement, and PageRank  ...  PageRank scores are better correlated to human movement rates than the space syntax metrics, and (2) the underlying space-space topology demonstrates small world and scale free properties.  ...  Acknowledgement The study reported in the paper was financially supported by a Hong Kong Polytechnical University research grant.  ... 
doi:10.1080/13658810802022822 fatcat:gmwqgnkkvvh2jdiysujenzi46u

Centrality measures and thermodynamic formalism for complex networks

Jean-Charles Delvenne, Anne-Sophie Libert
2011 Physical Review E  
to the medium-scale details of the graph.  ...  If the graph is weighted, then a free energy is optimised instead of entropy rate.  ...  This paper has benefitted from discussions with the team GYROWEB at INRIA, Rocquencourt (France) and the team Large Graphs  ... 
doi:10.1103/physreve.83.046117 pmid:21599250 fatcat:sfafdjc575bfzgweoaeggpof5u

Simulating Network Influence Algorithms Using Particle-Swarms: PageRank and PageRank-Priors [article]

Marko A. Rodriguez, Johan Bollen
2006 arXiv   pre-print
PageRank is compared against the particle-swarm method on artificially generated scale-free networks of 1,000 nodes constructed using a common gamma value, γ = 2.5.  ...  This paper will describe a particular implementation of a particle-swarm that can simulate the behavior of the popular PageRank algorithm in both its global-rank and relative-rank incarnations.  ...  For example, a γ = 2.0 scale-free network with |N| = 1000 only requires 12.52 iterations for PageRank to converge.  ... 
arXiv:cs/0602002v1 fatcat:av4oab33pbdlhpfdpd63tg3maa

Adiabatic Quantum Algorithm for Search Engine Ranking

Silvano Garnerone, Paolo Zanardi, Daniel A. Lidar
2012 Physical Review Letters  
We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution.  ...  We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of webpages  ...  These models are based on two different network evolution mechanisms, both of which yield sparse random graphs with small-world and scale-free (power-law) features.  ... 
doi:10.1103/physrevlett.108.230506 pmid:23003933 fatcat:o4qx4fb5sfg67a2udpcih7kibq

Power-law scaling for the adiabatic algorithm for search-engine ranking

Adam Frees, John King Gamble, Kenneth Rudinger, Eric Bach, Mark Friesen, Robert Joynt, S. N. Coppersmith
2013 Physical Review A. Atomic, Molecular, and Optical Physics  
Recently, a quantum algorithm for preparing this eigenvector and evidence of an exponential speedup for some scale-free networks were presented.  ...  For a sample of graphs with degree distributions that more closely resemble the Web than in previous work, the proposed algorithm for eigenvector preparation does not appear to run exponentially faster  ...  In order for a graph to be scale-free, Prob(d in = k) and Prob(d out = k), the probabilities that the in degree d in and the out degree d out of a random node have the value k, must satisfy Prob(d in =  ... 
doi:10.1103/physreva.88.032307 fatcat:27hhfhjelbgshlzl62afb4hsiq

Reducing the History in Decentralized Interaction-Based Reputation Systems [chapter]

Dimitra Gkorou, Tamás Vinkó, Nitin Chiluka, Johan Pouwelse, Dick Epema
2012 Lecture Notes in Computer Science  
on the computed reputations showing its effectiveness in both synthetic and real-world graphs.  ...  In this paper, we propose a scheme for reducing the amount of history maintained in decentralized interaction-based reputation systems based on such elements as the age of nodes, and we explore its effect  ...  We conclude that for scale-free and real-world graphs, the reduced history is reasonably accurate while for random graphs, due to their structural properties, the reduced history causes high error.  ... 
doi:10.1007/978-3-642-30054-7_19 fatcat:w6mfrwybzbbxdipmptbcsi7wq4

Ranking on large-scale graphs with rich metadata

Bin Gao, Taifeng Wang, Tie-Yan Liu
2011 Proceedings of the 20th international conference companion on World wide web - WWW '11  
Assume a random surfer walking on the link graph Web link graph Impact of PageRank • A key technology of Google  ...  Vertex weight C i : Number of visits for page i User Browsing Graph • Another scale-free network -Real users tend to visit important pages frequently -Web masters and web users perform differently  ...  Output of the Learning Process • π: can be used to direct rank nodes in the given graph. • ϕ and ω can be used to rank nodes in new graphs with similar generating mechanisms to the given graph (advantages  ... 
doi:10.1145/1963192.1963313 dblp:conf/www/GaoWL11 fatcat:gn7iwht3hrggbbybgoehh5d26y

Quantum centrality testing on directed graphs via PT -symmetric quantum walks

J. A. Izaac, J. B. Wang, P. C. Abbott, X. S. Ma
2017 Physical Review A  
Finally, we perform a statistical analysis over ensembles of random graphs, and show strong agreement with the classical PageRank measure on directed acyclic graphs.  ...  In this paper, we discuss a method for simulating directed graphs using PT-symmetric quantum walks, allowing probability conserving non-unitary evolution.  ...  in-degree scale-free graphs, and (b) 100 directed out-degree scale-free graphs.  ... 
doi:10.1103/physreva.96.032305 fatcat:hyzw5zbkbnacdfqg47pcczhq5e

Analysis of function-call graphs of open-source software systems using complex network analysis

Volkan Tunalı, Mehmet Ali Aksoy Tüysüz
2020 Pamukkale University Journal of Engineering Sciences  
We found the call graphs to reveal scale-free and small-world network properties similar to the findings of the previous studies.  ...  In addition, we identified the most central and important functions in each call-graph using several centrality measures.  ...  We showed that the function-call graphs of different size had the scale-free property [21] .  ... 
doi:10.5505/pajes.2019.63239 fatcat:wu4g7lafb5dixgn4bxoe7ki7za
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