Wikipedia mining of hidden links between political leaders

Frahm, Klaus M.; Jaffrès‐Runser, Katia; Shepelyansky, Dima L.

doi:10.1140/epjb/e2016-70526-3

Cited by 37 publications

(183 citation statements)

References 26 publications

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“…The weights of these three G R components are W rr =0.0644, W pr =0.8769 and W qr =0.0587 (the weight is given by the sum of all matrix elements divided by N r , thus W rr + W qr + W qr = 1). The dominant component is G pr but as stated above it is approximately given by columns of the PageRank vector so that the most interesting information is provided by G rr and especially the component G qr given by indirect links [8,9].…”

Section: Resultsmentioning

confidence: 99%

“…We order all nodes by decreasing probability P getting them ordered by the PageRank index K = 1, 2, ...N with a maximal probability at K = 1. From this global ranking we obtain the local ranking of groups and countries given in Tables 1, 2. The reduced Google matrix G R is constructed for a selected subset of nodes (articles) following the method described in [7,8] and based on concepts of scattering theory used in different fields of mesoscopic and nuclear physics or quantum chaos [15]. This matrix has N r nodes and belongs to the class of Google matrices.…”

Section: Reduced Google Matrixmentioning

confidence: 99%

“…In addition the PageRank probabilities of selected N r nodes are the same as for the global network with N nodes, up to a constant multiplicative factor taking into account that the sum of PageRank probabilities over N r nodes is unity. The matrix G R is represented as a sum of three matrices (components) G R = G rr + G pr + G qr [8]. The first term G rr is given by the direct links between selected N r nodes in the global G matrix with N nodes, the second term G pr is rather close to the matrix in which each column is given by the PageRank vector P r , ensuring that PageRank probabilities of G R are the same as for G (up to a constant multiplier).…”

Section: Reduced Google Matrixmentioning

confidence: 99%

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Analysis of world terror networks from the reduced Google matrix of Wikipedia

2018

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Abstract. We apply the reduced Google matrix method to analyse interactions between 95 terrorist groups and determine their relationships and influence on 64 world countries. This is done on the basis of the Google matrix of the English Wikipedia (2017) composed of 5 416 537 articles which accumulate a great part of global human knowledge. The reduced Google matrix takes into account the direct and hidden links between a selection of 159 nodes (articles) appearing due to all paths of a random surfer moving over the whole network. As a result we obtain the network structure of terrorist groups and their relations with selected countries. Using the sensitivity of PageRank to a weight variation of specific links we determine the geopolitical sensitivity and influence of specific terrorist groups on world countries. We argue that this approach can find useful application for more extensive and detailed data bases analysis.

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Section: Resultsmentioning

confidence: 99%

Section: Reduced Google Matrixmentioning

confidence: 99%

Section: Reduced Google Matrixmentioning

confidence: 99%

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Analysis of world terror networks from the reduced Google matrix of Wikipedia

2018

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“…The reduced Google matrix G R is constructed on the mathematical basis described below. The main element of this construction is to keep the same PageRank probabilities of N r nodes as in the global network (up to a fixed multiplier coefficient) and to take into account all indirect links between N r nodes coupled by transitions via N − N r nodes of the global network (see also [20]). …”

Section: Reduced Google Matrixmentioning

confidence: 99%

“…We refer the reader to [20] to get the proof that G R also fulfills the condition of column sum normalization being unity. …”

Section: Reduced Google Matrixmentioning

confidence: 99%

Multi-cultural Wikipedia mining of geopolitics interactions leveraging reduced Google matrix analysis

2017

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Geopolitics focuses on political power in relation to geographic space. Interactions among world countries have been widely studied at various scales, observing economic exchanges, world history or international politics among others. This work exhibits the potential of Wikipedia mining for such studies. Indeed, Wikipedia stores valuable fine-grained dependencies among countries by linking webpages together for diverse types of interactions (not only related to economical, political or historical facts). We mine herein the Wikipedia networks of several language editions using the recently proposed method of reduced Google matrix analysis. This approach allows to establish direct and hidden links between a subset of nodes that belong to a much larger directed network. Our study concentrates on 40 major countries chosen worldwide. Our aim is to offer a multicultural perspective on their interactions by comparing networks extracted from five different Wikipedia language editions, emphasizing English, Russian and Arabic ones. We demonstrate that this approach allows to recover meaningful direct and hidden links among the 40 countries of interest.

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Contagion in Bitcoin Networks

Coquidé¹,

Lages²,

Shepelyansky³

2019

Business Information Systems Workshops

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We construct the Google matrices of bitcoin transactions for all year quarters during the period of January 11, 2009 till April 10, 2013. During the last quarters the network size contains about 6 million users (nodes) with about 150 million transactions. From PageRank and CheiRank probabilities, analogous to trade import and export, we determine the dimensionless trade balance of each user and model the contagion propagation on the network assuming that a user goes bankrupt if its balance exceeds a certain dimensionless threshold κ. We find that the phase transition takes place for κ < κc ≈ 0.1 with almost all users going bankrupt. For κ > 0.55 almost all users remain safe. We find that even on a distance from the critical threshold κc the top PageRank and CheiRank users, as a house of cards, rapidly drop to the bankruptcy. We attribute this effect to strong interconnections between these top users which we determine with the reduced Google matrix algorithm. This algorithm allows to establish efficiently the direct and indirect interactions between top PageRank users. We argue that this study models the contagion on real financial networks.

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Wikipedia mining of hidden links between political leaders

Cited by 37 publications

References 26 publications

Analysis of world terror networks from the reduced Google matrix of Wikipedia

Analysis of world terror networks from the reduced Google matrix of Wikipedia

Multi-cultural Wikipedia mining of geopolitics interactions leveraging reduced Google matrix analysis

Contagion in Bitcoin Networks

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