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, 14 (12), e0225500
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Interactions of Pharmaceutical Companies With World Countries, Cancers and Rare Diseases From Wikipedia Network Analysis

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Interactions of Pharmaceutical Companies With World Countries, Cancers and Rare Diseases From Wikipedia Network Analysis

Guillaume Rollin et al. PLoS One.

Abstract

Using the English Wikipedia network of more than 5 million articles we analyze interactions and interlinks between the 34 largest pharmaceutical companies, 195 world countries, 47 rare renal diseases and 37 types of cancer. The recently developed algorithm using a reduced Google matrix (REGOMAX) allows us to take account both of direct Markov transitions between these articles and also of indirect transitions generated by the pathways between them via the global Wikipedia network. This approach therefore provides a compact description of interactions between these articles that allows us to determine the friendship networks between them, as well as the PageRank sensitivity of countries to pharmaceutical companies and rare renal diseases. We also show that the top pharmaceutical companies in terms of their Wikipedia PageRank are not those with the highest market capitalization.

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Density of Wikipedia articles in the PageRank-CheiRank plane (K, K*).
Data are averaged over a 100 × 100 grid for (log10 K, log10 K*) spanning the domain [0, log10 N] × [0, log10 N]. Density of articles ranges from very low (purple tiles) to very high (bright yellow tiles). The absence of any article is represented by black tiles. The superimposed white circles give the positions of articles devoted to the 195 countries, the red circles represent the positions of articles devoted to the 230 kinds of infectious diseases studied in [19], the green circles represent the positions of 37 articles on the cancers studied in [20], the gold circles mark the positions of 47 articles on rare renal diseases and the purple circles give the positions of 34 articles on pharmaceutical companies.
Fig 2
Fig 2. Distribution of pharmaceutical companies ranked by largest market capitalization index, KLMC, and by the relative PageRank index, Kr, of their article in Wikipedia.
See rankings in Table 1.
Fig 3
Fig 3. Overlap between the PageRanking of articles on pharmaceutical companies in Wikipedia and the ranking of pharmaceutical companies by market capitalization.
The overlap function is η(j) = jph/j, where jph is the number of pharmaceutical companies present in the top j of both lists: the PageRanking of pharmaceutical companies articles in Wikipedia (see first column of Table 1) and the list of pharmaceutical companies ranked by market capitalization in 2017 (red curve, see third column in Table 1) and ranked in terms of the largest market capitalization since 2000 (black curve, see second column in Table 1).
Fig 4
Fig 4. Distribution of Nrd = 47 articles on rare renal diseases on the plane of relative PageRank-CheiRank indexes (Kr,Kr*); positions in the plane are indicated by golden circles with short names for the diseases.
Fig 5
Fig 5. Reduced Google matrix GR of pharmaceutical companies and rare renal diseases.
We show the reduced Google matrix GR (top left panel) and its three components Grr (top right panel), Gpr (bottom left panel), and Gqrnd (bottom right panel). Each “pixel” represents a matrix entry with the amplitude given by a color. Color bars give the corresponds between matrix entry amplitudes and colors. For each 81 × 81 matrix the first 34 entries correspond to pharmaceutical companies (ordered as in Table 1) and the other 47 entries correspond to rare renal diseases (ordered by categories then by PageRank order inside each category, see Table 2). The first 34 × 34 block diagonal sub-matrix (purple square) corresponds to directed interactions between pharmaceutical companies. The other five smallest block diagonal sub-matrices correspond to directed interactions between rare renal diseases belonging to one of the five categories defined in Table 2. The colors of the squares correspond to color categories given in Table 2. For the sake of visibility horizontal and vertical white dashed lines are drawn after every 20 entries.
Fig 6
Fig 6. Reduced network of pharmaceutical companies with the addition of their best connected countries.
We consider the first five pharmaceutical companies from the Wikipedia PageRank list: Pfizer, GSK, Bayer, J&J, and Novartis (see Table 1). Each one of these companies are represented by purple circles (with a black dot in the middle) placed along the main grey circle (the grey circle with the largest radius). From these five most influential pharmaceuticals in Wikipedia, we determine the two best connected companies, i.e., for a pharmaceutical company ph, we determine the two companies ph1 and ph2 giving the highest (Grr+Gqr)ph1or2,ph values. If not already present in the network, we add these best connected companies along secondary circles centered on the previous companies. The newly added companies are represented by purple circles. Also from the initial five pharmaceutical companies we determine the two best connected countries, i.e., for a company ph, we determine the two countries c1 and c2 giving the highest (Grr+Gqr)c1or2,ph values. From the newly added pharmaceutical of the first iteration, we determine the two best connected pharmaceutical companies and the two best connected countries. This constitutes the second iteration, an so on. At the fourth iteration of this process, no new pharmaceutical companies are added, and consequently the network construction process stops. The links obtained at the first iteration are represented by solid line arrows, at the second iteration by dashed line arrows, at the third iteration by dashed-dotted line arrows, and at the fourth iteration by dotted line arrows. Black color arrows correspond to links existing in the adjacency matrix (direct hyperlinks in Wikipedia), and red color arrows are purely hidden links absent from the adjacency matrix but present in Gqr component of the reduced Google matrix GR. The obtained network is drawn with the Cytoscape software [44]. Countries are marked by their ISO 3166-1 alpha-2 codes.
Fig 7
Fig 7. Reduced network of pharmaceutical companies with the addition of their best connected cancers.
The construction algorithm is the same as the one used to generate Fig 6 excepting that we replace at each iteration the two best connected countries by the two best connected cancers. Pharmaceutical companies are represented by purple circles and cancers by green circles.
Fig 8
Fig 8. Reduced network of pharmaceutical companies with the addition of their best connected rare renal diseases.
The construction algorithm is the same as the one used to generate Fig 6 excepting that we replace at each iteration the two best connected countries by the two best connected rare renal diseases. Pharmaceutical companies are represented by purple circles and rare renal diseases by red circles for congenital abnormalities of the kidney and urinary tract, blue circles for glomerular diseases, gold circles for renal tubular diseases and metabolic diseases, cyan circles for nephrolithiasis, and green circles for ciliopathies.
Fig 9
Fig 9. Sensitivity of countries to the Pfizer company (top panel) and the Bayer company (bottom panel).
A country c is colored according to its diagonal PageRank sensitivity D(phc, c), where ph is the pharmaceutical company. Color categories are obtained using the Jenks natural breaks classification method [47].
Fig 10
Fig 10. Sensitivity of countries to rare renal diseases; here to Kallmann syndrome (top panel) and to Bardet–Biedl syndrome (bottom panel).
A country c is colored according to its diagonal PageRank sensitivity D(rdc, c), where rd is the rare renal disease. Color categories are obtained using the Jenks natural breaks classification method [47].

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Publication types

Grant support

J.L. was supported by ANR-15-IDEX-0003, Programme Investissements d’Avenir, ISITE-BFC (project GNETWORKS), http://i-site.ubfc.fr; and Bourgogne Franche-Comté region (project APEX), https://www.bourgognefranchecomte.fr. D.S. was supported by ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT, Programme Investissements d’Avenir (project THETRACOM), http://www.next-toulouse.fr. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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