Google matrix

First we construct the matrix S_ij of Markov transitions by normalizing the sum of the elements in each column of A to unity (S_ij = A_ij/∑_i A_ij, ∑_i S_ij = 1) and replacing columns with zero elements by elements 1/N with N being the matrix size. Then the Google matrix is given by the relation G_ij = αS_ij + (1 − α)/N, where α is the damping factor [30]. As in [21] we use the conventional value α = 0.85. It is known that the variation of α in a range 0.5 ≤ α < 0.95 does not significantly affect the probability distribution of ranks discussed below (see e.g. [18, 19, 30]).

PageRank algorithm

PageRank is a widely used algorithm to rank nodes in a directed network. It was originally introduced for Google web search engine to rank web pages of the World Wide Web based on the idea of academic citations [31]. Currently PageRank is used to rank nodes of network systems from scientific papers [32] to social network services [33], world trade [34] and biological systems [35]. Here we briefly outline the iteration method of PageRank computation. The PageRank vector P(i, t) of a node i at iteration t in a network with N nodes is given by (1)

The stationary state P(i) of P(i, t) is the PageRank of node i. More detailed information about the PageRank algorithm is described in [30]. Ordering all nodes by their decreasing probability P(i), we obtain the PageRank ranking index K(i). In qualitative terms, the PageRank probability of a node is proportional to the number of incoming links weighted according to their own probability. A random network surfer spends on a given node a time given on average by the PageRank probability.

CheiRank algorithm

In a directed network, outgoing links can be as important as ingoing links. In this sense, as a complementary to PageRank, the CheiRank algorithm is defined and used in [18, 28, 36]. The CheiRank vector P*(i, t) of a node at iteration time t is given by (2)

Same as the case of PageRank, we consider the stationary state P*(i) of P*(i, t) as the CheiRank probability of node i with α = 0.85. High CheiRank nodes in the network have large out-degree. Ordering all nodes by their decreasing probability P*(i), we obtain the CheiRank ranking index K*(i). The PageRank probability of an article is proportional to the number of incoming links, while the CheiRank probability of an article is proportional to the number of outgoing links. Thus a top PageRank article is important since other articles refer to it, while a top CheiRank article is highly connected because it refers to other articles.

2DRank algorithm

PageRank and CheiRank algorithms focus only on in-degree and out-degree of nodes, respectively. The 2DRank algorithm considers both types of information simultaneously to rank nodes with a balanced point of view in a directed network. Briefly speaking, nodes with both high PageRank and CheiRank get high 2DRank ranking. Consider a node i which is K_i-th ranked by PageRank and K*_i ranked by CheiRank. Then we can assign a secondary ranking $K_i^{\prime }=max\{K_i,{K^{*}}_i\}$ to the node. If $K_i^{\prime }<K_j^{\prime }$, then node j has lower 2DRank and vice versa. A detailed illustration and description of this algorithm is given in [18].

We note that the studies reported in [21] show that the overlap between top CheiRank persons of different editions is rather small and due to that the statistical accuracy of this data is not sufficient for determining interactions between different cultures for the CheiRank list. Moreover, CheiRank, based on outgoing links only, selects mainly persons from such activity fields like sports and arts where the historical trace is not so important. Due to these reasons we restrict our study to PageRank and 2DRank. It can be also interesting to use other algorithms of ranking, e.g. LeaderRank [37], but here we restrict ourselves to the methods which we already tested, leaving investigation of other raking methods for further studies.

Spatial distribution

The birth places of historical figures are attributed to the country containing their geographical location of birth according to the present geographical territories of all world countries. The list of countries appeared for the top 100 persons in all editions is given in Table 3. We also attribute each country to one of the 24 languages of the considered editions. This attribution is done according to the language spoken by the largest part of population in the given country. Thus e.g. Belgium is attributed to Dutch (NL) since the majority of the population speaks Dutch. If the main language of a country is not among our 24 languages, then this country is attributed to an additional section WR corresponding to the remaining world (e.g. Ukraine, Norway are attributed to WR). If the birth place of a person is not known, then it is also attributed to WR. The choice of attribution of a person to a given country in its current geographic territory, and as a result to a certain language, may have some fluctuations due to historical variations of country borders (e.g. Immanuel Kant was born in the current territory of Russia and hence is attributed to Russian language). However, the number of such cases is small, being on a level of 3.5 percent (see Section “Network of cultures” below). We think that the way in which a link between person, language and country is fixed by the birth place avoids much larger ambiguity of attribution of a person according to the native language which is not so easy to fix in an automatic manner.

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Table 3. List of country code (CC), countries as birth places of historical figures, and language code (LC) for each country.

LC is determined by the most spoken language in the given country. Country codes are based on country codes of Internet top-level domains and language codes are based on language edition codes of Wikipedia; WR represents all languages other than the considered 24 languages.

https://doi.org/10.1371/journal.pone.0114825.t003

The obtained spatial distribution of historical figures of Wikipedia over countries is shown in Fig. 1. This averaged distribution gives the average number of top 100 persons born in a specific country as birth place, with averaging done over our 24 Wikipedia editions. Thus an average over the 24 editions gives for Germany (DE) approximately 9.7 persons in the top 100 of PageRank, being at the first position, followed by USA with approximately 9.5 persons. For 2DRank we have USA at the first position with an average of 9.8 persons and Germany at the second with an average of 8.0 persons.

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Fig 1. Birth place distribution of top historical figures averaged over 24 Wikipedia edition for (A) PageRank historical figures (71 countries) and (B) 2DRank historical figures (91 countries).

Two letter country codes are represented in Table 3.

https://doi.org/10.1371/journal.pone.0114825.g001

Western (Europe and USA) skewed patterns are observed in both top PageRank historical figures (Fig. 1. (A)) and top 2DRank historical figures (Fig. 1. (B)). This Western skewed pattern is remarkable since 11 Wikipedia editions of the 24 considered editions are not European language editions. Germany, USA, Italy, UK and France are the top five birth places of top PageRank historical figures among 71 countries. On the other hand, USA, Germany, UK, Italy and Japan are top five birth places of the top 2DRank historical figures among 91 countries.

In Fig. 2 we show the world map of countries, where color indicates the number of persons from a given country among the 24 × 100 top persons for PageRank and 2DRank. Additional figures showing these distributions for different centuries are available at [39].

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Fig 2. Sum of appearances of historical figures from a given country in the 24 lists of top 100 persons for PageRank (top panel) and 2DRank (bottom panel).

Color changes from zero (white) to maximum (black). Maximal values are 233 appearances for Germany (top) and 236 for USA (bottom). Values are proportional to the averages per country shown in Fig. 1.

https://doi.org/10.1371/journal.pone.0114825.g002

We also observed local skewness in the spatial distribution of the top historical figures for the PageRank (2DRank) ranking algorithm as shown in Fig. 3A (in Fig. 3B). For example, 47 percent of the top PageRank historical figures in the English Wikipedia were born in USA (25 percent) and UK (22 percent) and 56 percent of the top historical figures in the Hindi Wikipedia were born in India. A similar strong locality pattern of the top historical figures was observed in our previous research [21]. However it should be noted that in the previous study we considered the native language of the top historical figure as a criterion of locality, while in the current study we considered ‘birth place’ as criterion of locality.

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Fig 3. Birth place distributions over countries of top historical figures from each Wikipedia edition; two letter country codes are represented in Table 3.

Panels: (A) distributions of PageRank historical figures over 71 countries for each Wikipedia edition; (B) distributions of 2DRank historical figures over 91 countries for each Wikipedia edition; (C) column normalized birth place distributions of PageRank historical figures of panel (A); (D) column normalized birth place distributions of 2DRank historical figures of panel (B).

https://doi.org/10.1371/journal.pone.0114825.g003

Regional skewness, the preferences of Wikipedia editions for historical figures who were born in geographically or culturally related countries, is also observed. For example, 18 (5) of the top 100 PageRank historical figures in the Korean (Japanese) Wikipedia were born in China. Also 9 of the top 100 PageRank historical figures in the Persian Wikipedia were born in Saudi Arabia. The distribution of top persons from each Wikipedia edition over world countries is shown in Fig. 3A and Fig. 3B. The countries on a horizontal axis are grouped by clusters of corresponding language so that the links inside a given culture (or language) become well visible.

To observe patterns in a better way at low numbers of historical figures, we normalized each column of Fig. 3A and Fig. 3B corresponding to a given country. In this way we obtain a rescaled distribution with better visibility for each birth country level as shown in Fig. 3C and Fig. 3D, respectively. We can observe a clear birth pattern of top PageRank historical figures born in Lebanon, Libya, Oman, and Tunisia in the case of the Arabic Wikipedia, and historical figures born in N. Korea appearing not only in the Korean but also in the Japanese Wikipedia.

In the case of the top 2DRank historical figures shown in Fig. 3B and Fig. 3D, we observe overall patterns of locality and regions being similar to the case of PageRank, but the locality is stronger.

In short, we observed that most of the top historical figures in Wikipedia were born in Western countries, but also that each edition shows its own preference to the historical figures born in countries which are closely related to the corresponding language edition.

Temporal distribution

The analysis of the temporal distribution of top historical figures is done based on their birth dates. As shown in Fig. 4A for PageRank, most of historical figures were born after the 17th century on average, which shows similar pattern with world population growth [40]. However, there are some distinctive peaks around BC 5th century and BC 1st century for the case of PageRank because of Greek scholars (Socrates, Plato, and Herodotus), Roman politicians (Julius Caesar, Augustus) and Christianity leaders (Jesus, Paul the Apostle, and Mary (mother of Jesus)). We also observe that the Arabic and the Persian Wikipedia have more historical figures than Western language Wikipedia editions from AD 6th century to AD 12th century. For the case of 2DRank in Fig. 4B, there is only one small peak around BC 1C, which is also smaller than the peak in the case of PageRank, and all the distribution is dominated by a strong growth on the 20th century.

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Fig 4. Birth date distributions of top historical figures.

(A) Birth date distribution of PageRank historical figures averaged over 24 Wikipedia editions (B) Birth date distribution of 2DRank historical figures averaged over 24 Wikipedia editions (C) Birth date distributions of PageRank historical figures for each Wikipedia edition. (D) Birth date distributions of 2DRank historical figures for each Wikipedia edition. (E) Column normalized birth date distributions of PageRank historical figures for each Wikipedia edition. (F) Column normalized birth date distributions of 2DRank historical figures for each Wikipedia edition.

https://doi.org/10.1371/journal.pone.0114825.g004

The distributions of the top PageRank historical figures over the 24 Wikipedia editions for each century are shown in Fig. 4C. The same distribution, but normalized to unity over all editions for each century, is shown in Fig. 4E. The Persian (FA) and the Arabic (AR) Wikipedia have more historical figures than other language editions (in particular European language editions) from the 6th to the 12th century due to Islamic leaders and scholars. On the other hand, the Greek Wikipedia has more historical figures in BC 5th century because of Greek philosophers. Also most of western-southern European language editions, including English, Dutch, German, French, Spanish, Italian, Portuguese, and Greek, have more top historical figures because they have Augustine the Hippo and Justinian I in common. Similar distributions obtained from 2DRank are shown in Fig. 4D and Fig. 4F respectively.

The data of Figs. 4E, F clearly show well pronounced patterns, corresponding to strong interactions between cultures: from BC 5th century to AD 15th century for JA, KO, ZH, VI; from AD 6th century to AD 12th century for FA, AR; and a common birth pattern in EN, EL, PT, IT, ES, DE, NL (Western European languages) from BC 5th century to AD 6th century. In supporting Figure S1 we show distributions of historical figures over languages according to their birth place. In this case the above patterns become even more pronounced.

At a first glance from Figs. 4E, F we observe for persons born in AD 20th century a significantly more homogeneous distribution over cultures compared to early centuries. However, as noted in [21], each Wikipedia edition favors historical figures speaking the corresponding language. We investigate how this preference to same-language historical figures changes in time. For this analysis, we define two variables M_{L, C} and N_{L, C} for a given language edition L and a given century C. Here M_{L, C} is the number of historical figures born in all countries being attributed to a given language L, and N_{L, C} is the total number of historical figures for a given century C and a given language edition L. For example, among the 21 top PageRank historical figures from the English Wikipedia, who were born in AD 20th century, two historical figures (Pope John Paul II and Pope Benedict XVI) were not born in English speaking countries. Thus in this case N_{EN, 20} = 21 and M_{EN, 20} = 19. Fig. 5 represents the ratio r_{L, C} = M_{L, C}/N_{L, C} for each edition and each century. In ancient times (i.e. before AD 5th century), most historical figures for each Wikipedia edition are not born in the same language region except for the Greek, Italian, Hebrew, and Chinese Wikipedia. However, after AD 5th century, the ratio of same language historical figures is rising. Thus, in AD 20th century, most Wikipedia editions have significant numbers of historical figures born in countries speaking the corresponding language. For PageRank persons and AD 20th century, we find that the English edition has the largest fraction of its own language, followed by Arabic and Persian editions while other editions have significantly large connections with other cultures. For the English edition this is related to a significant number of USA presidents appearing in the top 100 list (see [18, 19]). For 2DRank persons the largest fractions were found for Greek, Arabic, Chinese and Japanese cultures. These data show that even in age of globalization there is a significant dominance of local historical figures for certain cultures.

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Fig 5. The locality property of cultures represented by the ratio r_{L, C} = M_{L, C}/N_{L, C} for each edition L and each century C.

Here M_{L, C} is the number of historical figures born in countries attributed to a given language edition L at century C and N_{L, C} is the total number of historical figures in a given edition at a given century, regardless of language of their birth countries. Black color (-0.2 in the color bars) shows that there is no historical figure at all for a given edition and century; blue (0 in the color bars) shows there there are some historical figures but no same language historical figures. Here (A) panel shows PageRank historical figures, and (B) panel shows 2DRank historical figures.

https://doi.org/10.1371/journal.pone.0114825.g005

Gender distribution

From the gender distributions of historical figures, we observe a strong male-skewed pattern across many Wikipedia editions regardless of the ranking algorithm. On average, 5.2(10.1) female historical figures are observed among the 100 top PageRank (2DRank) persons for each Wikipedia edition. Fig. 6 shows the number of top female historical figures for each Wikipedia edition. Thai, Hindi, Swedish, and Hebrew have more female historical figures than the average over our 24 editions in the case of PageRank. On the other hand, the Greek and the Korean versions have a lower number of females than the average. In the case of 2DRank, English, Hindi, Thai, and Hungarian Wikipedia have more females than the average while German, Chinese, Korean, and Persian Wikipedia have less females than the average. In short, the top historical figures in Wikipedia are quite male-skewed. This is not surprising since females had little chance to be historical figures for most of human history. We compare the gender skewness to other cases such as the number of female editors in Wikipedia (9 percent) in 2011 [41] and the share of women in parliaments, which was 18.7 percent in 2012 by UN Statistics and indicators on women and men [42], the male skewness for the PageRank list is stronger in the contents of Wikipedia [43]. However, the ratio of females among the top historical figures is growing by time as shown in Fig. 6 C. It is notable that the peak in Fig. 6C at BC 1st is due to “Mary (mother of Jesus)”. In the 20th century 2DRank gives a larger percentage of women compared to PageRank. This is due to the fact that 2DRank has a larger fraction of singers and artists comparing to PageRank (see [18, 19]) and that the fraction of women in these fields of activity is larger.

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Fig 6. Number of females of top historical figures from each Wikipedia edition (A) Top PageRank historical figures (B) Top 2DRank historical figures.

(C) The average female ratio of historical figures in given centuries across 24 Wikipedia editions.

https://doi.org/10.1371/journal.pone.0114825.g006

Global historical figures

Above we analyzed how top historical figures in Wikipedia are distributed in terms of space, time, and gender. Now we identify how these top historical figures are distributed in each Wikipedia edition and which are global historical figures. According to previous research [21], there are some global historical figures who are recognized as important historical figures across Wikipedia editions. We identify global historical figures based on the ranking score for a given person determined by her number of appearances and ranking index over our 24 Wikipedia editions.

Following [21], the ranking score Θ_{P, A} of a historical figure P is given by (3)

Here R_{P, E, A} is the ranking of a historical figure P in Wikipedia edition E by ranking algorithm A. According to this definition, a historical figure who appears more often in the lists of top historical figures for the given 24 Wikipedia editions or has higher ranking in the lists gets a higher ranking score. Table 4 represents the top 10 global historical figures for PageRank and 2DRank. Carl Linnaeus is the 1st global historical figure by PageRank followed by Jesus, Aristotle. Adolf Hitler is the 1st global historical figure by 2DRank followed by Michael Jackson, Madonna (entertainer). On the other hand, the lists of the top 10 local historical figures ordered by our ranking score for each language are represented in supporting Tables S1–S25 and [39].

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Table 4. List of global historical figures by PageRank and 2DRank for all 24 Wikipedia editions.

All names are represented by the corresponding article titles in the English Wikipedia. Here, Θ_A is the ranking score of algorithm A (3); N_A is the number of appearances of a given person in the top 100 rank for all editions.

https://doi.org/10.1371/journal.pone.0114825.t004

The reason for a somewhat unexpected PageRank leader Carl Linnaeus is related to the fact that he laid the foundations for the modern biological naming scheme so that plenty of articles about animals, insects and plants point to the Wikipedia article about him, which strongly increases the PageRank probability. This happens for all 24 languages where Carl Linnaeus always appears on high positions since articles about animals and plants are an important fraction of Wikipedia. Even if in a given language the top persons are often politicians (e.g. Napoleon, Barak Obama at K = 1, 2 in EN), these politicians have mainly local importance and are not highly ranked in other languages (e.g. in ZH Carl Linnaeus is at K = 1, Napoleon at K = 3 and Barak Obama is at K = 24). As a result when the global contribution is counted over all 24 languages Carl Linnaeus appears on the top PageRank position.

Our analysis suggests that there might be three groups of historical figures. Fig. 7 shows these three groups of top PageRank historical figures in Wikipedia: (i) global historical figures who appear in most of Wikipedia editions (N_A ≥ 18) and are highly ranked (⟨K⟩ ≤ 50) for each Wikipedia such as Carl Linnaeus, Plato, Jesus, and Napoleon (Right-Top of the Fig. 7A); (ii) local-highly ranked historical figures who appear in a few Wikipedia editions (N_A < 18) but are highly ranked (⟨K⟩ ≤ 50) in the Wikipedia editions in which they appear, such as Tycho Brahe, Sejong the Great, and Sun Yat-sen (Left-Top of the Fig. 7A); (iii) locally-low ranked historical figures who appear in a few Wikipedia editions (N_A < 18) and who are not highly ranked (⟨K⟩ > 50). Here N_A is the number of appearances in different Wikipedia editions for a given person and ⟨K⟩ is the average ranking of the given persons across Wikipedia editions for each ranking algorithm. In the case of 2DRank historical figures, due to the absence of global historical figures, most of them belong to two types of local historical figures (i.e. local-highly ranked or local-lowly ranked).

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Fig 7. The distribution of 1045 top PageRank persons (A) and 1616 top 2DRank persons (B) as a function of number of appearances N_A of a given person and the rank ⟨K⟩ of this person averaged over Wikipedia editions where this person appeared.

https://doi.org/10.1371/journal.pone.0114825.g007

Following ranking of persons via Θ_{P, A} we determine also the top global female historical figures, presented in Table 5 for PageRank and 2DRank persons. The full lists of global female figures are available at [39] (63 and 165 names for PageRank and 2DRank).

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Table 5. List of the top 10 global female historical figures by PageRank and 2DRank for all the 24 Wikipedia editions.

All names are represented by article titles in the English Wikipedia. Here, Θ_A is the ranking score of the algorithm A (Eq.3); N_A is the number of appearances of a given person in the top 100 rank for all editions. Here CC is the birth country code and LC is the language code of the given historical figure.

https://doi.org/10.1371/journal.pone.0114825.t005

The comparison of our 100 global historical figures with the top 100 from Hart’s list [27] gives an overlap of 43 persons for PageRank and 26 persons for 2DRank. We note that for the top 100 from the English Wikipedia we obtain a lower overlap of 37 (PageRank) and 4 (2DRank) persons. Among all editions the highest overlaps with the Hart list are 42 (VI), 37 (EN, ES, PT, TR) and 33 (IT), 32 (DE), 31 (FR) for PageRank; while for 2DRank we find 18 (EL) and 17 (VI). We give the overlap numbers for all editions at [39]. This shows that the consideration of 24 editions provides us the global list of the top 100 persons with a more balanced selection of top historical figures. Our overlap of the top 100 global historical figures by PageRank with the top 100 people from Pantheon MIT ranking list [23] is 44 percent, while the overlap of this Pantheon list with Hart’s list is 43 percent. We note that the Pantheon method is significantly based on a number of page views while our approach is based on the network structure of the whole Wikipedia network. The top 100 persons from [22] are not publicly available but nevertheless we present the overlaps between the top 100 persons from the lists of Hart, Pantheon, Stony-Brook and our global PageRank and 2DRank lists in Figures S2, S3 (we received the Stony-Brook list as a private message from the authors of [22]). We have an average overlap between the 4 methods on a level of 40 percent (2DRank is on average lower by a few percent), we find a larger overlap between our PageRank list and the Stony-Brook list since the Stony-Brook method, applied only for the English Wikipedia, is significantly based on PageRank.

We also compared the distributions of our global top 100 persons of PageRank and 2DRank with the distribution of Hart’s top 100 over centuries and over 24 languages with the additional WR category (see Figure S4). We find that these 3 distributions have very similar shapes. Thus the largest number of persons appears in centuries AD 18th, 19th, 20th for the 3 distributions. Among languages, the main peaks for the 3 distributions appear for EN, DE, IT, EL, AR, ZH. The deviations from Hart’s distribution are larger for the 2DRank list. Thus the comparison of distributions over centuries and languages shows that the PageRank list has not only a strong overlap with the Hart list in the number of persons but that they also have very similar statistical distributions of the top 100 persons over centuries and languages.

The overlap of the top 100 global persons found here with the previous study [21] gives 54 and 47 percent for PageRank and 2DRank lists, respectively. However, we note that the global list in [21] was obtained from the top 30 persons in each edition while here we use the top 100 persons.

It is interesting to note that for the top 100 PageRank universities from the English Wikipedia edition the overlap with Shanghai top 100 list of universities is on a even higher level of 75 percent [18].

Finally, we note that the ranking of historical figures using the whole PageRank (or 2DRank) list of all Wikipedia articles of a given edition provides a more stable approach compared to the network of biographical articles used in [20]. Indeed, the number of nodes and links in such a biographical network is significantly smaller compared to the whole network of Wikipedia articles and thus the fluctuations become rather large. For example, from the biographical network of the Russian edition one finds as the top person Napoleon III (and even not Napoleon I) [20], who has a rather low importance for Russia. In contrast to that the present study gives us the top PageRank historical figure of the Russian edition to be Peter the Great, that has much more historical grounds. In a similar way for FR the results of [20] give at the first position Adolf Hitler, that is rather strange for the French culture, while we find a natural result Napoleon.

Network of cultures

We consider the selected top persons from each Wikipedia edition as important historical figures recognized by people who speak the language of that Wikipedia edition. Therefore, if a top person from a language edition A appears in another edition B, then we can consider this as a ‘cultural’ influence from culture A to B. Here we consider each language as a proxy for a cultural group and assign each historical figure to one of these cultural groups based on the most spoken language of her/his birth place at the country level. For example, Adolf Hitler was born in modern Austria and since German language is the most spoken language in Austria, he is considered as a German historical figure in our analysis. This method may lead to some misguiding results due to discrepancy between territories of country and cultures, e.g. Jesus was born in the modern State of Palestine (Bethlehem), which is an Arabic speaking country. Thus Jesus is from the Arabic culture in our analysis while usually one would say that he belongs to the Hebrew culture. Other similar examples we find are: Charlemagne (Belgium—Dutch), Immanuel Kant (Russia—Russian, while usually he is attributed to DE), Moses (Egypt—Arabic), Catherine the Great (Poland—Polish, while usually she would be attributed to DE or RU).

In total there are such 36 cases from the global PageRank list of 1045 names (these 36 names are given in SI). However, in our knowledge, the birth place is the best way to assign a given historical figure to a certain cultural background computationally and systematically and with the data we have available. In total we have only about 3.4 percent of cases which can be discussed and where a native speaking language can be a better indicator of belonging to a given culture. For the global 2DRank list of 1616 names we identified 53 similar cases where an attribution to a culture via a native language or a birth place could be discussed (about 3.3 percent). These 53 names are given in SI. About half of such cases are linked with birth places in ancient Russian Empire where people from Belarus, Litvania and Ukraine moved to RU, IL, PL, WR. However, the percentage of such cases is small and the corresponding errors also remain small.

Based on the above assumption and following the approach developed in [21], we construct two weighted networks of cultures (or language groups) based on the top PageRank historical figures and top 2DRank historical figures respectively. Each culture (i.e. language) is represented as a node of the network, and the weight of a directed link from culture A to culture B is given by the number of historical figures belonging to culture B (e.g. French) appearing in the list of top 100 historical figures for a given culture A (e.g. English). The persons in a given edition, belonging to the language of the edition, are not taken into account since they do not create links between cultures. In Table 6 we give the number of such persons for each language. This table also gives the number of persons of a given language among the top 100 persons of the global PageRank and 2DRank listings.

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Table 6. Numbers of certain historical figures for top 100 list of each language: N₁ is the number of historical figures of a given language among the top 100 PageRank global historical figures; N₂ is the number of historical figures of a given language among the top 100 PageRank historical figures for the given language edition; N₃ is the number of historical figures of a given language among the top 100 2DRank global historical figures; N₄ is the number of historical figures of a given language among the top 100 2DRank historical figures for the given language edition.

https://doi.org/10.1371/journal.pone.0114825.t006

For example, there are 5 French historical figures among the top 100 PageRank historical figures of the English Wikipedia, so we can assign weight 5 to the link from English to French. Fig. 8A and Fig. 8B represent the constructed networks of cultures defined by appearances of the top PageRank historical figures and top 2DRank historical figures, respectively. In total we have two networks with 25 nodes which include our 24 editions and an additional node WR for all the other world cultures.

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Fig 8. Network of cultures obtained from 24 Wikipedia languages and the remaining world (WR) consider (A) top PageRank historical figures and (B) 2DRank historical figures.

The link width and darkness are proportional to a number of foreign historical figures quoted in top 100 of a given culture, the link direction goes from a given culture to cultures of quoted foreign historical figures, links inside cultures are not considered. The size of nodes is proportional to their PageRank.

https://doi.org/10.1371/journal.pone.0114825.g008

The Google matrix G_ij for each network is constructed following the standard rules described in [21] and in the Methods Section. In a standard way we determine the PageRank index K and the CheiRank index K* that order all cultures according to decreasing PageRank and CheiRank probabilities (see Methods and Figure S5). The structure of matrix elements G_KK^′ is shown in Fig. 9.

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Fig 9. Google matrix of network of cultures shown in Fig. 8 respectively.

The matrix elements G_ij are shown by color with damping factor α = 0.85.

https://doi.org/10.1371/journal.pone.0114825.g009

To identify which cultures (or language groups) are more influential than others, we calculated PageRank and CheiRank of the constructed networks of cultures by considering link weights. Briefly speaking, a culture has high PageRank (CheiRank) if it has many ingoing (outgoing) links from (to) other cultures (see Methods). The distribution of cultures on a PageRank-CheiRank plane is shown in Fig. 10. In both cases of PageRank and 2DRank historical figures, historical figures of English culture (i.e. born in English language spoken countries) are the most influential (highest PageRank) and German culture is the second one (Fig. 10A, B). Here we consider the historical figures for the whole range of centuries. Fig. 10 represents the detailed features of how each culture is located on the plane of PageRank ranking K and CheiRank ranking K* based on the top PageRank historical figures (Fig. 10A) and top 2DRank historical figures (Fig. 10B). Here K indicates the ranking of a given culture ordered by how many of its own top historical figures appear in other Wikipedia editions, and K* indicates the ranking of a given culture according to how many of the top historical figures in the considered culture are from other cultures. As described above, English is on (K = 1, K* = 19) and German is on (K = 2, K* = 21) in the case of PageRank historical figures (Fig. 10A). In the case of 2DRank historical figures, English is on (K = 1, K* = 14) and German is on (K = 2, K* = 9).

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Fig 10. PageRank ranking versus CheiRank ranking plane of cultures with corresponding indexes K and K* obtained from the network of cultures based on (A) all PageRank historical figures, (B) all 2DRank historical figures, (C) PageRank historical figure born before AD 19th century, and (D) 2DRank historical figure born before AD 19th century, respectively.

https://doi.org/10.1371/journal.pone.0114825.g010

It is important to note that there is a significant difference compared to the previous study [21]: there, only 9 editions had been considered and the top positions were attributed to the world node WR which captured a significant fraction of the top persons. This indicated that 9 editions are not sufficient to cover the whole world. Now for 24 editions we see that the importance of the world node WR is much lower (it moves from K = 1 for 9 editions [21] to K = 4 and 3 in Fig. 10A and Fig. 10B). Thus our 24 editions cover the majority the world. Still it would be desirable to add a few additional editions (e.g. Ukraine, Baltic Republics, Serbia etc.) to fill certain gaps.

It is interesting to note that the ranking plane of cultures (K, K*) changes significantly in time. Indeed, if we take into account only persons born before the 19th century then the ranking is modified with EN going to 4th (Fig. 10C for PageRank figures) and 6th position (Fig. 10C for 2DRank figures) while the top positions are taken by IT, DE, FR and DE, IT, AR, respectively.

At the same time, we may also argue that for cultures it is important not only to be cited but also to be communicative with other cultures. To characterize communicative properties of nodes on the network of cultures shown in Fig. 8 we use again the concepts of PageRank, CheiRank and 2DRank for these networks as described in Methods and [21]. Thus, for the network of cultures of Fig. 8, the 2DRank index of cultures highlights their influence in a more balanced way taking into account their importance (incoming links) and communicative (outgoing links) properties in a balanced manner.

Thus we find for all centuries at the top positions Greek, Turkish and Arabic (for PageRank persons) and French, Russian and Arabic (for 2DRank persons). For historical figures before the 19th century, we find respectively Arabic, Turkish and Greek (for PageRank) and Arabic, Greek and Hebrew (for 2DRank). The high position of Turkish is due to its close links both with Greek culture in ancient times and with Arabic culture in more recent times. We see also that with time the positions of Greek in 2DRank improves due to a global improved ranking of Western cultures closely connected with Greece.