Relations of society concepts and religions from Wikipedia networks

TL;DR

This study uses the reduced Google matrix REGOMAX on eight Wikipedia editions to uncover how 23 society concepts and 17 religions relate within and across cultures. By constructing and analyzing a 40-node subset across editions, it reveals strong intra-block (within society or within religion) interactions and comparatively weaker inter-block transitions, while PageRank tends to favor religion entries. The authors extract both direct and indirect links, producing pole-based friend and follower diagrams that highlight cultural differences in how concepts and religions are interconnected. The approach provides a quantitative, cross-cultural snapshot of how society concepts and religions are positioned and connected in large-scale knowledge networks, with potential applications to other topic subsets and multilingual contexts.

Abstract

We analyze the Google matrix of directed networks of Wikipedia articles related to 8 recent Wikipedia language editions representing different cultures (English, Arabic, German, Spanish, French, Italian, Russian, Chinese). Using the reduced Google matrix algorithm we determine relations and interactions of 23 society concepts and 17 religions represented by their respective articles for each of the 8 editions. The effective Markov transitions are found to be more intense inside the two blocks of society concepts and religions while transitions between the blocks are significantly reduced. We establish 5 poles of influence for society concepts (Law, Society, Communism, Liberalism, Capitalism) as well as 5 poles for religions (Christianity, Islam, Buddhism, Hinduism, Chinese folk religion) and determine how they affect other entries. We compute inter edition correlations for different key quantities providing a quantitative analysis of the differences or the proximity of views of the 8 cultures with respect to the selected society concepts and religions.

Figures (16)

• Figure S1: Density of nodes $W(K_{\rm M},K_{\rm M}^*)$ on PageRank-CheiRank plane $(K_{\rm M},K_{\rm M}^*)$ averaged over $100\times100$ logarithmically equidistant grids for $0 \leq \ln K_{\rm M}, \ln K_{\rm M}^* \leq \ln N$ ($1 \leq K_{\rm M},K_{\rm M}^* \leq N$) for the four Wikipedia editions EN (top-left), AR (top-right), DE (bottom-left) and ES (bottom-right); the values of node number $N$ for each edition are given in Table \ref{['table1']}; the density is averaged over all nodes inside each cell of the grid, the normalization condition is $\sum_{K_{\rm M},K_{\rm M}^*}W(K_{\rm M},K_{\rm M}^*)=1$. Color varies from blue at zero value to red at maximal density value. The numbers at the color bar correspond to $W(K_{\rm M},K_{\rm M}^*)/W_{\rm cut}$ where $W_{\rm cut}=\max W(K_{\rm M},K_{\rm M}^*)/16$ and values of $W(K_{\rm M},K_{\rm M}^*)>W_{\rm cut}$ have been saturated to $W_{\rm cut}$. The non-linear color scale (corresponding to $x^8$ if $x\in[0,1]$ represents the linear scale of the visible color bar) and the saturation at $W_{\rm max}/16$ have been chosen in order to increase the visibility of low density values. The $x$-axis corresponds to $\ln K_{\rm M}$ and the $y$-axis to $\ln K_{\rm M}^*$ with $K_{\rm M}$ ($K_{\rm M}^*$) being the global PageRank (CheiRank) index for the Wikipedia network of the corresponding edition. The red (white) crosses mark the positions of the 23 society nodes with $K_g\le 23$ (17 religion nodes with $K_g\ge 24$) of Tables \ref{['table2']} and \ref{['table3']}.
• Figure S2: As Figure \ref{['fig1']} but for the four Wikipedia editions FR (top-left), IT (top-right), RU (bottom-left) and ZH (bottom-right).
• Figure S3: Color density plots of the matrix components $G_{\rm R}, {G_{\rm pr}}, {G_{\rm rr}}, {G_{\rm rr}}+{G_{\rm qr}^{\rm (nd)}}$ for the group of Table \ref{['table2']} and Wikipedia EN edition; the $y$-axis corresponds to the first (row) index (increasing values of $K_g$ from top to down) and the $x$-axis corresponds to the second (column) index of the matrix (increasing values of $K_g$ from left to right). The outside tics indicate multiples of 10 of $K_g$. The red arrows indicate the separation between society nodes ($K_g\le 23$) and religion nodes ($K_g\ge 24$) in both axis. The numbers in the color bar correspond to $g/g_{\rm max}$ with $g$ being the value of the matrix element and $g_{\rm max}$ being the maximum value. For ${G_{\rm qr}^{\rm (nd)}}$ there are some small negative matrix elements corresponding to values $g/g_{\rm max}>-0.035$ ($g/g_{\rm max}>-0.038$ for other editions shown in other figures below) which are shown with a color very close to blue for zero values.
• Figure S4: Color density plots of the matrix components $G_{\rm R}, {G_{\rm rr}}+{G_{\rm qr}^{\rm (nd)}}$ for the edition specific group/network (see also Table \ref{['table3']}) of AR and DE. The technical details for the color plot presentation are exactly as in Figure \ref{['fig3']}.
• Figure S5: Color density plots of the matrix components $G_{\rm R}, {G_{\rm rr}}+{G_{\rm qr}^{\rm (nd)}}$ for the edition specific group/network (see also Table \ref{['table3']}) of ES and FR. The technical details for the color plot presentation are exactly as in Figure \ref{['fig3']}.