Signification of data files:
----------------------------

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Files in GWORK_* folders (for the cases of the 8 editions)
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1) G-matrix files for different variants of reduced Google matrix
with extension G*.txt


(i) Name format: GXX_NETWORK_GROUPNAME_dalpha_Nr.txt

with XX=pr, qr, R, rr, rrplusGqr for 5 G-matrix variants (see below in 
(iii) for explanations).

NETWORK = name of used basis network, e.g. mbnetwork_falseids.txt_1_double

GROUPNAME = name of group of nodes used, e.g. infl_20

dalpha=1-alpha (=1-0.85=0.15) with alpha beeing the ususal damping factor

Nr = matrix dimension 

(ii) Content format: 
There are 6 columns with each line representing one matrix element G(i,j)
The columns are: i, j, value of G(i,j), name of node i, the symbols "###" 
(to better separate visually both node names) and finally name of node j
all separated by tab-symbols ("\t" in C). Note that now everywhere node 
numbers (either groups or total network) start with 1 (and no longer with 0).


(iii) Signification of different G-matrix variants:

The names GR etc. correspond (mostly) to the definitions of the paper:
Eur. Phys. J. B (2016) 89: 269

in detail:
Grr is defined as the 11-Block of eq. (3) of the above paper and 
  corresponds to the direct links inside the group of nodes. 
GR is the full reduced Google matrix given by eqs. (8) and (16). 
Gpr is the main projector part given by eq. (17).
Gqr is the given by eq. (18).
(GI = Gpr + Gqr is the full "indirect" or Interaction contribution, also given 
  by the second term of second equation in (8), no longer given here since 
it is less important)
GrrplusGqr is the renormalized effective Google matrix obtained from the 
  sum of Grr and Gqr but only using non-diagonal terms of Gqr (the large 
  diagonal elements of Gqr are not taken into account here). Eventual negative 
  elements are made positive and afterwards the columns are sum normalized 
  such that GrrplusGqr will have the symmetries of a Google matrix.
  Note that Gqr may have negative elements.

(iv) the File Gweight_(....).dat gives the realive weights of the these 
G-matrices. Note that GrrplusGqr has allways weight 1 due to the 
renormalization which is purely artifical. 


2) Gmatrix files with extensions G*.mat:

(i) Name format: GXX_NETWORK_GROUPNAME_Nr.mat
similar as above.

(ii) Content format: 
1st line: => Nr^2
2nd line: => Nr
further lines all matrix elements G(i,j)
with i=1,...,Nr outer loop and j=1,...,Nr inner loop 
(i.e. Nr lines in file for first row of G, than Nr lines for second row etc.).

These files are typically used to create png files which are also present 
in the file collection


3) pagerank files: 

(i) Name fomat: pagerank_YYYY_GROUPNAME_NETWORK_ALPHA.dat
with GROUPNAME and NETWORK as above, ALPHA=0.15 = 1-damping factor 
with damping factor = 0.85).
YYYY corresponds to:
"full" => full PageRank vector of the NETWORK
"left" => left eigenvector of G_{ss} (see page 4, first column, last paragraph 
	of above paper for explanations).
"right" => right eigenvector of G_{ss}; note that the latter two were crucial 
	to compute GR etc. according to eqs. (12) to (18).
"small" => the PageRank vector of the reduced Google matrix GR
"GrrplusGqr" => the PageRank vector of the effective Google matrix GrrplusGqr
	as explained above, the latter two were directly computed by the 
	powermethod using the small reduced matrices
Now here all node indices and Kranks etc. are starting with 1 (and no longer 0)
These files are ordered in decreasing PageRank values and contain also 
node names 

(ii) Content format:
first line: "# size =    <size_of_vector>
further lines: four columns and the lines are ordered 
according to K-index of each vector (i.e. first line => largest value 
of vector etc.).
1st column = K-index (note in the file K-index starts with 1 and 
  no longer 0), 
2nd column = the value of the vector
3rd column = original node index (also starting with 1)
3th column = node name


4) subpagerank files

(i) Name format: similar as above but name starting with "subpagerank" 
instead of "pagerank"

(ii) Content format: These file give the different (pagerank and other) 
vectors but only in the small space of reduced nodes with 6 columns which 
ares explained in second lines of each each file:
# reduced index, value, normalized value, original index, K index, name
For the three cases full, left and right the normalization changes from big 
to small network. For left and right the shown vectors are not \psi_L/R 
(which are actually "0" on reduced nodes !) but the related vectors 
in small space given by 
a=G_{rs}\psi_R and b=G_{sr}^T\psi_L such that G_{pr}=ab^T 
according to eq. (17) of above paper. Here G_{rs} and G_{sr} are the 
12 and 21 blocks in (3).
For small and GrrplusGqr "small" and "big" space are the same (i.e. only 
"small" space).
These files are NOT PageRank ordered but there are in original Group-node 
order.


5) lambda.dat

a small file containing essentially 
the leading eigenvalue lambda_c of G_{ss} (typically 
very close to unity) for the left and right eigenvectors \psi_L,R.

6) two files 
GROUPNAME.txt_names => names of used subgroup 
GROUPNAME.txt_nodes => node indicies of used subgroup

----------------------
Files in 2Drank folder
----------------------


6) 2Drank files: png files for 2Drank 

2Drank_NETWORK_GROUPNAME_100_2Drank.png
=> log-log 2Drank density with red/white crosses for group nodes

2Drank_NETWORK_GROUPNAME_100_2Dranksat.png
=> similar as above but with some saturation value for the color-codes to 
increase "smaller" values

similar png files but with *_200_* or *_400_* in the file name (instead of *_100_*) 
correspond to the same figures but with higher resoution (either 200x200 or 400x400 
cells in the ln(K_M)-ln(K_M^*) plane.



2Drank_NETWORK_GROUPNAME_Nr_2Dranklocal.png
=> 2Drank in small space of 40x40 local K-K^* plane (red/white boxes in blue back ground)

2Drank_NETWORK_GROUPNAME_Nr.gdat
=> data file file with 6 columns for K, K*, original index, K_M, K_M^* and node name 
these are the raw files used for tables 2 and 3. The NETWORK name is of type xxwiki where 
xx is the country/edition code (e.g. en, ar, de etc.). Here name = english versions of article 
titles (even for other editions)

Ktop_*, Kstartop_* files top 10000 nodes for PageRank or CheiRank (16 files, 
2 files per edition), with 6 columns in the header of the files
Here the 6th column corresponds to the article title in the original language edition, eventually 
with special characters for AR, RU and ZH.

