select/read WAc network Network/Create Vector/Centrality/Degree/Output Network/2-Mode Network/Partition into 2 Modes Operations/Vector+Partition/Extract Subvector [1] = V1 Vector/Create Constant Vector [5695,1] = V2 select V1 as Second vector Vectors/Max(First,Second) Vector/Transform/Invert Operations/Network+Vector/Vector#Network/Output = N select V1 as First vector select V2 as Second vector Vectors/Subtract (First-Second) Vectors/Max(First,Second) Vector/Transform/Invert select/read WAc network Operations/Network+Vector/Vector#Network/Output = N' select network N Network/2-Mode/Transpose 2-Mode select N' as Second network Networks/Multiply Networks [Yes] Network/Create New Network/Transform/Remove/Loops Network/Create New Network/Transform/Arcs -> Edges/Biderected Only/Sum File/Network/Change Label [Ct'(WAc)]
Ct'(WAc) n = 13376) m = 4081577 AveDegree = 610.28364234
pS cores
Rank Vertex Value Id
--------------------------------------------------------
1 218 15.8333 BORGATTI_S
2 192 15.8333 EVERETT_M
3 444 7.6667 FERLIGOJ_A
4 440 7.6667 BATAGELJ_V
5 1603 7.6667 MRVAR_A
6 164 7.6667 DOREIAN_P
7 3379 6.4333 STEINLEY_D
8 3378 6.4333 BRUSCO_M
9 989 6.3333 YANG_J
10 3790 6.3333 LESKOVEC_J
11 3910 6.0000 LANCICHI_A
12 3034 6.0000 FORTUNAT_S
13 7240 5.3333 QIAN_X
14 190 5.3333 WANG_Y
15 8053 5.0000 HERO_A
16 6838 5.0000 AMELIO_A
17 5458 5.0000 BAJEC_M
18 5328 5.0000 SUBELJ_L
19 308 5.0000 CHEN_P
20 4558 5.0000 PIZZUTI_C
21 2779 5.0000 REICHARD_J
22 2262 5.0000 BORNHOLD_S
23 3911 4.8333 SALES-PA_M
24 2625 4.8333 GUIMERA_R
25 3866 4.5833 NUSSINOV_Z
26 4356 4.5833 RONHOVDE_P
27 3648 4.3333 ROSVALL_M
28 4446 4.3333 BERGSTRO_C
29 608 4.3333 WILSON_R
30 2346 4.3333 HANCOCK_E
read network CiteC transform CiteC to bipartite read network WAc transpose WAc = AWc select AWc as second multiply networks select WAc as second multiply networks one-mode
C:\Users\batagelj\work\Python\WoS\BM
I computed the derived normalized network of citations among authors t(n(WAc)) * n(CiteC) * n(WAc). Every work has 1 point. They are distributed on arcs of the derived network. We first remove loops.
Let's first look at the largest weighted input degrees - the most cited authors:
Rank Vertex Value Id Rank Vertex Value Id
--------------------------------- ---------------------------------
1 1072 329.8886 NEWMAN_M 51 532 13.6097 DIETERIC_J
2 3034 155.4974 FORTUNAT_S 52 1957 13.3569 MEADE_B
3 2397 80.8228 GIRVAN_M 53 3189 13.2003 BLEI_D
4 1740 51.6716 BARABASI_A 54 562 13.1853 MACQUEEN_J
5 88 45.1972 BURT_R 55 2779 12.8176 REICHARD_J
6 2263 42.5944 ALBERT_R 56 626 12.7497 SAVAGE_J
7 2631 39.6466 ZACHARY_W 57 444 12.5424 FERLIGOJ_A
8 3910 38.8163 LANCICHI_A 58 538 12.5064 LANGER_J
9 2991 38.1660 CLAUSET_A 59 725 12.2316 KNOPOFF_L
10 3185 31.8938 SCHAEFFE_S 60 4332 12.2182 GREGORY_S
11 826 31.7021 STROGATZ_S 61 42 12.0322 ARABIE_P
12 89 30.9933 FREEMAN_L 62 275 11.9246 BURRIDGE_R
13 145 29.1247 WASSERMA_S 63 2389 11.6503 NG_A
14 4554 29.0661 MOORE_C 64 3749 11.6379 JORDAN_M
15 168 26.1896 FAUST_K 65 2262 11.4995 BORNHOLD_S
16 2146 24.8884 WATTS_D 66 49 11.4380 HARARY_F
17 38 24.7421 WHITE_H 67 676 11.2859 SNIJDERS_T
18 480 24.5679 NEWMARK_N 68 3030 11.2303 DANON_L
19 3208 23.8077 BLONDEL_V 69 249 11.0762 JOHNSON_D
20 440 23.0214 BATAGELJ_V 70 55 11.0430 LORRAIN_F
21 3872 22.6844 LAMBIOTT_R 71 578 10.7718 TANG_C
22 2339 22.5521 VANDONGE_S 72 1201 10.6267 NOWICKI_K
23 824 20.9136 ARENAS_A 73 2334 10.4957 BRANDES_U
24 3790 19.8478 LESKOVEC_J 74 51 10.4213 HOLLAND_P
25 241 19.8113 SHI_J 75 3615 10.2568 KUMARA_S
26 11535 19.7797 MALIK_J 76 3614 10.2302 RAGHAVAN_U
27 3648 19.7317 ROSVALL_M 77 2623 10.2084 FIEDLER_M
28 4203 19.2631 VONLUXBU_U 78 134 10.1968 GAREY_M
29 4446 19.1634 BERGSTRO_C 79 3031 10.1012 DIAZ-GUI_A
30 2998 19.1422 BARTHELE_M 80 143 10.0321 LEINHARD_S
31 3979 18.6968 LEFEBVRE_E 81 137 9.9847 SCOTT_J
32 3886 18.6552 GUILLAUM_J 82 274 9.8897 BAK_P
33 164 18.6261 DOREIAN_P 83 272 9.4798 SCHOLZ_C
34 2775 18.3258 KLEINBER_J 84 3032 9.4052 BAGROW_J
35 40 18.1618 BREIGER_R 85 2104 9.3647 RAND_W
36 844 17.4888 VICSEK_T 86 2627 9.2402 LUSSEAU_D
37 218 17.4204 BORGATTI_S 87 941 9.2348 GOLDBERG_D
38 3036 16.9268 PALLA_G 88 1750 9.1468 KERTESZ_J
39 919 16.8126 OKADA_Y 89 1984 9.0590 RENYI_A
40 39 16.7620 BOORMAN_S 90 560 9.0590 ERDOS_P
41 2336 15.8376 CHUNG_F 91 3035 8.9879 LATAPY_M
42 2625 15.8216 GUIMERA_R 92 989 8.8951 YANG_J
43 2629 15.7187 RADICCHI_F 93 83 8.8018 WARD_J
44 276 14.9995 CARLSON_J 94 4558 8.7767 PIZZUTI_C
45 192 14.9914 EVERETT_M 95 2266 8.7543 JEONG_H
46 2990 14.6212 DUCH_J 96 252 8.5407 LIN_S
47 2829 14.5231 AMARAL_L 97 1056 8.5407 KERNIGHA_B
48 47 14.4554 GRANOVET_M 98 429 8.5187 CHRISTEN_K
49 3412 13.7216 DERENYI_I 99 6786 8.4475 OLTVAI_Z
50 3259 13.7216 FARKAS_I 100 57 8.3670 MILGRAM_S
--------------------------------- ---------------------------------
http://vladowiki.fmf.uni-lj.si/doku.php?id=pro:bm2 https://github.com/bavla/biblio/tree/master/Pajek/macro https://raw.githubusercontent.com/bavla/biblio/master/Pajek/macro/norm1.mcr https://raw.githubusercontent.com/bavla/biblio/master/Pajek/macro/norm2.mcr C:\Programi\Pajek\macro\biblio
read CiteC play norm1 [5695] convert to 2-mode read WAc play norm2 [5695] transpose 2-mode select n(CiteC) as Second multiply select n(WAc) as Second multiply [yes] remove loops weighted indegees
10. Deleted loops in N9 (13376) ================================================== Lowest value of line: 0.00010254 Highest value of line: 2.51388889 > 1/2.52 [1] 0.3968254
nACiA weights are similarities, s ∈ [ ∞, 0 ]. To convert them to distances d we can use different transformations. For example
We selected the second option.
Network/Create hierarchy/Clustering RC/Run [maximum, leader]
C:\Users\batagelj\work\Python\WoS\BM\results\Acite
> wdir <- "C:/Users/batagelj/work/Python/WoS/BM/results/Acite"
> setwd(wdir)
> source("https://raw.githubusercontent.com/bavla/biblio/master/Pajek/R/readCluRC.R")
> RM <- readCluRC("MaxLeader.clu")
> n <- RM$n; nm <- n-1; np <- n+1
> n
[1] 13376
> HM <- read.csv("MaxLeaderHeig.vec",header=FALSE,skip=np)[[1]]
> RM$height <- HM
> RM$method <- "Maximum/Tolerant"
> RM$dist.method <- "nACiA"
> class(RM) <- "hclust"
> RM$call <- "Pajek.data"
> size <- read.csv("MaxLeaderSize.vec",header=FALSE,skip=np)[[1]]
> RM$labels <- read.csv("nACIA.net",header=FALSE,skip=1,sep="",colClasses="character",nrows=n)$V2
> length(size)
[1] 13375
We determine the partition of units into clusters of size at most 50.
select size vector as First Networ/Create hierarchy/Make partition/with threshold determined by vector [50] save partition as cut50.clu
Since Pajek hasn't an option to select among them only those with the size at least 20 we do this in R:
> clu <- read.csv("cut50.clu",header=FALSE,skip=1)[[1]]
> S <- table(clu)
> length(S)
[1] 258
> table(S)
S
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
45 39 25 13 20 12 6 8 5 4 5 1 3 4 4 1
18 19 20 21 22 23 24 25 26 27 29 31 32 33 35 38
3 1 2 1 1 3 1 2 3 1 3 2 1 1 2 2
39 40 44 45 46 47 48 50 9961
1 1 1 1 2 1 1 25 1
> P <- integer(n)
> for(i in 1:n) if(S[clu[i]+1]>19) P[i] <- clu[i] else P[i] <- 0
> table(P)
P
0 1 3 4 7 8 9 10 11 12 13 14 15
11080 50 29 50 31 50 35 47 50 46 50 50 50
17 20 21 23 24 26 27 29 31 32 35 36 39
50 50 50 26 50 50 23 50 50 46 50 50 50
40 41 43 44 45 49 53 56 58 60 61 62 67
26 29 25 33 45 35 25 38 39 50 50 23 44
68 69 70 75 77 79 81 87 92 93 95 96 106
38 48 29 50 50 26 50 23 50 31 20 50 27
127 134 139 145 161 164 226
20 50 24 21 40 32 22
> T <- table(P); length(T)
[1] 59
> out <- file("cut50-20.clu","w"); cat("*vertices 13376",P,sep="\n",file=out); close(out)
The reduced partition is saved on the file cut50-20.clu and read into Pajek. It still contains 58 clusters. We extracted the corresponding subnetworks of citations among authors for visual inspection, cut50-20.net. Most of them are (double) star like formed around prominent scientists:
Albert R + Barabasi A,
Bergstro C + Rosvall M,
Bezdek J,
Blei D,
Blondel V,
Bonacich P + Kleinberg J,
Breiger R,
Burt R + Doreian P,
Chung F + Von Luxbu U,
Clauset A,
Dietric J + Maede B,
Fortunato S,
Freeman L,
Ghosh J,
Girvan M,
Goldberg D,
Jaccard P,
Jain A,
Johnson D,
Jordan M,
Kaufman L,
Knuth D,
Leskovec J,
Mac Queen J,
Newman M,
Newmark N,
Okada Y,
Palla G + Viscek T,
Prescott W,
Schaeffe S,
Scott J,
Sporus O,
Stein C,
Strehl A,
Strogatz S,
Van Donge S,
and some “cliques” of co-authors with attachments. We visually selected 12 clusters (Adamic L,
Batagelj V + Ferligoj A,
Bollobas B,
Burt R + Doreian P,
Faust K + Watts D,
Fiedler M + Harary F,
Granovet M,
Mizruchi M,
Murtagh F,
Nowicki K + Wasserman S,
Robins G,
Ward J,
White H + Zachary W) with more interesting network structure for detailed inspection, cut50select.net. The separate subnetworks are saved as cut50_xy.net.
Most of the subnetworks of clusters for the Leader strategy have almost acyclic structure. This has to be considered also in their visualization. We identified some interesting clusters: {21,8,15,13,1,20,10,39,70,43,23,14}. Because of limited space we present here only subnetworks induced by four among the selected clusters.
C:\Users\batagelj\work\Python\WoS\BM\results\Acite