Network Analysis of Code Similarity
Kellen Funk and Lincoln Mullen
November 21, 2014
There are the codes that we currently have:
names(codes)## [1] "AK1900" "AL1852" "AR1868" "AR1874"
## [5] "AZ1865" "AZ1887" "CA1850" "CA1851"
## [9] "CA1858" "CA1868" "CA1868extended" "CA1872"
## [13] "CO1877" "CT1854" "CT1879" "CT1879extended"
## [17] "DE1852" "FL1870" "GA1851" "GA1860"
## [21] "HI1859" "HI1897" "IA1839" "IA1851"
## [25] "ID1864" "ID1881" "IL1933" "IN1843"
## [29] "IN1852" "KS1859" "KY1851" "LA1825"
## [33] "MA1836" "MA1858" "MD1855" "MD1859"
## [37] "ME1840" "MI1853" "MN1851" "MO1835"
## [41] "MO1849" "MO1856" "MT1865" "NC1868"
## [45] "NE1866" "NM1897" "NV1861" "NV1869"
## [49] "NY1848" "NY1849" "NY1850" "OH1853"
## [53] "OH1853extended" "OK1891" "OR1862" "SC1870"
## [57] "UT1853" "UT1870" "WA1855" "WI1856"
## [61] "WY1870"Create the comparison matrix:
cf <- outer_for_lists(codes, codes, compare_codes_by_shared_ngrams)Remove obviously incorrect values:
cf2 <- cf
diag(cf2) <- NA # remove codes compared to themselves
cf2 <- rm_anachronism(cf2) # remove anachronistic comparisons
significance_threshold <- 0.03
cf2[cf2 < significance_threshold] <- NA
cf2[is.na(cf2)] <- 0Now we can create a graph object from the comparison matrix, which we will treat as an adjacency matrix.
g <- graph.adjacency(cf2, mode = "directed", weighted = TRUE, diag = FALSE)
set.seed(4821)
l <- layout.fruchterman.reingold(g, weights = E(g)$weight)
par(mar=c(0,0,1,0))
plot(g, edge.width = E(g)$weight * 10, layout = l,
edge.arrow.size= 0.15, vertex.size = 5)
title("Codes of Civil Procedure")
Community detection
g %>%
walktrap.community() %>%
plot(., g, vertex.label = NA, layout = l, vertex.size = 3)
Get just the component graphs
sub <- decompose.graph(g, mode = "weak", min.vertices = 3)[[1]]
l2 <- layout.fruchterman.reingold(sub, weights = E(sub)$weight)
par(mar=c(0,0,1,0))
plot(sub, edge.width = E(sub)$weight * 10, layout = l2,
edge.arrow.size= 0.15, vertex.size = 5)
title("Largest family of codes")
Neighborhood of NY 1850
ny <- which(V(g)$name == "NY1850")
neighbors(g, ny)## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 15 18 21 22 24 25 26 27 29 30
## [24] 31 38 39 42 43 44 45 46 47 48 52 53 54 55 56 57 58 59 60 61graph.neighborhood(g, order = 1, nodes = ny)[[1]] %>%
plot_graph()
Get all the influences for people who need words.
influences <- colnames(cf2) %>%
lapply(., function(name) { get_influences(cf2, name, 10) })
names(influences) <- colnames(cf2)
print(influences)## $AK1900
## OR1862 NY1850 CA1872 MN1851 CA1868extended
## 0.47317067 0.17184229 0.14053933 0.10764131 0.10579703
## NV1861 ID1881 CA1851 AZ1865 CA1858
## 0.10128601 0.09961619 0.09470641 0.09302413 0.09301166
##
## $AL1852
## IN1843 NY1850 AK1900 AL1852 AR1868 AR1874
## 0.03596337 0.03424898 0.00000000 0.00000000 0.00000000 0.00000000
## AZ1865 AZ1887 CA1850 CA1851
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $AR1868
## KY1851 OH1853extended OH1853 KS1859 NE1866
## 0.40421551 0.14304845 0.13616935 0.13211528 0.12936364
## IN1852 NY1850 OR1862 CA1868extended WA1855
## 0.07921046 0.07550493 0.06479188 0.06403977 0.05310660
##
## $AR1874
## AR1868 KY1851 OH1853extended KS1859 OH1853
## 0.6509167 0.5406496 0.2442116 0.2409115 0.2386590
## NE1866 WY1870 IN1852 CA1872 NY1850
## 0.2231535 0.2117339 0.1529073 0.1297014 0.1166579
##
## $AZ1865
## CA1851 CA1858 NV1861 ID1864 MT1865 NY1850 OR1862
## 0.7680503 0.7251191 0.6902161 0.5627385 0.4818773 0.3729568 0.2616672
## MN1851 WA1855 NY1849
## 0.2149456 0.1915454 0.1623806
##
## $AZ1887
## CA1872 CA1868extended NV1861 AZ1865 NV1869
## 0.50307695 0.07596682 0.06427645 0.06223887 0.06153909
## CA1851 ID1881 CA1858 OR1862 ID1864
## 0.06110688 0.06092165 0.05779324 0.05769033 0.05653776
##
## $CA1850
## NY1849 NY1850 NY1848 MO1849 IN1843 MA1836
## 0.42283632 0.33325235 0.28241725 0.13185545 0.05441846 0.04640146
## ME1840 AK1900 AL1852 AR1868
## 0.03054965 0.00000000 0.00000000 0.00000000
##
## $CA1851
## NY1850 MN1851 NY1849 CA1850 NY1848 KY1851
## 0.38662783 0.21691415 0.17449874 0.13939094 0.11497152 0.06452032
## MO1849 IA1851 IN1843 AK1900
## 0.05606845 0.04192131 0.04017892 0.00000000
##
## $CA1858
## CA1851 NY1850 MN1851 WA1855 NY1849
## 0.60233594 0.29615945 0.16031365 0.14413860 0.12482296
## CA1850 WI1856 OH1853extended NY1848 OH1853
## 0.10349570 0.09811770 0.09378656 0.08364637 0.06933925
##
## $CA1868
## CA1868extended CA1858 NV1861 CA1851 AZ1865
## 0.9667502 0.4513866 0.4124454 0.4076054 0.3810087
## ID1864 MT1865 NY1850 OR1862 MN1851
## 0.3396711 0.2884327 0.2052531 0.1436882 0.1161141
##
## $CA1868extended
## CA1868 CA1858 NV1861 CA1851 AZ1865 ID1864
## 0.25826233 0.13798840 0.12234609 0.12158377 0.11385528 0.10123698
## MT1865 NY1850 OR1862 MN1851
## 0.08624749 0.06474669 0.04628674 0.03673036
##
## $CA1872
## CA1868extended NY1850 CA1868 CA1858 NV1861
## 0.2725151 0.2482254 0.2370803 0.2148091 0.2140342
## CA1851 NV1869 AZ1865 ID1864 OR1862
## 0.2083612 0.2059313 0.1959820 0.1733474 0.1704965
##
## $CO1877
## CA1868extended NV1861 CA1868 NV1869 CA1858
## 0.4722423 0.4115375 0.4075247 0.3874909 0.3768103
## CA1851 CA1872 AZ1865 ID1864 MT1865
## 0.3757543 0.3665218 0.3599747 0.3368030 0.3282344
##
## $CT1854
## IN1843 MA1836 ME1840 AK1900 AL1852 AR1868
## 0.04116095 0.03619432 0.03026540 0.00000000 0.00000000 0.00000000
## AR1874 AZ1865 AZ1887 CA1850
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $CT1879
## CT1879extended OH1853extended NC1868 CA1868extended SC1870
## 0.85120696 0.07004353 0.06687772 0.06529482 0.06489909
## NE1866 OR1862 OH1853 NY1850 CA1872
## 0.06410764 0.06252473 0.06173328 0.06133755 0.05935892
##
## $CT1879extended
## CT1879 AK1900 AL1852 AR1868 AR1874 AZ1865
## 0.04168766 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## AZ1887 CA1850 CA1851 CA1858
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $DE1852
## MA1836 IN1843 ME1840 AK1900 AL1852 AR1868
## 0.06000711 0.05101315 0.03757554 0.00000000 0.00000000 0.00000000
## AR1874 AZ1865 AZ1887 CA1850
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $FL1870
## NC1868 SC1870 NY1849 NY1850 WI1856
## 0.5392728 0.5354019 0.4254320 0.3350910 0.3346643
## NY1848 CA1868extended OR1862 MN1851 CA1851
## 0.2368557 0.2277424 0.2201225 0.2166174 0.2118931
##
## $GA1851
## IN1843 AK1900 AL1852 AR1868 AR1874 AZ1865
## 0.03394086 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## AZ1887 CA1850 CA1851 CA1858
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $GA1860
## GA1851 IN1843 AK1900 AL1852 AR1868 AR1874
## 0.12318738 0.03720733 0.00000000 0.00000000 0.00000000 0.00000000
## AZ1865 AZ1887 CA1850 CA1851
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $HI1859
## CA1851 NY1850 CA1858 WA1855 MN1851
## 0.14935491 0.12705008 0.11677236 0.08681391 0.08528318
## OH1853extended NY1849 MA1858 OH1853 KS1859
## 0.08222174 0.07566149 0.07544282 0.07325607 0.07063197
##
## $HI1897
## HI1859 MA1836 MA1858 ME1840 CA1868extended
## 0.16704999 0.09500117 0.08824220 0.08326684 0.06646327
## CA1872 NM1897 IN1843 NY1850 MN1851
## 0.06608777 0.05763905 0.05665337 0.05477587 0.05163107
##
## $IA1839
## MA1836 MO1835 AK1900 AL1852 AR1868 AR1874
## 0.03984226 0.03209138 0.00000000 0.00000000 0.00000000 0.00000000
## AZ1865 AZ1887 CA1850 CA1851
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $IA1851
## NY1850 MN1851 CA1851 IN1843 MA1836 AK1900
## 0.07884678 0.05441193 0.04401005 0.03958720 0.03079611 0.00000000
## AL1852 AR1868 AR1874 AZ1865
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $ID1864
## NV1861 CA1858 CA1851 NY1850 OR1862 MN1851
## 0.57764762 0.45674508 0.41505521 0.22918867 0.17373020 0.13975996
## WA1855 NY1849 CA1850 WI1856
## 0.13630341 0.10235238 0.08430149 0.08101776
##
## $ID1881
## CA1872 CA1868extended CA1868 NV1861 NV1869
## 0.5952388 0.3113029 0.2740861 0.2634035 0.2523045
## CA1858 CA1851 NY1850 AZ1865 ID1864
## 0.2483847 0.2419952 0.2390231 0.2358355 0.2154036
##
## $IL1933
## CA1868extended OK1891 IN1843 NE1866 NM1897
## 0.04389871 0.03770624 0.03660347 0.03651864 0.03639140
## CA1872 IN1852 OR1862 OH1853extended NY1850
## 0.03554311 0.03545829 0.03410103 0.03405862 0.03282860
##
## $IN1843
## MA1836 ME1840 AK1900 AL1852 AR1868 AR1874
## 0.04868312 0.03472535 0.00000000 0.00000000 0.00000000 0.00000000
## AZ1865 AZ1887 CA1850 CA1851
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $IN1852
## IN1843 NY1850 KY1851 MN1851 CA1851 NY1849
## 0.10470063 0.07156940 0.05862820 0.05075676 0.04448628 0.04298907
## IA1851 CA1850 MA1836 AK1900
## 0.03407996 0.03406514 0.03227145 0.00000000
##
## $KS1859
## OH1853extended OH1853 KY1851 NY1850 IN1852
## 0.75013435 0.73437986 0.21111583 0.14444916 0.11056428
## MN1851 CA1851 CA1858 NY1849 WA1855
## 0.10544477 0.10323858 0.09919389 0.09548862 0.09297129
##
## $KY1851
## NY1850 CA1851 MN1851 NY1849 CA1850 NY1848
## 0.11476072 0.07161000 0.06875253 0.06315303 0.04976043 0.04748023
## MO1849 IN1843 AK1900 AL1852
## 0.04384345 0.03769555 0.00000000 0.00000000
##
## $LA1825
## AK1900 AL1852 AR1868 AR1874 AZ1865 AZ1887 CA1850 CA1851 CA1858 CA1868
## 0 0 0 0 0 0 0 0 0 0
##
## $MA1836
## AK1900 AL1852 AR1868 AR1874 AZ1865 AZ1887 CA1850 CA1851 CA1858 CA1868
## 0 0 0 0 0 0 0 0 0 0
##
## $MA1858
## MA1836 ME1840 IN1843 MN1851 AK1900 AL1852
## 0.39223113 0.10526415 0.04457344 0.03334249 0.00000000 0.00000000
## AR1868 AR1874 AZ1865 AZ1887
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $MD1855
## IN1843 AK1900 AL1852 AR1868 AR1874 AZ1865
## 0.03270327 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## AZ1887 CA1850 CA1851 CA1858
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $MD1859
## MD1855 IN1843 MA1858 GA1851 IN1852
## 0.22191174 0.05270765 0.04904606 0.03603777 0.03497784
## OH1853extended MA1836 AK1900 AL1852 AR1868
## 0.03401426 0.03218347 0.00000000 0.00000000 0.00000000
##
## $ME1840
## MA1836 AK1900 AL1852 AR1868 AR1874 AZ1865 AZ1887
## 0.2306124 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## CA1850 CA1851 CA1858
## 0.0000000 0.0000000 0.0000000
##
## $MI1853
## IN1843 NY1850 AK1900 AL1852 AR1868 AR1874
## 0.04013756 0.03247359 0.00000000 0.00000000 0.00000000 0.00000000
## AZ1865 AZ1887 CA1850 CA1851
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $MN1851
## NY1850 CA1851 NY1849 NY1848 MA1836 CA1850
## 0.28165516 0.12330914 0.10327750 0.06327336 0.05735996 0.05696081
## IN1843 KY1851 AK1900 AL1852
## 0.04576970 0.03521429 0.00000000 0.00000000
##
## $MO1835
## AK1900 AL1852 AR1868 AR1874 AZ1865 AZ1887 CA1850 CA1851 CA1858 CA1868
## 0 0 0 0 0 0 0 0 0 0
##
## $MO1849
## NY1849 NY1848 MO1835 IN1843 MA1836 AK1900
## 0.21138484 0.20460495 0.04430422 0.04296167 0.03047593 0.00000000
## AL1852 AR1868 AR1874 AZ1865
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $MO1856
## MO1835 MO1849 NY1849 NY1850 OH1853extended
## 0.24265151 0.20002795 0.09782457 0.09563516 0.08888061
## NY1848 WI1856 CA1850 OH1853 CA1851
## 0.08510737 0.08296455 0.08287138 0.08282480 0.08058881
##
## $MT1865
## NV1861 ID1864 CA1858 AZ1865 CA1851
## 0.5609569 0.5272380 0.4581249 0.4260117 0.4250809
## NY1850 OR1862 MN1851 WA1855 OH1853extended
## 0.2528099 0.1888628 0.1497219 0.1487678 0.1066018
##
## $NC1868
## NY1849 NY1850 WI1856 OR1862 CA1868extended
## 0.2703077 0.2263339 0.2149364 0.1594392 0.1587885
## CA1851 MN1851 NV1861 NY1848 AZ1865
## 0.1484195 0.1471601 0.1466143 0.1440955 0.1404433
##
## $NE1866
## OH1853extended OH1853 KS1859 KY1851 NY1850
## 0.48819028 0.36489621 0.35896123 0.10747748 0.10042780
## IA1851 NV1861 MN1851 OR1862 MT1865
## 0.08551502 0.07251529 0.06923146 0.06903564 0.06883982
##
## $NM1897
## MO1856 OR1862 NY1850 OH1853extended NE1866
## 0.07189750 0.06832267 0.06685265 0.06556638 0.06501512
## CA1872 MN1851 WA1855 NC1868 CA1868extended
## 0.06463091 0.06444715 0.06249269 0.06159063 0.06053823
##
## $NV1861
## CA1858 CA1851 NY1850 MN1851 WA1855
## 0.60394499 0.55435256 0.29962873 0.17727584 0.16576442
## NY1849 CA1850 WI1856 OH1853extended NY1848
## 0.13000643 0.10634061 0.10372721 0.09827225 0.08665713
##
## $NV1869
## CA1868extended NV1861 CA1858 CA1868 CA1851
## 0.6799773 0.6389106 0.6312741 0.6125730 0.5964016
## AZ1865 ID1864 MT1865 NY1850 OR1862
## 0.5790482 0.5137480 0.4408823 0.3207320 0.2312694
##
## $NY1848
## IN1843 MA1836 AK1900 AL1852 AR1868 AR1874
## 0.03840209 0.03226741 0.00000000 0.00000000 0.00000000 0.00000000
## AZ1865 AZ1887 CA1850 CA1851
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $NY1849
## NY1848 MO1849 IN1843 MA1836 AK1900 AL1852
## 0.36254698 0.10116619 0.04137887 0.03273685 0.00000000 0.00000000
## AR1868 AR1874 AZ1865 AZ1887
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $NY1850
## NY1849 NY1848 CA1850 AK1900 AL1852 AR1868
## 0.11937376 0.07547865 0.05319180 0.00000000 0.00000000 0.00000000
## AR1874 AZ1865 AZ1887 CA1851
## 0.00000000 0.00000000 0.00000000 0.00000000
##
## $OH1853
## OH1853extended KY1851 NY1850 IN1852 MN1851
## 1.00000000 0.22415233 0.14951171 0.10880650 0.10327543
## CA1851 NY1849 CA1850 NY1848 IN1843
## 0.10062513 0.09757151 0.07737735 0.06452914 0.05712557
##
## $OH1853extended
## OH1853 KY1851 NY1850 CA1851 IN1852 MN1851
## 0.65349498 0.15056759 0.13407632 0.08588264 0.08051733 0.07509554
## IN1843 NY1849 CA1850 NY1848
## 0.07470020 0.06897720 0.05312600 0.04508745
##
## $OK1891
## IN1852 CA1872 WA1855 IN1843 ID1881
## 0.38093350 0.12836018 0.12185048 0.10831888 0.10357703
## CA1868extended NE1866 OH1853extended NV1861 NY1850
## 0.09900041 0.09234201 0.08945064 0.08821148 0.08715407
##
## $OR1862
## NY1850 MN1851 CA1851 NV1861 CA1858
## 0.28687936 0.13373827 0.12644700 0.12522975 0.12235707
## WA1855 NY1849 WI1856 CA1850 OH1853extended
## 0.09005149 0.07849987 0.05747812 0.05741726 0.05596874
##
## $SC1870
## FL1870 NC1868 NY1849 NY1850 WI1856
## 0.5003846 0.4930352 0.3836775 0.3061387 0.2968238
## NY1848 OR1862 MN1851 CA1868extended CA1851
## 0.2082894 0.2024498 0.1949865 0.1891753 0.1816550
##
## $UT1853
## IA1851 IN1843 MN1851 MA1836 GA1851
## 0.12718064 0.05289814 0.03967361 0.03911086 0.03882949
## OH1853extended NY1850 ME1840 AK1900 AL1852
## 0.03798537 0.03460889 0.03179516 0.00000000 0.00000000
##
## $UT1870
## NV1869 CA1868extended NV1861 CA1858 CA1868
## 0.5430257 0.4755664 0.4651915 0.4447403 0.4273188
## CA1851 AZ1865 ID1864 MT1865 NY1850
## 0.4204558 0.4179999 0.3935088 0.3184979 0.2323318
##
## $WA1855
## IN1852 NY1850 CA1851 MN1851 NY1849
## 0.16730757 0.16227559 0.16225362 0.12665627 0.11120877
## CA1850 OH1853extended OH1853 NY1848 IN1843
## 0.09149838 0.08556549 0.06923905 0.06912918 0.06886550
##
## $WI1856
## NY1849 NY1850 NY1848 CA1851 MN1851
## 0.4665080 0.3548828 0.2652917 0.2271285 0.2205623
## CA1850 WA1855 OH1853extended OH1853 IN1852
## 0.2204301 0.1802397 0.1259034 0.1185880 0.1065133
##
## $WY1870
## NE1866 KS1859 OH1853extended OH1853 AR1868
## 0.5805341 0.4411214 0.4281402 0.4199891 0.1302554
## KY1851 CA1868extended NY1850 NV1869 NV1861
## 0.1285849 0.1190050 0.1134905 0.1119810 0.1079558