Sebastian Heath sebastian.heath@nyu.edu
Assisi in Italy (Maximum dimension not known? Arena 65 x 38 Meters)
Carsulae in Italy (84 x 62 Meters)
http://upload.wikimedia.org/wikipedia/commons/8/8d/Bestiarii.jpg
http://www.maumburyrings.co.uk or “Peak Amphitheater”
ramphs.all <- ramphs
ramphs.all.sp <- ramphs.sp
ramphs <- ramphs[ramphs$include,]
ramphs.sp <- ramphs.sp[ramphs.sp$include,]
  
ramphs$imputed.capacity <- NA
ramphs$imputed.capacity[!(is.na(ramphs$capacity))] <- ramphs[!(is.na(ramphs$capacity)),]$capacity
lm.imp.1 <- lm ( capacity ~ latitude +
                   ext.major + ext.minor + arena.major +
                   arena.minor + arena.major:ext.minor + arena.minor * ext.minor,
                data=ramphs )
pred.1 <- predict (lm.imp.1, ramphs)
ramphs$imputed.capacity <- ifelse (is.na(ramphs$capacity), pred.1, ramphs$capacity)
lm(capacity ~ ext.major, ramphs[(ramphs$ext.major < 120) & (ramphs$ext.major > 50),]) -> lm.ext.major
ramphs$imputed.capacity[(!is.na(ramphs$ext.major)) & (is.na(ramphs$imputed.capacity))] <- ramphs$ext.major[(!is.na(ramphs$ext.major)) & (is.na(ramphs$imputed.capacity))] * lm.ext.major$coefficients[2]
length(ramphs$imputed.capacity[is.na(ramphs$imputed.capacity)])## [1] 73ramphs$imputed.capacity[is.na(ramphs$imputed.capacity)] <- 5000
sum(ramphs$imputed.capacity)## [1] 2259062With many thanks to Katie Anderson of NYU Libaries Data Services who is in no way responsible for my (mis?)use of her work.
R. White. What is Spatial History? Spatial History Lab: Working paper; Submitted 1 February 2010;
Paragraph 36 (emphasis author): “One of the important points that I want to make about visualizations, spatial relations, and spatial history is something that I did not fully understand until I started doing this work and which I have had a hard time communicating fully to my colleagues: visualization and spatial history are not about producing illustrations or maps to communicate things that you have discovered by other means. It is a means of doing research; it generates questions that might otherwise go unasked, it reveals historical relations that might otherwise go unnoticed, and it undermines, or substantiates, stories upon which we build our own versions of the past.”
Who should know how to do this?
#generate distances of all amphitheaters to all other amphitheaters
ramphs.dists <- spDists(ramphs.sp,ramphs.sp,longlat = TRUE)
# but let's use names
colnames(ramphs.dists) <- ramphs$id
rownames(ramphs.dists) <- ramphs$id
# Would be nice to have a d.f in the form from,to,km
as.data.frame(ramphs.dists) -> ramphs.dists.df
#add column of names, in anticipation of using gather()
cbind(from = ramphs$id,ramphs.dists.df) -> ramphs.dists.df
gather(ramphs.dists.df, to, km, 2:dim(ramphs.dists.df)[2]) -> ramphs.dists.df
# data now in nice columns but...
# we still have the 0Km rows.
#set phasers to kill...
ramphs.dists.df[ramphs.dists.df$km > 0,] -> ramphs.dists.df| from | to | km | |
|---|---|---|---|
| 2 | arlesAmphitheater | duraEuroposAmphitheater | 3241.8637 | 
| 3 | lyonAmphitheater | duraEuroposAmphitheater | 3255.7344 | 
| 4 | romeFlavianAmphitheater | duraEuroposAmphitheater | 2579.4293 | 
| 5 | eleutheropolisAmphitheater | duraEuroposAmphitheater | 645.7789 | 
| 6 | meridaAmphitheater | duraEuroposAmphitheater | 4177.5360 | 
| 7 | newsteadAmphitheater | duraEuroposAmphitheater | 4025.3811 | 
| 8 | conimbrigaAmphitheater | duraEuroposAmphitheater | 4341.4319 | 
| 9 | cumaeAmphitheater | duraEuroposAmphitheater | 2433.6452 | 
| 10 | pozzuoliFlavianAmphitheater | duraEuroposAmphitheater | 2427.6184 | 
| 11 | pozzuoliEarlyAmphitheater | duraEuroposAmphitheater | 2427.4305 | 
| 12 | syracuseAmphitheater | duraEuroposAmphitheater | 2304.6697 | 
| 13 | carthageAmphitheater | duraEuroposAmphitheater | 2747.3387 | 
| 14 | hadrianVillaAmphitheater | duraEuroposAmphitheater | 2556.7911 | 
| 15 | corinthAmphitheater | duraEuroposAmphitheater | 1636.6076 | 
| 16 | marcianopolisAmphitheater | duraEuroposAmphitheater | 1474.9250 | 
| 17 | porolissumAmphitheater | duraEuroposAmphitheater | 2013.5727 | 
| 18 | nijmegenAmphitheater | duraEuroposAmphitheater | 3355.6355 | 
| 19 | carnuntumMilitaryAmphitheater | duraEuroposAmphitheater | 2466.9678 | 
| 20 | carnuntumCivilianAmphitheater | duraEuroposAmphitheater | 2468.8220 | 
| 21 | leptisMagnaAmphitheater | duraEuroposAmphitheater | 2453.6977 | 
| 22 | empuriesAmphitheater | duraEuroposAmphitheater | 3355.0218 | 
| 23 | tarragonaAmphitheater | duraEuroposAmphitheater | 3509.8708 | 
| 24 | cagliariAmphitheater | duraEuroposAmphitheater | 2843.1324 | 
| 25 | italicaAmphitheater | duraEuroposAmphitheater | 4179.6454 | 
| 26 | segobrigaAmphitheater | duraEuroposAmphitheater | 3862.8982 | 
| 27 | catiniaAmphitheater | duraEuroposAmphitheater | 2321.2086 | 
| 28 | paestumAmphitheater | duraEuroposAmphitheater | 2347.9264 | 
| 29 | lunaAmphitheater | duraEuroposAmphitheater | 2818.9115 | 
| 30 | casinumAmphitheater | duraEuroposAmphitheater | 2463.0371 | 
| 31 | viminaciumAmphitheater | duraEuroposAmphitheater | 1997.6238 | 
| 32 | flaviaSolvaAmphitheater | duraEuroposAmphitheater | 2491.4773 | 
| 33 | rusellaeAmphitheater | duraEuroposAmphitheater | 2704.1570 | 
| 34 | parisAmphitheater | duraEuroposAmphitheater | 3503.1993 | 
| 35 | octodurusForumClaudiiVallensiumAmphitheater | duraEuroposAmphitheater | 3091.3570 | 
| 36 | cyreneAmphitheater | duraEuroposAmphitheater | 1758.7145 | 
| 37 | libarnaAmphitheater | duraEuroposAmphitheater | 2922.8465 | 
| 38 | luceriaNoukeriaAmphitheater | duraEuroposAmphitheater | 2338.2406 | 
| 39 | avellaAmphitheater | duraEuroposAmphitheater | 2389.3544 | 
| 40 | nimesAmphitheater | duraEuroposAmphitheater | 3265.2724 | 
| 41 | charterhouseAmphitheater | duraEuroposAmphitheater | 3913.4313 | 
| 42 | chesterAmphitheater | duraEuroposAmphitheater | 3968.2666 | 
| 43 | gennesAmphitheater | duraEuroposAmphitheater | 3665.4275 | 
| 44 | scylletiumScolaciumAmphitheater | duraEuroposAmphitheater | 2194.2565 | 
| 45 | oudnaAmphitheater | duraEuroposAmphitheater | 2762.5166 | 
| 46 | carthagoNovaAmphitheater | duraEuroposAmphitheater | 3734.8512 | 
| 47 | virunumAmphitheater | duraEuroposAmphitheater | 2573.2558 | 
| 48 | carsulaeAmphitheater | duraEuroposAmphitheater | 2587.5644 | 
| 49 | florenceAmphitheater | duraEuroposAmphitheater | 2715.0934 | 
| 50 | ocriculumAmphitheater | duraEuroposAmphitheater | 2590.6507 | 
| 51 | lixusAmphitheater | duraEuroposAmphitheater | 4236.4306 | 
| 52 | arezzoAmphitheater | duraEuroposAmphitheater | 2659.1569 | 
| 53 | larinumAmphitheater | duraEuroposAmphitheater | 2379.4143 | 
| 54 | lucusFeroniaeAmphitheater | duraEuroposAmphitheater | 2575.1280 | 
| 55 | allifaeAmphitheater | duraEuroposAmphitheater | 2418.0908 | 
| 56 | cimiezAmphitheater | duraEuroposAmphitheater | 3030.6213 | 
| 57 | hydataHypsitanaForumTraianiAmphitheatre | duraEuroposAmphitheater | 2870.7728 | 
| 58 | luccaAmphitheater | duraEuroposAmphitheater | 2776.2445 | 
| 59 | hispellumAmphitheatre | duraEuroposAmphitheater | 2586.4036 | 
| 60 | veronaAmphitheatre | duraEuroposAmphitheater | 2777.8239 | 
| 61 | aquincumCivilAmphitheater | duraEuroposAmphitheater | 2295.8815 | 
| 62 | aquincumMilitaryAmphitheater | duraEuroposAmphitheater | 2294.5178 | 
| 63 | aldburoughAmphitheater | duraEuroposAmphitheater | 3897.0494 | 
| 64 | perigueuxAmphitheatre | duraEuroposAmphitheater | 3567.3616 | 
| 65 | cividateCamunoAmphitheater | duraEuroposAmphitheater | 2845.9662 | 
| 66 | grumentoAmphitheater | duraEuroposAmphitheater | 2269.7408 | 
| 67 | albaFucensAmphitheater | duraEuroposAmphitheater | 2507.4774 | 
| 68 | colAugustaRauricaAmphitheatre | duraEuroposAmphitheater | 3080.9122 | 
| 69 | sutriumAmphitheatre | duraEuroposAmphitheater | 2606.8748 | 
| 70 | sarmizegetusaAmphitheatre | duraEuroposAmphitheater | 1932.7637 | 
| 71 | salonaAmphitheatre | duraEuroposAmphitheater | 2300.9942 | 
| 72 | londonAmphitheatre | duraEuroposAmphitheater | 3739.6890 | 
| 73 | tiburAmphitheater | duraEuroposAmphitheater | 2555.5455 | 
| 74 | caerleonAmphitheater | duraEuroposAmphitheater | 3935.9530 | 
| 75 | telesiaAmphitheatre | duraEuroposAmphitheater | 2402.6495 | 
| 76 | urbisagliaAmphitheater | duraEuroposAmphitheater | 2533.6269 | 
| 77 | saintesAmphitheatre | duraEuroposAmphitheater | 3678.1577 | 
| 78 | assisiAmphitheatre | duraEuroposAmphitheater | 2591.6974 | 
| 79 | durresAmphitheatre | duraEuroposAmphitheater | 1998.7495 | 
| 80 | lambaesisAmphitheater | duraEuroposAmphitheater | 3127.0012 | 
| 81 | mactarisAmphitheater | duraEuroposAmphitheater | 2857.1786 | 
| 82 | cirencesterAmphitheater | duraEuroposAmphitheater | 3871.4994 | 
| 83 | vindonissaAmphitheater | duraEuroposAmphitheater | 3043.5466 | 
| 84 | thysdrusSmallAmphitheater | duraEuroposAmphitheater | 2730.0252 | 
| 85 | frejusAmphitheater | duraEuroposAmphitheater | 3070.4752 | 
| 86 | gortynAmphitheater | duraEuroposAmphitheater | 1440.7413 | 
| 87 | leptiminusAmphitheater | duraEuroposAmphitheater | 2710.4584 | 
| 88 | miciaAmphitheater | duraEuroposAmphitheater | 1954.3939 | 
| 89 | gemellaeAmphitheater | duraEuroposAmphitheater | 3209.0205 | 
| 90 | cherchellAmphitheater | duraEuroposAmphitheater | 3470.7413 | 
| 91 | pulaAmphitheater | duraEuroposAmphitheater | 2544.6444 | 
| 92 | carmonaAmphitheater | duraEuroposAmphitheater | 4144.6798 | 
| 93 | caesareaAmphitheater | duraEuroposAmphitheater | 595.2877 | 
| 94 | pergamumAmphitheater | duraEuroposAmphitheater | 1299.6263 | 
| 95 | anazarbusAmphitheater | duraEuroposAmphitheater | 516.0525 | 
| 96 | antiochAmphitheater | duraEuroposAmphitheater | 444.7205 | 
| 97 | cyzicusAmphitheater | duraEuroposAmphitheater | 1294.0974 | 
| 98 | sabrathaAmphitheater | duraEuroposAmphitheater | 2615.5671 | 
| 99 | salamisAmphitheater | duraEuroposAmphitheater | 625.1647 | 
| 100 | paphosAmphitheater | duraEuroposAmphitheater | 761.9085 | 
| 101 | carmarthenAmphitheater | duraEuroposAmphitheater | 4032.1211 | 
| from | to | km | |
|---|---|---|---|
| 250 | nimesAmphitheater | arlesAmphitheater | 27.9687539 | 
| 644 | hadrianVillaAmphitheater | romeFlavianAmphitheater | 24.4592422 | 
| 680 | ocriculumAmphitheater | romeFlavianAmphitheater | 57.8988659 | 
| 684 | lucusFeroniaeAmphitheater | romeFlavianAmphitheater | 27.9206250 | 
| 697 | albaFucensAmphitheater | romeFlavianAmphitheater | 79.0177124 | 
| 699 | sutriumAmphitheatre | romeFlavianAmphitheater | 44.4399399 | 
| 703 | tiburAmphitheater | romeFlavianAmphitheater | 26.5447118 | 
| 756 | monteleoneAmphitheater | romeFlavianAmphitheater | 48.7236605 | 
| 809 | genzanoPrivateAmphitheater | romeFlavianAmphitheater | 27.7012943 | 
| 823 | statiliusTaurusAmphitheater | romeFlavianAmphitheater | 2.1340177 | 
| 831 | faleriiNoviAmphitheater | romeFlavianAmphitheater | 47.0474041 | 
| 1627 | bobadelaAmphitheater | conimbrigaAmphitheater | 58.7178710 | 
| 1690 | pozzuoliFlavianAmphitheater | cumaeAmphitheater | 6.1073447 | 
| 1691 | pozzuoliEarlyAmphitheater | cumaeAmphitheater | 6.2837252 | 
| 1710 | casinumAmphitheater | cumaeAmphitheater | 73.7562075 | 
| 1719 | avellaAmphitheater | cumaeAmphitheater | 48.4031736 | 
| 1735 | allifaeAmphitheater | cumaeAmphitheater | 58.5692162 | 
| 1755 | telesiaAmphitheatre | cumaeAmphitheater | 56.5159704 | 
| 1810 | beneventoAmphitheater | cumaeAmphitheater | 68.9187382 | 
| 1811 | calviRisortaAmphitheater | cumaeAmphitheater | 40.5962748 | 
| 1822 | capuaRepublicanAmphitheater | cumaeAmphitheater | 31.5102458 | 
| 1823 | capuaImperialAmphitheater | cumaeAmphitheater | 31.6279460 | 
| 1824 | liternoAmphitheater | cumaeAmphitheater | 9.0374043 | 
| 1825 | noleAmphitheater | cumaeAmphitheater | 40.2940775 | 
| 1836 | noceraSuperioreAmphitheater | cumaeAmphitheater | 51.8324988 | 
| 1851 | aquinoAmphitheater | cumaeAmphitheater | 78.6335590 | 
| 1889 | minturnaeAmphitheater | cumaeAmphitheater | 50.7130994 | 
| 1890 | sinuessaAmphitheater | cumaeAmphitheater | 38.8242914 | 
| 1899 | cumaeAmphitheater | pozzuoliFlavianAmphitheater | 6.1073447 | 
| 1901 | pozzuoliEarlyAmphitheater | pozzuoliFlavianAmphitheater | 0.1970432 | 
| 1920 | casinumAmphitheater | pozzuoliFlavianAmphitheater | 77.1704472 | 
| 1929 | avellaAmphitheater | pozzuoliFlavianAmphitheater | 43.4014628 | 
| 1945 | allifaeAmphitheater | pozzuoliFlavianAmphitheater | 58.1718231 | 
| 1965 | telesiaAmphitheatre | pozzuoliFlavianAmphitheater | 54.2711716 | 
| 2020 | beneventoAmphitheater | pozzuoliFlavianAmphitheater | 64.7172784 | 
| 2021 | calviRisortaAmphitheater | pozzuoliFlavianAmphitheater | 41.7859029 | 
| 2032 | capuaRepublicanAmphitheater | pozzuoliFlavianAmphitheater | 30.5667414 | 
| 2033 | capuaImperialAmphitheater | pozzuoliFlavianAmphitheater | 30.7001985 | 
| 2034 | liternoAmphitheater | pozzuoliFlavianAmphitheater | 13.2343994 | 
| 2035 | noleAmphitheater | pozzuoliFlavianAmphitheater | 35.1755547 | 
| 2046 | noceraSuperioreAmphitheater | pozzuoliFlavianAmphitheater | 45.7526823 | 
| 2099 | minturnaeAmphitheater | pozzuoliFlavianAmphitheater | 55.2462354 | 
| 2100 | sinuessaAmphitheater | pozzuoliFlavianAmphitheater | 43.2720751 | 
| 2109 | cumaeAmphitheater | pozzuoliEarlyAmphitheater | 6.2837252 | 
| 2110 | pozzuoliFlavianAmphitheater | pozzuoliEarlyAmphitheater | 0.1970432 | 
| 2130 | casinumAmphitheater | pozzuoliEarlyAmphitheater | 77.2015414 | 
| 2139 | avellaAmphitheater | pozzuoliEarlyAmphitheater | 43.2076626 | 
| 2155 | allifaeAmphitheater | pozzuoliEarlyAmphitheater | 58.0807452 | 
| 2175 | telesiaAmphitheatre | pozzuoliEarlyAmphitheater | 54.1308566 | 
| 2230 | beneventoAmphitheater | pozzuoliEarlyAmphitheater | 64.5340894 | 
| 2231 | calviRisortaAmphitheater | pozzuoliEarlyAmphitheater | 41.7470277 | 
| 2242 | capuaRepublicanAmphitheater | pozzuoliEarlyAmphitheater | 30.4682517 | 
| 2243 | capuaImperialAmphitheater | pozzuoliEarlyAmphitheater | 30.6020895 | 
| 2244 | liternoAmphitheater | pozzuoliEarlyAmphitheater | 13.3253543 | 
| 2245 | noleAmphitheater | pozzuoliEarlyAmphitheater | 34.9808437 | 
| 2256 | noceraSuperioreAmphitheater | pozzuoliEarlyAmphitheater | 45.5688926 | 
| 2309 | minturnaeAmphitheater | pozzuoliEarlyAmphitheater | 55.3241795 | 
| 2310 | sinuessaAmphitheater | pozzuoliEarlyAmphitheater | 43.3485126 | 
| 2337 | catiniaAmphitheater | syracuseAmphitheater | 50.9785638 | 
| 2565 | oudnaAmphitheater | carthageAmphitheater | 30.3648270 | 
| 2701 | uticaAmphitheater | carthageAmphitheater | 31.6378238 | 
| 2702 | tebourbaAmphitheater | carthageAmphitheater | 42.8836577 | 
| 2703 | hencherElKasbatAmphitheater | carthageAmphitheater | 62.5833037 | 
| 2709 | pupputAmphitheater | carthageAmphitheater | 55.9193622 | 
| 2717 | carpisAmphitheater | carthageAmphitheater | 24.1028949 | 
| 2734 | romeFlavianAmphitheater | hadrianVillaAmphitheater | 24.4592422 | 
| 2778 | carsulaeAmphitheater | hadrianVillaAmphitheater | 79.5150391 | 
| 2780 | ocriculumAmphitheater | hadrianVillaAmphitheater | 58.1566593 | 
| 2784 | lucusFeroniaeAmphitheater | hadrianVillaAmphitheater | 25.8478135 | 
| 2797 | albaFucensAmphitheater | hadrianVillaAmphitheater | 54.5782990 | 
| 2799 | sutriumAmphitheatre | hadrianVillaAmphitheater | 56.1999547 | 
| 2803 | tiburAmphitheater | hadrianVillaAmphitheater | 2.6290540 | 
| 2855 | sanBenedettoDeiMarsiAmphitheater | hadrianVillaAmphitheater | 70.6998945 | 
| 2856 | monteleoneAmphitheater | hadrianVillaAmphitheater | 32.6535029 | 
| 2862 | sanVittorinoAmphitheater | hadrianVillaAmphitheater | 67.0034237 | 
| 2909 | genzanoPrivateAmphitheater | hadrianVillaAmphitheater | 28.4519171 | 
| 2923 | statiliusTaurusAmphitheater | hadrianVillaAmphitheater | 26.0596583 | 
| 2931 | faleriiNoviAmphitheater | hadrianVillaAmphitheater | 52.9033948 | 
| 3722 | xantenAmphitheater | nijmegenAmphitheater | 43.8873024 | 
| 3800 | carnuntumCivilianAmphitheater | carnuntumMilitaryAmphitheater | 3.6214332 | 
| 3938 | sopronAmphitheater | carnuntumMilitaryAmphitheater | 53.2829375 | 
| 4009 | carnuntumMilitaryAmphitheater | carnuntumCivilianAmphitheater | 3.6214332 | 
| 4148 | sopronAmphitheater | carnuntumCivilianAmphitheater | 50.3097860 | 
| 5132 | carmonaAmphitheater | italicaAmphitheater | 35.1384584 | 
| 5472 | syracuseAmphitheater | catiniaAmphitheater | 50.9785638 | 
| 5709 | avellaAmphitheater | paestumAmphitheater | 68.6287749 | 
| 5736 | grumentoAmphitheater | paestumAmphitheater | 78.3291809 | 
| 5815 | noleAmphitheater | paestumAmphitheater | 69.5043023 | 
| 5826 | noceraSuperioreAmphitheater | paestumAmphitheater | 46.5007819 | 
| 5938 | luccaAmphitheater | lunaAmphitheater | 45.6785169 | 
| 6099 | cumaeAmphitheater | casinumAmphitheater | 73.7562075 | 
| 6100 | pozzuoliFlavianAmphitheater | casinumAmphitheater | 77.1704472 | 
| 6101 | pozzuoliEarlyAmphitheater | casinumAmphitheater | 77.2015414 | 
| 6145 | allifaeAmphitheater | casinumAmphitheater | 46.1903434 | 
| 6157 | albaFucensAmphitheater | casinumAmphitheater | 74.2807088 | 
| 6165 | telesiaAmphitheatre | casinumAmphitheater | 63.5208060 | 
| 6215 | sanBenedettoDeiMarsiAmphitheater | casinumAmphitheater | 60.3439850 | 
| 6221 | calviRisortaAmphitheater | casinumAmphitheater | 40.7579328 | 
| 6232 | capuaRepublicanAmphitheater | casinumAmphitheater | 56.8453689 | 
| 6233 | capuaImperialAmphitheater | casinumAmphitheater | 56.7178373 | 
http://www.slideshare.net/gcheliotis/social-network-analysis-3273045
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   1.000   3.000   6.096  10.000  20.000# print the top quartile
V(close.amphitheaters.nw)[degree >= summary(V(close.amphitheaters.nw)$degree/2)[5]]## Vertex sequence:
##  [1] "romeFlavianAmphitheater"          "cumaeAmphitheater"               
##  [3] "pozzuoliFlavianAmphitheater"      "pozzuoliEarlyAmphitheater"       
##  [5] "carthageAmphitheater"             "hadrianVillaAmphitheater"        
##  [7] "paestumAmphitheater"              "casinumAmphitheater"             
##  [9] "luceriaNoukeriaAmphitheater"      "avellaAmphitheater"              
## [11] "oudnaAmphitheater"                "carsulaeAmphitheater"            
## [13] "ocriculumAmphitheater"            "arezzoAmphitheater"              
## [15] "larinumAmphitheater"              "lucusFeroniaeAmphitheater"       
## [17] "allifaeAmphitheater"              "hispellumAmphitheatre"           
## [19] "albaFucensAmphitheater"           "sutriumAmphitheatre"             
## [21] "tiburAmphitheater"                "telesiaAmphitheatre"             
## [23] "urbisagliaAmphitheater"           "assisiAmphitheatre"              
## [25] "mactarisAmphitheater"             "thysdrusSmallAmphitheater"       
## [27] "leptiminusAmphitheater"           "sanBenedettoDeiMarsiAmphitheater"
## [29] "monteleoneAmphitheater"           "bolsenaAmphitheater"             
## [31] "anconaAmphitheater"               "ascoliPicenoAmphitheater"        
## [33] "beneventoAmphitheater"            "calviRisortaAmphitheater"        
## [35] "sanVittorinoAmphitheater"         "capuaRepublicanAmphitheater"     
## [37] "capuaImperialAmphitheater"        "liternoAmphitheater"             
## [39] "noleAmphitheater"                 "noceraSuperioreAmphitheater"     
## [41] "aquinoAmphitheater"               "seressiAmphitheater"             
## [43] "chemtouAmphitheater"              "bekaltaAmphitheater"             
## [45] "sidiBouArkoubAmphitheater"        "genzanoPrivateAmphitheater"      
## [47] "ainHedjahAmphitheater"            "uticaAmphitheater"               
## [49] "tebourbaAmphitheater"             "hencherElKasbatAmphitheater"     
## [51] "hencherZembraAmphitheater"        "bullaRegiaAmphitheater"          
## [53] "pupputAmphitheater"               "siccaVeneriaAmphitheater"        
## [55] "thibariAmphitheater"              "statiliusTaurusAmphitheater"     
## [57] "carpisAmphitheater"               "faleriiNoviAmphitheater"         
## [59] "venosaAmphitheater"               "teramoAmphitheater"              
## [61] "ordonaAmphitheater"               "bevanaAmphitheater"              
## [63] "minturnaeAmphitheater"            "sinuessaAmphitheater"| id | degree | |
|---|---|---|
| 82 | faleriiNoviAmphitheater | 16 | 
| 113 | liternoAmphitheater | 16 | 
| 118 | lucusFeroniaeAmphitheater | 16 | 
| 139 | ocriculumAmphitheater | 16 | 
| 3 | albaFucensAmphitheater | 17 | 
| 71 | cumaeAmphitheater | 17 | 
| 152 | pozzuoliEarlyAmphitheater | 17 | 
| 153 | pozzuoliFlavianAmphitheater | 17 | 
| 166 | sanBenedettoDeiMarsiAmphitheater | 17 | 
| 177 | sinuessaAmphitheater | 17 | 
| 44 | calviRisortaAmphitheater | 18 | 
| 46 | capuaImperialAmphitheater | 18 | 
| 47 | capuaRepublicanAmphitheater | 18 | 
| 53 | carsulaeAmphitheater | 18 | 
| 129 | minturnaeAmphitheater | 18 | 
| 137 | noleAmphitheater | 18 | 
| 6 | allifaeAmphitheater | 19 | 
| 16 | aquinoAmphitheater | 19 | 
| 56 | casinumAmphitheater | 19 | 
| 131 | monteleoneAmphitheater | 19 | 
| 167 | sanVittorinoAmphitheater | 19 | 
| 24 | avellaAmphitheater | 20 | 
| 26 | beneventoAmphitheater | 20 | 
| 188 | telesiaAmphitheatre | 20 | 
Though this is useful (student work):
http://www.willjfield.com/blog/2015/03/03/randomizing-with-r/