11.1、关联规则实例

实例一:通过arules包中的Aprior()函数求关联规则、eclat()函数求频繁项集

#1、加载数据并查看
library(arules)
## Loading required package: Matrix
## 
## Attaching package: 'arules'
## The following objects are masked from 'package:base':
## 
##     %in%, abbreviate, write
data("Groceries")
str(Groceries)
## Formal class 'transactions' [package "arules"] with 4 slots
##   ..@ transactionInfo:'data.frame':  9835 obs. of  0 variables
##   ..@ data           :Formal class 'ngCMatrix' [package "Matrix"] with 5 slots
##   .. .. ..@ i       : int [1:43367] 13 60 69 78 14 29 98 24 15 29 ...
##   .. .. ..@ p       : int [1:9836] 0 4 7 8 12 16 21 22 27 28 ...
##   .. .. ..@ Dim     : int [1:2] 169 9835
##   .. .. ..@ Dimnames:List of 2
##   .. .. .. ..$ : NULL
##   .. .. .. ..$ : NULL
##   .. .. ..@ factors : list()
##   ..@ itemInfo       :'data.frame':  169 obs. of  3 variables:
##   .. ..$ labels: chr [1:169] "frankfurter" "sausage" "liver loaf" "ham" ...
##   .. ..$ level2: Factor w/ 55 levels "baby food","bags",..: 44 44 44 44 44 44 44 42 42 41 ...
##   .. ..$ level1: Factor w/ 10 levels "canned food",..: 6 6 6 6 6 6 6 6 6 6 ...
##   ..@ itemsetInfo    :'data.frame':  9835 obs. of  1 variable:
##   .. ..$ itemsetID: chr [1:9835] "1" "2" "3" "4" ...
summary(Groceries)
## transactions as itemMatrix in sparse format with
##  9835 rows (elements/itemsets/transactions) and
##  169 columns (items) and a density of 0.02609146 
## 
## most frequent items:
##       whole milk other vegetables       rolls/buns             soda 
##             2513             1903             1809             1715 
##           yogurt          (Other) 
##             1372            34055 
## 
## element (itemset/transaction) length distribution:
## sizes
##    1    2    3    4    5    6    7    8    9   10   11   12   13   14   15 
## 2159 1643 1299 1005  855  645  545  438  350  246  182  117   78   77   55 
##   16   17   18   19   20   21   22   23   24   26   27   28   29   32 
##   46   29   14   14    9   11    4    6    1    1    1    1    3    1 
## 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   2.000   3.000   4.409   6.000  32.000 
## 
## includes extended item information - examples:
##        labels  level2           level1
## 1 frankfurter sausage meet and sausage
## 2     sausage sausage meet and sausage
## 3  liver loaf sausage meet and sausage
dim(Groceries)
## [1] 9835  169
#以Groceries数据为例,超市购物的例子,每一行为一个顾客的购买记录,格式为transactions 也就是以稀疏矩阵储存的物品矩阵数据 

inspect(Groceries[1:3])
##   items                
## 1 {citrus fruit,       
##    semi-finished bread,
##    margarine,          
##    ready soups}        
## 2 {tropical fruit,     
##    yogurt,             
##    coffee}             
## 3 {whole milk}
#2、数据清洗
#1)查看某些数据项出现的频率
itemFrequency(Groceries[, 1:3])
## frankfurter     sausage  liver loaf 
## 0.058973055 0.093950178 0.005083884
#2)数据探索
itemFrequencyPlot(Groceries, support=0.1)

#有8项支持度大于0.1
itemFrequencyPlot(Groceries, topN=20)

# 画出前20个频率最大的项

#3)稀疏矩阵可视化
image(Groceries[1:5])

image(sample(Groceries, 100))

#4)对稀疏矩阵进行转换,把transaction类型转化为data.frame类型
df_Gro <- as(Groceries, "data.frame")
dim(df_Gro)
## [1] 9835    1
head(df_Gro, 3)
##                                                      items
## 1 {citrus fruit,semi-finished bread,margarine,ready soups}
## 2                           {tropical fruit,yogurt,coffee}
## 3                                             {whole milk}
#对transactions类型的Groceries数据做处理:aprior()函数求关联规则,eclat()函数求频繁项集
#3、创建关联规则:aprior()函数求关联规则
rules <- apriori(Groceries, parameter = list(support=0.01, confidence=0.2))
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport support minlen maxlen
##         0.2    0.1    1 none FALSE            TRUE    0.01      1     10
##  target   ext
##   rules FALSE
## 
## Algorithmic control:
##  filter tree heap memopt load sort verbose
##     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
## 
## Absolute minimum support count: 98 
## 
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [88 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [232 rule(s)] done [0.00s].
## creating S4 object  ... done [0.00s].
summary(rules)
## set of 232 rules
## 
## rule length distribution (lhs + rhs):sizes
##   1   2   3 
##   1 151  80 
## 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   2.000   2.000   2.341   3.000   3.000 
## 
## summary of quality measures:
##     support          confidence          lift       
##  Min.   :0.01007   Min.   :0.2006   Min.   :0.8991  
##  1st Qu.:0.01200   1st Qu.:0.2470   1st Qu.:1.4432  
##  Median :0.01490   Median :0.3170   Median :1.7277  
##  Mean   :0.02005   Mean   :0.3321   Mean   :1.7890  
##  3rd Qu.:0.02227   3rd Qu.:0.4033   3rd Qu.:2.0762  
##  Max.   :0.25552   Max.   :0.5862   Max.   :3.2950  
## 
## mining info:
##       data ntransactions support confidence
##  Groceries          9835    0.01        0.2
#保存数据到磁盘
df_rules <- as(rules, "data.frame")
write.csv(df_rules, "F:/R/GeroRules.csv")
#直接保存
#write(rules, file="F:/R/GeroRules1.csv", sep=",", col.names=NA)

#4、按支持度对求得的关联规则子集排序并查看前3条规则
inspect(sort(rules)[1:3])  #默认decreasing=T,按支持度排序
##     lhs                   rhs                support    confidence
## 1   {}                 => {whole milk}       0.25551601 0.2555160 
## 151 {other vegetables} => {whole milk}       0.07483477 0.3867578 
## 152 {whole milk}       => {other vegetables} 0.07483477 0.2928770 
##     lift    
## 1   1.000000
## 151 1.513634
## 152 1.513634
inspect(sort(rules, decreasing = F)[1:3])
##     lhs              rhs                support    confidence lift    
## 2   {hard cheese} => {whole milk}       0.01006609 0.4107884  1.607682
## 20  {waffles}     => {other vegetables} 0.01006609 0.2619048  1.353565
## 153 {curd,yogurt} => {whole milk}       0.01006609 0.5823529  2.279125
inspect(sort(rules, by="lift")[1:3])
##   lhs                   rhs                     support confidence     lift
## 1 {citrus fruit,                                                           
##    other vegetables} => {root vegetables}    0.01037112  0.3591549 3.295045
## 2 {other vegetables,                                                       
##    yogurt}           => {whipped/sour cream} 0.01016777  0.2341920 3.267062
## 3 {tropical fruit,                                                         
##    other vegetables} => {root vegetables}    0.01230300  0.3427762 3.144780
#5、求所需要的关联规则子集:用subset做规则的筛选,取"右手边"含有whole milk且lift大于1.2的规则
sub_rules <- subset(rules, subset=rhs %in% "whole milk" & lift>1.2)
berryrules <- subset(Groceries, items %in% "berries")
inspect(berryrules[1:3])
##   items                   
## 1 {pork,                  
##    berries,               
##    other vegetables,      
##    whole milk,            
##    whipped/sour cream,    
##    artif. sweetener,      
##    soda,                  
##    abrasive cleaner}      
## 2 {berries,               
##    yogurt}                
## 3 {tropical fruit,        
##    pip fruit,             
##    berries,               
##    whole milk,            
##    frozen potato products,
##    rolls/buns,            
##    pickled vegetables,    
##    chocolate}
class(sub_rules)
## [1] "rules"
## attr(,"package")
## [1] "arules"
head(as(sub_rules, "data.frame"))
##                             rules    support confidence     lift
## 2   {hard cheese} => {whole milk} 0.01006609  0.4107884 1.607682
## 4   {butter milk} => {whole milk} 0.01159126  0.4145455 1.622385
## 5           {ham} => {whole milk} 0.01148958  0.4414062 1.727509
## 6 {sliced cheese} => {whole milk} 0.01077783  0.4398340 1.721356
## 7           {oil} => {whole milk} 0.01128622  0.4021739 1.573968
## 9        {onions} => {whole milk} 0.01209964  0.3901639 1.526965
#6、eclat()函数求频繁项集
sets <- eclat(Groceries, parameter = list(support=0.05, maxlen=10))
## Eclat
## 
## parameter specification:
##  tidLists support minlen maxlen            target   ext
##     FALSE    0.05      1     10 frequent itemsets FALSE
## 
## algorithmic control:
##  sparse sort verbose
##       7   -2    TRUE
## 
## Absolute minimum support count: 491 
## 
## create itemset ... 
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [28 item(s)] done [0.00s].
## creating sparse bit matrix ... [28 row(s), 9835 column(s)] done [0.00s].
## writing  ... [31 set(s)] done [0.00s].
## Creating S4 object  ... done [0.00s].
summary(sets)
## set of 31 itemsets
## 
## most frequent items:
##       whole milk other vegetables           yogurt       rolls/buns 
##                4                2                2                2 
##      frankfurter          (Other) 
##                1               23 
## 
## element (itemset/transaction) length distribution:sizes
##  1  2 
## 28  3 
## 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   1.000   1.000   1.097   1.000   2.000 
## 
## summary of quality measures:
##     support       
##  Min.   :0.05236  
##  1st Qu.:0.05831  
##  Median :0.07565  
##  Mean   :0.09212  
##  3rd Qu.:0.10173  
##  Max.   :0.25552  
## 
## includes transaction ID lists: FALSE 
## 
## mining info:
##       data ntransactions support
##  Groceries          9835    0.05
#7、按支持度对求得的频繁项集排序并查看前6条频繁项集:
inspect(sort(sets, by="support")[1:6])
##    items              support  
## 4  {whole milk}       0.2555160
## 5  {other vegetables} 0.1934926
## 6  {rolls/buns}       0.1839349
## 8  {soda}             0.1743772
## 7  {yogurt}           0.1395018
## 11 {bottled water}    0.1105236
#8、针对transcation数据画频繁项的图
itemFrequencyPlot(Groceries, support=0.05, cex.names=0.8)

#9、简单介绍一下关联规则的可视化包:
 #每个画图包背后都有一堆包,像ggplot2 library(arulesViz)
 #载入需要的程辑包:scatterplot3d #载入需要的程辑包:vcd
 #载入需要的程辑包:MASS
 #载入需要的程辑包:grid
 #载入需要的程辑包:colorspace
 #载入需要的程辑包:seriation
 #载入需要的程辑包:cluster
 #载入需要的程辑包:TSP
 #载入需要的程辑包:gclus
 #arulesViz中有很多图形,介绍几个好看的,画图的对象都是rules

library(arulesViz)
## Loading required package: grid
## 
## Attaching package: 'arulesViz'
## The following object is masked from 'package:arules':
## 
##     abbreviate
## The following object is masked from 'package:base':
## 
##     abbreviate
plot(rules, shading="order", control=list(main="Two-key plot"))

plot(rules, method="grouped")

plot(rules, method="graph")

实例二、

购物篮数据,每行表示一个篮子,篮子里用逗号分隔出一个个品牌。 现在采用频繁模式挖掘出品牌关联,主要是频繁二项集。将关联看成一条边,出现次数看作边的权重,这样就得到了一张图,对图进行社区发现,可以看到品牌间是否有关联。 原始数据下载:http://pan.baidu.com/s/1jGHr8iy

#1、加载数据并查看
x <- readLines("F:\\R\\Rworkspace\\实验数据/user2items.csv")
str(x)
##  chr [1:475] "6805" "4750,19394,25651,6395,5592" ...
#2、数据预处理
data <- list()
for(n in 1:length(x)) {
  data[n] <- strsplit(x[n], ",")
}
data[1]
## [[1]]
## [1] "6805"
data[2]
## [[1]]
## [1] "4750"  "19394" "25651" "6395"  "5592"
trans <- as(data, "transactions")

#3、建模
library(arules)
frequentsets <- eclat(trans, parameter = list(support=0.004, maxlen=10))
## Eclat
## 
## parameter specification:
##  tidLists support minlen maxlen            target   ext
##     FALSE   0.004      1     10 frequent itemsets FALSE
## 
## algorithmic control:
##  sparse sort verbose
##       7   -2    TRUE
## 
## Absolute minimum support count: 1
## Warning in eclat(trans, parameter = list(support = 0.004, maxlen = 10)): You chose a very low absolute support count of 1. You might run out of memory! Increase minimum support.
## create itemset ... 
## set transactions ...[1642 item(s), 475 transaction(s)] done [0.00s].
## sorting and recoding items ... [520 item(s)] done [0.00s].
## creating sparse bit matrix ... [520 row(s), 475 column(s)] done [0.00s].
## writing  ... [753 set(s)] done [0.00s].
## Creating S4 object  ... done [0.00s].
#查看频繁项集
inspect(frequentsets[1:10])
##    items         support    
## 1  {13471,7868}  0.004210526
## 2  {12688,15217} 0.004210526
## 3  {15921,7105}  0.004210526
## 4  {18712,26737} 0.004210526
## 5  {1282,18180}  0.004210526
## 6  {11196,14048} 0.004210526
## 7  {26576,6571}  0.004210526
## 8  {29078,5598}  0.004210526
## 9  {11330,26614} 0.004210526
## 10 {7868,9899}   0.004210526
inspect(sort(frequentsets, by="support")[1:3])
##     items   support   
## 234 {7868}  0.05052632
## 237 {27791} 0.04421053
## 235 {29099} 0.03789474
inspect(sort(frequentsets, by="support", decreasing=F)[1:3])
##   items         support    
## 1 {13471,7868}  0.004210526
## 2 {12688,15217} 0.004210526
## 3 {15921,7105}  0.004210526
#4、求关联规则
rules <- apriori(trans, parameter = list(support=0.004, confidence=0.001))
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport support minlen maxlen
##       0.001    0.1    1 none FALSE            TRUE   0.004      1     10
##  target   ext
##   rules FALSE
## 
## Algorithmic control:
##  filter tree heap memopt load sort verbose
##     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
## 
## Absolute minimum support count: 1
## Warning in apriori(trans, parameter = list(support = 0.004, confidence = 0.001)): You chose a very low absolute support count of 1. You might run out of memory! Increase minimum support.
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[1642 item(s), 475 transaction(s)] done [0.00s].
## sorting and recoding items ... [520 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [1026 rule(s)] done [0.00s].
## creating S4 object  ... done [0.00s].
summary(rules)
## set of 1026 rules
## 
## rule length distribution (lhs + rhs):sizes
##   1   2   3   4 
## 520 396  90  20 
## 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    1.00    1.00    1.62    2.00    4.00 
## 
## summary of quality measures:
##     support           confidence           lift       
##  Min.   :0.004211   Min.   :0.00421   Min.   :  1.00  
##  1st Qu.:0.004211   1st Qu.:0.00421   1st Qu.:  1.00  
##  Median :0.004211   Median :0.02947   Median :  1.00  
##  Mean   :0.005836   Mean   :0.25990   Mean   : 24.92  
##  3rd Qu.:0.006316   3rd Qu.:0.40000   3rd Qu.: 31.67  
##  Max.   :0.050526   Max.   :1.00000   Max.   :237.50  
## 
## mining info:
##   data ntransactions support confidence
##  trans           475   0.004      0.001
inspect(rules)
##      lhs                    rhs     support     confidence  lift      
## 1    {}                  => {3658}  0.004210526 0.004210526   1.000000
## 2    {}                  => {14294} 0.004210526 0.004210526   1.000000
## 3    {}                  => {7963}  0.004210526 0.004210526   1.000000
## 4    {}                  => {7150}  0.004210526 0.004210526   1.000000
## 5    {}                  => {28438} 0.004210526 0.004210526   1.000000
## 6    {}                  => {5094}  0.004210526 0.004210526   1.000000
## 7    {}                  => {11790} 0.004210526 0.004210526   1.000000
## 8    {}                  => {21899} 0.004210526 0.004210526   1.000000
## 9    {}                  => {11280} 0.004210526 0.004210526   1.000000
## 10   {}                  => {9829}  0.004210526 0.004210526   1.000000
## 11   {}                  => {26722} 0.004210526 0.004210526   1.000000
## 12   {}                  => {4039}  0.004210526 0.004210526   1.000000
## 13   {}                  => {25193} 0.004210526 0.004210526   1.000000
## 14   {}                  => {17237} 0.004210526 0.004210526   1.000000
## 15   {}                  => {9301}  0.004210526 0.004210526   1.000000
## 16   {}                  => {25596} 0.004210526 0.004210526   1.000000
## 17   {}                  => {20902} 0.006315789 0.006315789   1.000000
## 18   {}                  => {13975} 0.004210526 0.004210526   1.000000
## 19   {}                  => {24193} 0.004210526 0.004210526   1.000000
## 20   {}                  => {4808}  0.004210526 0.004210526   1.000000
## 21   {}                  => {22240} 0.004210526 0.004210526   1.000000
## 22   {}                  => {12055} 0.004210526 0.004210526   1.000000
## 23   {}                  => {4960}  0.004210526 0.004210526   1.000000
## 24   {}                  => {14360} 0.004210526 0.004210526   1.000000
## 25   {}                  => {15831} 0.004210526 0.004210526   1.000000
## 26   {}                  => {1481}  0.006315789 0.006315789   1.000000
## 27   {}                  => {3185}  0.004210526 0.004210526   1.000000
## 28   {}                  => {9193}  0.004210526 0.004210526   1.000000
## 29   {}                  => {12453} 0.004210526 0.004210526   1.000000
## 30   {}                  => {12647} 0.004210526 0.004210526   1.000000
## 31   {}                  => {20506} 0.004210526 0.004210526   1.000000
## 32   {}                  => {11857} 0.006315789 0.006315789   1.000000
## 33   {}                  => {5015}  0.004210526 0.004210526   1.000000
## 34   {}                  => {9195}  0.004210526 0.004210526   1.000000
## 35   {}                  => {13390} 0.004210526 0.004210526   1.000000
## 36   {}                  => {24274} 0.004210526 0.004210526   1.000000
## 37   {}                  => {15672} 0.004210526 0.004210526   1.000000
## 38   {}                  => {20578} 0.004210526 0.004210526   1.000000
## 39   {}                  => {11159} 0.004210526 0.004210526   1.000000
## 40   {}                  => {19814} 0.004210526 0.004210526   1.000000
## 41   {}                  => {22094} 0.004210526 0.004210526   1.000000
## 42   {}                  => {12586} 0.004210526 0.004210526   1.000000
## 43   {}                  => {15911} 0.004210526 0.004210526   1.000000
## 44   {}                  => {13998} 0.004210526 0.004210526   1.000000
## 45   {}                  => {24788} 0.004210526 0.004210526   1.000000
## 46   {}                  => {5403}  0.004210526 0.004210526   1.000000
## 47   {}                  => {14159} 0.004210526 0.004210526   1.000000
## 48   {}                  => {13093} 0.004210526 0.004210526   1.000000
## 49   {}                  => {16243} 0.004210526 0.004210526   1.000000
## 50   {}                  => {18575} 0.006315789 0.006315789   1.000000
## 51   {}                  => {17153} 0.006315789 0.006315789   1.000000
## 52   {}                  => {6096}  0.004210526 0.004210526   1.000000
## 53   {}                  => {2891}  0.004210526 0.004210526   1.000000
## 54   {}                  => {8816}  0.004210526 0.004210526   1.000000
## 55   {}                  => {20548} 0.004210526 0.004210526   1.000000
## 56   {}                  => {4691}  0.004210526 0.004210526   1.000000
## 57   {}                  => {16009} 0.004210526 0.004210526   1.000000
## 58   {}                  => {14795} 0.004210526 0.004210526   1.000000
## 59   {}                  => {9220}  0.004210526 0.004210526   1.000000
## 60   {}                  => {20701} 0.004210526 0.004210526   1.000000
## 61   {}                  => {4300}  0.004210526 0.004210526   1.000000
## 62   {}                  => {12063} 0.004210526 0.004210526   1.000000
## 63   {}                  => {13471} 0.004210526 0.004210526   1.000000
## 64   {}                  => {3555}  0.004210526 0.004210526   1.000000
## 65   {}                  => {24459} 0.004210526 0.004210526   1.000000
## 66   {}                  => {25960} 0.004210526 0.004210526   1.000000
## 67   {}                  => {5845}  0.004210526 0.004210526   1.000000
## 68   {}                  => {1533}  0.004210526 0.004210526   1.000000
## 69   {}                  => {1831}  0.004210526 0.004210526   1.000000
## 70   {}                  => {26972} 0.004210526 0.004210526   1.000000
## 71   {}                  => {7936}  0.004210526 0.004210526   1.000000
## 72   {}                  => {2610}  0.004210526 0.004210526   1.000000
## 73   {}                  => {10908} 0.004210526 0.004210526   1.000000
## 74   {}                  => {21392} 0.004210526 0.004210526   1.000000
## 75   {}                  => {11357} 0.004210526 0.004210526   1.000000
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## 361  {}                  => {24172} 0.006315789 0.006315789   1.000000
## 362  {}                  => {1773}  0.006315789 0.006315789   1.000000
## 363  {}                  => {3313}  0.006315789 0.006315789   1.000000
## 364  {}                  => {4479}  0.008421053 0.008421053   1.000000
## 365  {}                  => {23019} 0.004210526 0.004210526   1.000000
## 366  {}                  => {5306}  0.006315789 0.006315789   1.000000
## 367  {}                  => {5598}  0.010526316 0.010526316   1.000000
## 368  {}                  => {12795} 0.004210526 0.004210526   1.000000
## 369  {}                  => {26546} 0.008421053 0.008421053   1.000000
## 370  {}                  => {18829} 0.004210526 0.004210526   1.000000
## 371  {}                  => {5185}  0.012631579 0.012631579   1.000000
## 372  {}                  => {17060} 0.008421053 0.008421053   1.000000
## 373  {}                  => {2999}  0.006315789 0.006315789   1.000000
## 374  {}                  => {3804}  0.006315789 0.006315789   1.000000
## 375  {}                  => {3647}  0.006315789 0.006315789   1.000000
## 376  {}                  => {10840} 0.008421053 0.008421053   1.000000
## 377  {}                  => {554}   0.008421053 0.008421053   1.000000
## 378  {}                  => {24541} 0.008421053 0.008421053   1.000000
## 379  {}                  => {18167} 0.010526316 0.010526316   1.000000
## 380  {}                  => {3181}  0.006315789 0.006315789   1.000000
## 381  {}                  => {23861} 0.012631579 0.012631579   1.000000
## 382  {}                  => {22489} 0.006315789 0.006315789   1.000000
## 383  {}                  => {23656} 0.008421053 0.008421053   1.000000
## 384  {}                  => {3913}  0.004210526 0.004210526   1.000000
## 385  {}                  => {21110} 0.012631579 0.012631579   1.000000
## 386  {}                  => {4078}  0.010526316 0.010526316   1.000000
## 387  {}                  => {25366} 0.006315789 0.006315789   1.000000
## 388  {}                  => {19405} 0.006315789 0.006315789   1.000000
## 389  {}                  => {27205} 0.008421053 0.008421053   1.000000
## 390  {}                  => {17706} 0.008421053 0.008421053   1.000000
## 391  {}                  => {21146} 0.008421053 0.008421053   1.000000
## 392  {}                  => {13020} 0.012631579 0.012631579   1.000000
## 393  {}                  => {24601} 0.014736842 0.014736842   1.000000
## 394  {}                  => {4281}  0.008421053 0.008421053   1.000000
## 395  {}                  => {19166} 0.004210526 0.004210526   1.000000
## 396  {}                  => {1031}  0.008421053 0.008421053   1.000000
## 397  {}                  => {24196} 0.010526316 0.010526316   1.000000
## 398  {}                  => {23779} 0.014736842 0.014736842   1.000000
## 399  {}                  => {2367}  0.016842105 0.016842105   1.000000
## 400  {}                  => {23662} 0.008421053 0.008421053   1.000000
## 401  {}                  => {12352} 0.010526316 0.010526316   1.000000
## 402  {}                  => {23284} 0.010526316 0.010526316   1.000000
## 403  {}                  => {8278}  0.006315789 0.006315789   1.000000
## 404  {}                  => {8628}  0.012631579 0.012631579   1.000000
## 405  {}                  => {21672} 0.008421053 0.008421053   1.000000
## 406  {}                  => {1739}  0.006315789 0.006315789   1.000000
## 407  {}                  => {14942} 0.012631579 0.012631579   1.000000
## 408  {}                  => {12754} 0.012631579 0.012631579   1.000000
## 409  {}                  => {20551} 0.006315789 0.006315789   1.000000
## 410  {}                  => {13592} 0.006315789 0.006315789   1.000000
## 411  {}                  => {21838} 0.008421053 0.008421053   1.000000
## 412  {}                  => {28641} 0.006315789 0.006315789   1.000000
## 413  {}                  => {28985} 0.008421053 0.008421053   1.000000
## 414  {}                  => {7248}  0.010526316 0.010526316   1.000000
## 415  {}                  => {6571}  0.021052632 0.021052632   1.000000
## 416  {}                  => {16331} 0.010526316 0.010526316   1.000000
## 417  {}                  => {13784} 0.008421053 0.008421053   1.000000
## 418  {}                  => {14153} 0.010526316 0.010526316   1.000000
## 419  {}                  => {19394} 0.010526316 0.010526316   1.000000
## 420  {}                  => {12220} 0.014736842 0.014736842   1.000000
## 421  {}                  => {21657} 0.006315789 0.006315789   1.000000
## 422  {}                  => {24869} 0.014736842 0.014736842   1.000000
## 423  {}                  => {23896} 0.006315789 0.006315789   1.000000
## 424  {}                  => {12977} 0.012631579 0.012631579   1.000000
## 425  {}                  => {14482} 0.010526316 0.010526316   1.000000
## 426  {}                  => {18180} 0.012631579 0.012631579   1.000000
## 427  {}                  => {25169} 0.008421053 0.008421053   1.000000
## 428  {}                  => {18075} 0.016842105 0.016842105   1.000000
## 429  {}                  => {19973} 0.010526316 0.010526316   1.000000
## 430  {}                  => {2963}  0.016842105 0.016842105   1.000000
## 431  {}                  => {12068} 0.010526316 0.010526316   1.000000
## 432  {}                  => {16463} 0.018947368 0.018947368   1.000000
## 433  {}                  => {16944} 0.006315789 0.006315789   1.000000
## 434  {}                  => {5053}  0.008421053 0.008421053   1.000000
## 435  {}                  => {21865} 0.014736842 0.014736842   1.000000
## 436  {}                  => {10999} 0.012631579 0.012631579   1.000000
## 437  {}                  => {5043}  0.012631579 0.012631579   1.000000
## 438  {}                  => {530}   0.008421053 0.008421053   1.000000
## 439  {}                  => {27625} 0.010526316 0.010526316   1.000000
## 440  {}                  => {22043} 0.008421053 0.008421053   1.000000
## 441  {}                  => {18741} 0.014736842 0.014736842   1.000000
## 442  {}                  => {16110} 0.012631579 0.012631579   1.000000
## 443  {}                  => {7059}  0.004210526 0.004210526   1.000000
## 444  {}                  => {29547} 0.010526316 0.010526316   1.000000
## 445  {}                  => {5814}  0.004210526 0.004210526   1.000000
## 446  {}                  => {679}   0.014736842 0.014736842   1.000000
## 447  {}                  => {22359} 0.012631579 0.012631579   1.000000
## 448  {}                  => {251}   0.014736842 0.014736842   1.000000
## 449  {}                  => {25329} 0.010526316 0.010526316   1.000000
## 450  {}                  => {11524} 0.004210526 0.004210526   1.000000
## 451  {}                  => {1461}  0.006315789 0.006315789   1.000000
## 452  {}                  => {28270} 0.016842105 0.016842105   1.000000
## 453  {}                  => {7230}  0.010526316 0.010526316   1.000000
## 454  {}                  => {26614} 0.014736842 0.014736842   1.000000
## 455  {}                  => {18515} 0.004210526 0.004210526   1.000000
## 456  {}                  => {14415} 0.006315789 0.006315789   1.000000
## 457  {}                  => {26288} 0.012631579 0.012631579   1.000000
## 458  {}                  => {22749} 0.012631579 0.012631579   1.000000
## 459  {}                  => {15534} 0.006315789 0.006315789   1.000000
## 460  {}                  => {21071} 0.006315789 0.006315789   1.000000
## 461  {}                  => {29224} 0.006315789 0.006315789   1.000000
## 462  {}                  => {7037}  0.004210526 0.004210526   1.000000
## 463  {}                  => {17061} 0.004210526 0.004210526   1.000000
## 464  {}                  => {11022} 0.006315789 0.006315789   1.000000
## 465  {}                  => {22126} 0.012631579 0.012631579   1.000000
## 466  {}                  => {24669} 0.012631579 0.012631579   1.000000
## 467  {}                  => {8842}  0.006315789 0.006315789   1.000000
## 468  {}                  => {17214} 0.006315789 0.006315789   1.000000
## 469  {}                  => {21092} 0.008421053 0.008421053   1.000000
## 470  {}                  => {16540} 0.018947368 0.018947368   1.000000
## 471  {}                  => {10325} 0.004210526 0.004210526   1.000000
## 472  {}                  => {2128}  0.006315789 0.006315789   1.000000
## 473  {}                  => {29203} 0.018947368 0.018947368   1.000000
## 474  {}                  => {19421} 0.006315789 0.006315789   1.000000
## 475  {}                  => {22313} 0.006315789 0.006315789   1.000000
## 476  {}                  => {11196} 0.031578947 0.031578947   1.000000
## 477  {}                  => {18730} 0.018947368 0.018947368   1.000000
## 478  {}                  => {9563}  0.014736842 0.014736842   1.000000
## 479  {}                  => {1000}  0.006315789 0.006315789   1.000000
## 480  {}                  => {21919} 0.010526316 0.010526316   1.000000
## 481  {}                  => {3151}  0.014736842 0.014736842   1.000000
## 482  {}                  => {26523} 0.010526316 0.010526316   1.000000
## 483  {}                  => {10014} 0.010526316 0.010526316   1.000000
## 484  {}                  => {21336} 0.006315789 0.006315789   1.000000
## 485  {}                  => {7096}  0.014736842 0.014736842   1.000000
## 486  {}                  => {8637}  0.023157895 0.023157895   1.000000
## 487  {}                  => {25651} 0.008421053 0.008421053   1.000000
## 488  {}                  => {11176} 0.021052632 0.021052632   1.000000
## 489  {}                  => {4807}  0.006315789 0.006315789   1.000000
## 490  {}                  => {14065} 0.006315789 0.006315789   1.000000
## 491  {}                  => {22556} 0.008421053 0.008421053   1.000000
## 492  {}                  => {18712} 0.012631579 0.012631579   1.000000
## 493  {}                  => {14917} 0.008421053 0.008421053   1.000000
## 494  {}                  => {17959} 0.008421053 0.008421053   1.000000
## 495  {}                  => {12285} 0.023157895 0.023157895   1.000000
## 496  {}                  => {4571}  0.025263158 0.025263158   1.000000
## 497  {}                  => {15315} 0.016842105 0.016842105   1.000000
## 498  {}                  => {7061}  0.010526316 0.010526316   1.000000
## 499  {}                  => {20979} 0.016842105 0.016842105   1.000000
## 500  {}                  => {7105}  0.025263158 0.025263158   1.000000
## 501  {}                  => {4949}  0.018947368 0.018947368   1.000000
## 502  {}                  => {3228}  0.029473684 0.029473684   1.000000
## 503  {}                  => {11080} 0.031578947 0.031578947   1.000000
## 504  {}                  => {18805} 0.021052632 0.021052632   1.000000
## 505  {}                  => {3627}  0.023157895 0.023157895   1.000000
## 506  {}                  => {23628} 0.021052632 0.021052632   1.000000
## 507  {}                  => {15584} 0.012631579 0.012631579   1.000000
## 508  {}                  => {18024} 0.029473684 0.029473684   1.000000
## 509  {}                  => {4411}  0.012631579 0.012631579   1.000000
## 510  {}                  => {11679} 0.025263158 0.025263158   1.000000
## 511  {}                  => {8689}  0.029473684 0.029473684   1.000000
## 512  {}                  => {23928} 0.016842105 0.016842105   1.000000
## 513  {}                  => {9111}  0.016842105 0.016842105   1.000000
## 514  {}                  => {155}   0.023157895 0.023157895   1.000000
## 515  {}                  => {10702} 0.014736842 0.014736842   1.000000
## 516  {}                  => {14261} 0.023157895 0.023157895   1.000000
## 517  {}                  => {27791} 0.044210526 0.044210526   1.000000
## 518  {}                  => {14020} 0.037894737 0.037894737   1.000000
## 519  {}                  => {29099} 0.037894737 0.037894737   1.000000
## 520  {}                  => {7868}  0.050526316 0.050526316   1.000000
## 521  {13471}             => {7868}  0.004210526 1.000000000  19.791667
## 522  {7868}              => {13471} 0.004210526 0.083333333  19.791667
## 523  {15217}             => {12688} 0.004210526 1.000000000 118.750000
## 524  {12688}             => {15217} 0.004210526 0.500000000 118.750000
## 525  {15921}             => {7105}  0.004210526 1.000000000  39.583333
## 526  {7105}              => {15921} 0.004210526 0.166666667  39.583333
## 527  {1282}              => {18180} 0.004210526 1.000000000  79.166667
## 528  {18180}             => {1282}  0.004210526 0.333333333  79.166667
## 529  {26737}             => {18712} 0.004210526 1.000000000  79.166667
## 530  {18712}             => {26737} 0.004210526 0.333333333  79.166667
## 531  {29078}             => {5598}  0.004210526 1.000000000  95.000000
## 532  {5598}              => {29078} 0.004210526 0.400000000  95.000000
## 533  {26576}             => {6571}  0.004210526 1.000000000  47.500000
## 534  {6571}              => {26576} 0.004210526 0.200000000  47.500000
## 535  {14048}             => {11196} 0.004210526 1.000000000  31.666667
## 536  {11196}             => {14048} 0.004210526 0.133333333  31.666667
## 537  {11330}             => {26614} 0.004210526 0.666666667  45.238095
## 538  {26614}             => {11330} 0.004210526 0.285714286  45.238095
## 539  {25570}             => {11176} 0.004210526 1.000000000  47.500000
## 540  {11176}             => {25570} 0.004210526 0.200000000  47.500000
## 541  {9899}              => {7868}  0.004210526 0.666666667  13.194444
## 542  {7868}              => {9899}  0.004210526 0.083333333  13.194444
## 543  {17087}             => {17060} 0.004210526 0.666666667  79.166667
## 544  {17060}             => {17087} 0.004210526 0.500000000  79.166667
## 545  {7680}              => {21110} 0.004210526 0.666666667  52.777778
## 546  {21110}             => {7680}  0.004210526 0.333333333  52.777778
## 547  {7680}              => {12754} 0.004210526 0.666666667  52.777778
## 548  {12754}             => {7680}  0.004210526 0.333333333  52.777778
## 549  {7680}              => {16463} 0.004210526 0.666666667  35.185185
## 550  {16463}             => {7680}  0.004210526 0.222222222  35.185185
## 551  {5667}              => {19405} 0.004210526 1.000000000 158.333333
## 552  {19405}             => {5667}  0.004210526 0.666666667 158.333333
## 553  {14580}             => {11080} 0.004210526 0.666666667  21.111111
## 554  {11080}             => {14580} 0.004210526 0.133333333  21.111111
## 555  {3438}              => {16331} 0.004210526 0.666666667  63.333333
## 556  {16331}             => {3438}  0.004210526 0.400000000  63.333333
## 557  {5661}              => {18741} 0.004210526 0.666666667  45.238095
## 558  {18741}             => {5661}  0.004210526 0.285714286  45.238095
## 559  {25372}             => {5598}  0.004210526 0.333333333  31.666667
## 560  {5598}              => {25372} 0.004210526 0.400000000  31.666667
## 561  {2729}              => {3151}  0.004210526 0.666666667  45.238095
## 562  {3151}              => {2729}  0.004210526 0.285714286  45.238095
## 563  {2729}              => {14020} 0.004210526 0.666666667  17.592593
## 564  {14020}             => {2729}  0.004210526 0.111111111  17.592593
## 565  {12717}             => {22043} 0.004210526 1.000000000 118.750000
## 566  {22043}             => {12717} 0.004210526 0.500000000 118.750000
## 567  {12717}             => {22359} 0.004210526 1.000000000  79.166667
## 568  {22359}             => {12717} 0.004210526 0.333333333  79.166667
## 569  {23774}             => {8689}  0.004210526 0.666666667  22.619048
## 570  {8689}              => {23774} 0.004210526 0.142857143  22.619048
## 571  {19416}             => {4571}  0.004210526 0.666666667  26.388889
## 572  {4571}              => {19416} 0.004210526 0.166666667  26.388889
## 573  {4220}              => {29203} 0.004210526 0.400000000  21.111111
## 574  {29203}             => {4220}  0.004210526 0.222222222  21.111111
## 575  {4220}              => {10014} 0.004210526 0.400000000  38.000000
## 576  {10014}             => {4220}  0.004210526 0.400000000  38.000000
## 577  {12688}             => {18741} 0.004210526 0.500000000  33.928571
## 578  {18741}             => {12688} 0.004210526 0.285714286  33.928571
## 579  {4931}              => {29099} 0.004210526 1.000000000  26.388889
## 580  {29099}             => {4931}  0.004210526 0.111111111  26.388889
## 581  {3047}              => {4949}  0.004210526 0.500000000  26.388889
## 582  {4949}              => {3047}  0.004210526 0.222222222  26.388889
## 583  {24944}             => {12068} 0.004210526 0.666666667  63.333333
## 584  {12068}             => {24944} 0.004210526 0.400000000  63.333333
## 585  {3032}              => {7105}  0.004210526 0.500000000  19.791667
## 586  {7105}              => {3032}  0.004210526 0.166666667  19.791667
## 587  {12541}             => {15315} 0.004210526 0.500000000  29.687500
## 588  {15315}             => {12541} 0.004210526 0.250000000  29.687500
## 589  {2251}              => {7868}  0.004210526 1.000000000  19.791667
## 590  {7868}              => {2251}  0.004210526 0.083333333  19.791667
## 591  {7692}              => {23019} 0.004210526 1.000000000 237.500000
## 592  {23019}             => {7692}  0.004210526 1.000000000 237.500000
## 593  {7692}              => {27791} 0.004210526 1.000000000  22.619048
## 594  {27791}             => {7692}  0.004210526 0.095238095  22.619048
## 595  {24172}             => {21838} 0.004210526 0.666666667  79.166667
## 596  {21838}             => {24172} 0.004210526 0.500000000  79.166667
## 597  {24172}             => {11080} 0.004210526 0.666666667  21.111111
## 598  {11080}             => {24172} 0.004210526 0.133333333  21.111111
## 599  {1773}              => {29203} 0.004210526 0.666666667  35.185185
## 600  {29203}             => {1773}  0.004210526 0.222222222  35.185185
## 601  {4479}              => {29099} 0.006315789 0.750000000  19.791667
## 602  {29099}             => {4479}  0.006315789 0.166666667  19.791667
## 603  {23019}             => {27791} 0.004210526 1.000000000  22.619048
## 604  {27791}             => {23019} 0.004210526 0.095238095  22.619048
## 605  {12795}             => {22126} 0.004210526 1.000000000  79.166667
## 606  {22126}             => {12795} 0.004210526 0.333333333  79.166667
## 607  {2999}              => {24669} 0.004210526 0.666666667  52.777778
## 608  {24669}             => {2999}  0.004210526 0.333333333  52.777778
## 609  {3647}              => {18741} 0.004210526 0.666666667  45.238095
## 610  {18741}             => {3647}  0.004210526 0.285714286  45.238095
## 611  {10840}             => {3151}  0.004210526 0.500000000  33.928571
## 612  {3151}              => {10840} 0.004210526 0.285714286  33.928571
## 613  {3913}              => {530}   0.004210526 1.000000000 118.750000
## 614  {530}               => {3913}  0.004210526 0.500000000 118.750000
## 615  {3913}              => {11679} 0.004210526 1.000000000  39.583333
## 616  {11679}             => {3913}  0.004210526 0.166666667  39.583333
## 617  {21110}             => {15534} 0.004210526 0.333333333  52.777778
## 618  {15534}             => {21110} 0.004210526 0.666666667  52.777778
## 619  {21146}             => {2963}  0.006315789 0.750000000  44.531250
## 620  {2963}              => {21146} 0.006315789 0.375000000  44.531250
## 621  {21146}             => {7096}  0.004210526 0.500000000  33.928571
## 622  {7096}              => {21146} 0.004210526 0.285714286  33.928571
## 623  {24601}             => {18024} 0.004210526 0.285714286   9.693878
## 624  {18024}             => {24601} 0.004210526 0.142857143   9.693878
## 625  {2367}              => {11679} 0.004210526 0.250000000   9.895833
## 626  {11679}             => {2367}  0.004210526 0.166666667   9.895833
## 627  {12352}             => {3627}  0.004210526 0.400000000  17.272727
## 628  {3627}              => {12352} 0.004210526 0.181818182  17.272727
## 629  {8278}              => {16331} 0.004210526 0.666666667  63.333333
## 630  {16331}             => {8278}  0.004210526 0.400000000  63.333333
## 631  {8278}              => {18024} 0.004210526 0.666666667  22.619048
## 632  {18024}             => {8278}  0.004210526 0.142857143  22.619048
## 633  {8628}              => {16463} 0.006315789 0.500000000  26.388889
## 634  {16463}             => {8628}  0.006315789 0.333333333  26.388889
## 635  {8628}              => {22359} 0.004210526 0.333333333  26.388889
## 636  {22359}             => {8628}  0.004210526 0.333333333  26.388889
## 637  {1739}              => {7096}  0.004210526 0.666666667  45.238095
## 638  {7096}              => {1739}  0.004210526 0.285714286  45.238095
## 639  {14942}             => {5043}  0.004210526 0.333333333  26.388889
## 640  {5043}              => {14942} 0.004210526 0.333333333  26.388889
## 641  {14942}             => {8637}  0.004210526 0.333333333  14.393939
## 642  {8637}              => {14942} 0.004210526 0.181818182  14.393939
## 643  {13592}             => {4949}  0.004210526 0.666666667  35.185185
## 644  {4949}              => {13592} 0.004210526 0.222222222  35.185185
## 645  {21838}             => {4571}  0.004210526 0.500000000  19.791667
## 646  {4571}              => {21838} 0.004210526 0.166666667  19.791667
## 647  {21838}             => {7105}  0.004210526 0.500000000  19.791667
## 648  {7105}              => {21838} 0.004210526 0.166666667  19.791667
## 649  {21838}             => {11080} 0.004210526 0.500000000  15.833333
## 650  {11080}             => {21838} 0.004210526 0.133333333  15.833333
## 651  {21838}             => {7868}  0.004210526 0.500000000   9.895833
## 652  {7868}              => {21838} 0.004210526 0.083333333   9.895833
## 653  {28985}             => {16463} 0.004210526 0.500000000  26.388889
## 654  {16463}             => {28985} 0.004210526 0.222222222  26.388889
## 655  {28985}             => {29203} 0.004210526 0.500000000  26.388889
## 656  {29203}             => {28985} 0.004210526 0.222222222  26.388889
## 657  {7248}              => {3151}  0.004210526 0.400000000  27.142857
## 658  {3151}              => {7248}  0.004210526 0.285714286  27.142857
## 659  {16331}             => {14261} 0.004210526 0.400000000  17.272727
## 660  {14261}             => {16331} 0.004210526 0.181818182  17.272727
## 661  {16331}             => {27791} 0.004210526 0.400000000   9.047619
## 662  {27791}             => {16331} 0.004210526 0.095238095   9.047619
## 663  {12220}             => {11080} 0.004210526 0.285714286   9.047619
## 664  {11080}             => {12220} 0.004210526 0.133333333   9.047619
## 665  {21657}             => {23628} 0.004210526 0.666666667  31.666667
## 666  {23628}             => {21657} 0.004210526 0.200000000  31.666667
## 667  {24869}             => {3228}  0.004210526 0.285714286   9.693878
## 668  {3228}              => {24869} 0.004210526 0.142857143   9.693878
## 669  {23896}             => {14261} 0.004210526 0.666666667  28.787879
## 670  {14261}             => {23896} 0.004210526 0.181818182  28.787879
## 671  {12977}             => {14020} 0.004210526 0.333333333   8.796296
## 672  {14020}             => {12977} 0.004210526 0.111111111   8.796296
## 673  {18180}             => {26614} 0.004210526 0.333333333  22.619048
## 674  {26614}             => {18180} 0.004210526 0.285714286  22.619048
## 675  {18180}             => {10014} 0.004210526 0.333333333  31.666667
## 676  {10014}             => {18180} 0.004210526 0.400000000  31.666667
## 677  {18180}             => {4411}  0.004210526 0.333333333  26.388889
## 678  {4411}              => {18180} 0.004210526 0.333333333  26.388889
## 679  {25169}             => {8637}  0.004210526 0.500000000  21.590909
## 680  {8637}              => {25169} 0.004210526 0.181818182  21.590909
## 681  {18075}             => {26523} 0.004210526 0.250000000  23.750000
## 682  {26523}             => {18075} 0.004210526 0.400000000  23.750000
## 683  {18075}             => {8689}  0.004210526 0.250000000   8.482143
## 684  {8689}              => {18075} 0.004210526 0.142857143   8.482143
## 685  {19973}             => {4571}  0.004210526 0.400000000  15.833333
## 686  {4571}              => {19973} 0.004210526 0.166666667  15.833333
## 687  {12068}             => {18024} 0.004210526 0.400000000  13.571429
## 688  {18024}             => {12068} 0.004210526 0.142857143  13.571429
## 689  {16944}             => {27791} 0.004210526 0.666666667  15.079365
## 690  {27791}             => {16944} 0.004210526 0.095238095  15.079365
## 691  {5053}              => {11679} 0.004210526 0.500000000  19.791667
## 692  {11679}             => {5053}  0.004210526 0.166666667  19.791667
## 693  {21865}             => {7105}  0.004210526 0.285714286  11.309524
## 694  {7105}              => {21865} 0.004210526 0.166666667  11.309524
## 695  {10999}             => {16110} 0.004210526 0.333333333  26.388889
## 696  {16110}             => {10999} 0.004210526 0.333333333  26.388889
## 697  {10999}             => {16540} 0.004210526 0.333333333  17.592593
## 698  {16540}             => {10999} 0.004210526 0.222222222  17.592593
## 699  {10999}             => {11679} 0.004210526 0.333333333  13.194444
## 700  {11679}             => {10999} 0.004210526 0.166666667  13.194444
## 701  {530}               => {22749} 0.006315789 0.750000000  59.375000
## 702  {22749}             => {530}   0.006315789 0.500000000  59.375000
## 703  {530}               => {12285} 0.004210526 0.500000000  21.590909
## 704  {12285}             => {530}   0.004210526 0.181818182  21.590909
## 705  {530}               => {23628} 0.004210526 0.500000000  23.750000
## 706  {23628}             => {530}   0.004210526 0.200000000  23.750000
## 707  {530}               => {11679} 0.004210526 0.500000000  19.791667
## 708  {11679}             => {530}   0.004210526 0.166666667  19.791667
## 709  {27625}             => {18805} 0.004210526 0.400000000  19.000000
## 710  {18805}             => {27625} 0.004210526 0.200000000  19.000000
## 711  {22043}             => {22359} 0.004210526 0.500000000  39.583333
## 712  {22359}             => {22043} 0.004210526 0.333333333  39.583333
## 713  {18741}             => {14020} 0.004210526 0.285714286   7.539683
## 714  {14020}             => {18741} 0.004210526 0.111111111   7.539683
## 715  {16110}             => {16540} 0.004210526 0.333333333  17.592593
## 716  {16540}             => {16110} 0.004210526 0.222222222  17.592593
## 717  {16110}             => {11679} 0.004210526 0.333333333  13.194444
## 718  {11679}             => {16110} 0.004210526 0.166666667  13.194444
## 719  {16110}             => {14261} 0.004210526 0.333333333  14.393939
## 720  {14261}             => {16110} 0.004210526 0.181818182  14.393939
## 721  {16110}             => {14020} 0.004210526 0.333333333   8.796296
## 722  {14020}             => {16110} 0.004210526 0.111111111   8.796296
## 723  {22359}             => {29203} 0.004210526 0.333333333  17.592593
## 724  {29203}             => {22359} 0.004210526 0.222222222  17.592593
## 725  {251}               => {11176} 0.004210526 0.285714286  13.571429
## 726  {11176}             => {251}   0.004210526 0.200000000  13.571429
## 727  {251}               => {4949}  0.004210526 0.285714286  15.079365
## 728  {4949}              => {251}   0.004210526 0.222222222  15.079365
## 729  {251}               => {3627}  0.004210526 0.285714286  12.337662
## 730  {3627}              => {251}   0.004210526 0.181818182  12.337662
## 731  {25329}             => {7096}  0.004210526 0.400000000  27.142857
## 732  {7096}              => {25329} 0.004210526 0.285714286  27.142857
## 733  {25329}             => {27791} 0.004210526 0.400000000   9.047619
## 734  {27791}             => {25329} 0.004210526 0.095238095   9.047619
## 735  {7230}              => {14415} 0.004210526 0.400000000  63.333333
## 736  {14415}             => {7230}  0.004210526 0.666666667  63.333333
## 737  {18515}             => {8842}  0.004210526 1.000000000 158.333333
## 738  {8842}              => {18515} 0.004210526 0.666666667 158.333333
## 739  {18515}             => {10702} 0.004210526 1.000000000  67.857143
## 740  {10702}             => {18515} 0.004210526 0.285714286  67.857143
## 741  {14415}             => {21919} 0.004210526 0.666666667  63.333333
## 742  {21919}             => {14415} 0.004210526 0.400000000  63.333333
## 743  {14415}             => {23928} 0.004210526 0.666666667  39.583333
## 744  {23928}             => {14415} 0.004210526 0.250000000  39.583333
## 745  {22749}             => {12285} 0.004210526 0.333333333  14.393939
## 746  {12285}             => {22749} 0.004210526 0.181818182  14.393939
## 747  {22749}             => {23628} 0.004210526 0.333333333  15.833333
## 748  {23628}             => {22749} 0.004210526 0.200000000  15.833333
## 749  {15534}             => {21092} 0.004210526 0.666666667  79.166667
## 750  {21092}             => {15534} 0.004210526 0.500000000  79.166667
## 751  {29224}             => {15315} 0.004210526 0.666666667  39.583333
## 752  {15315}             => {29224} 0.004210526 0.250000000  39.583333
## 753  {7037}              => {21092} 0.004210526 1.000000000 118.750000
## 754  {21092}             => {7037}  0.004210526 0.500000000 118.750000
## 755  {17061}             => {14261} 0.004210526 1.000000000  43.181818
## 756  {14261}             => {17061} 0.004210526 0.181818182  43.181818
## 757  {11022}             => {20979} 0.004210526 0.666666667  39.583333
## 758  {20979}             => {11022} 0.004210526 0.250000000  39.583333
## 759  {11022}             => {10702} 0.004210526 0.666666667  45.238095
## 760  {10702}             => {11022} 0.004210526 0.285714286  45.238095
## 761  {22126}             => {29099} 0.004210526 0.333333333   8.796296
## 762  {29099}             => {22126} 0.004210526 0.111111111   8.796296
## 763  {24669}             => {10702} 0.004210526 0.333333333  22.619048
## 764  {10702}             => {24669} 0.004210526 0.285714286  22.619048
## 765  {8842}              => {10702} 0.004210526 0.666666667  45.238095
## 766  {10702}             => {8842}  0.004210526 0.285714286  45.238095
## 767  {21092}             => {23928} 0.004210526 0.500000000  29.687500
## 768  {23928}             => {21092} 0.004210526 0.250000000  29.687500
## 769  {16540}             => {11196} 0.004210526 0.222222222   7.037037
## 770  {11196}             => {16540} 0.004210526 0.133333333   7.037037
## 771  {16540}             => {7105}  0.004210526 0.222222222   8.796296
## 772  {7105}              => {16540} 0.004210526 0.166666667   8.796296
## 773  {16540}             => {11679} 0.004210526 0.222222222   8.796296
## 774  {11679}             => {16540} 0.004210526 0.166666667   8.796296
## 775  {10325}             => {21336} 0.004210526 1.000000000 158.333333
## 776  {21336}             => {10325} 0.004210526 0.666666667 158.333333
## 777  {10325}             => {23928} 0.004210526 1.000000000  59.375000
## 778  {23928}             => {10325} 0.004210526 0.250000000  59.375000
## 779  {10325}             => {10702} 0.004210526 1.000000000  67.857143
## 780  {10702}             => {10325} 0.004210526 0.285714286  67.857143
## 781  {2128}              => {9111}  0.004210526 0.666666667  39.583333
## 782  {9111}              => {2128}  0.004210526 0.250000000  39.583333
## 783  {29203}             => {23628} 0.004210526 0.222222222  10.555556
## 784  {23628}             => {29203} 0.004210526 0.200000000  10.555556
## 785  {29203}             => {14020} 0.006315789 0.333333333   8.796296
## 786  {14020}             => {29203} 0.006315789 0.166666667   8.796296
## 787  {19421}             => {22313} 0.004210526 0.666666667 105.555556
## 788  {22313}             => {19421} 0.004210526 0.666666667 105.555556
## 789  {19421}             => {25651} 0.004210526 0.666666667  79.166667
## 790  {25651}             => {19421} 0.004210526 0.500000000  79.166667
## 791  {19421}             => {14261} 0.004210526 0.666666667  28.787879
## 792  {14261}             => {19421} 0.004210526 0.181818182  28.787879
## 793  {22313}             => {25651} 0.004210526 0.666666667  79.166667
## 794  {25651}             => {22313} 0.004210526 0.500000000  79.166667
## 795  {22313}             => {22556} 0.004210526 0.666666667  79.166667
## 796  {22556}             => {22313} 0.004210526 0.500000000  79.166667
## 797  {22313}             => {14261} 0.004210526 0.666666667  28.787879
## 798  {14261}             => {22313} 0.004210526 0.181818182  28.787879
## 799  {11196}             => {4949}  0.004210526 0.133333333   7.037037
## 800  {4949}              => {11196} 0.004210526 0.222222222   7.037037
## 801  {9563}              => {7105}  0.006315789 0.428571429  16.964286
## 802  {7105}              => {9563}  0.006315789 0.250000000  16.964286
## 803  {1000}              => {4807}  0.004210526 0.666666667 105.555556
## 804  {4807}              => {1000}  0.004210526 0.666666667 105.555556
## 805  {1000}              => {7061}  0.004210526 0.666666667  63.333333
## 806  {7061}              => {1000}  0.004210526 0.400000000  63.333333
## 807  {1000}              => {15584} 0.004210526 0.666666667  52.777778
## 808  {15584}             => {1000}  0.004210526 0.333333333  52.777778
## 809  {21919}             => {27791} 0.004210526 0.400000000   9.047619
## 810  {27791}             => {21919} 0.004210526 0.095238095   9.047619
## 811  {21919}             => {29099} 0.004210526 0.400000000  10.555556
## 812  {29099}             => {21919} 0.004210526 0.111111111  10.555556
## 813  {3151}              => {14020} 0.008421053 0.571428571  15.079365
## 814  {14020}             => {3151}  0.008421053 0.222222222  15.079365
## 815  {26523}             => {10014} 0.004210526 0.400000000  38.000000
## 816  {10014}             => {26523} 0.004210526 0.400000000  38.000000
## 817  {26523}             => {4411}  0.004210526 0.400000000  31.666667
## 818  {4411}              => {26523} 0.004210526 0.333333333  31.666667
## 819  {26523}             => {9111}  0.004210526 0.400000000  23.750000
## 820  {9111}              => {26523} 0.004210526 0.250000000  23.750000
## 821  {10014}             => {4411}  0.004210526 0.400000000  31.666667
## 822  {4411}              => {10014} 0.004210526 0.333333333  31.666667
## 823  {21336}             => {7061}  0.004210526 0.666666667  63.333333
## 824  {7061}              => {21336} 0.004210526 0.400000000  63.333333
## 825  {21336}             => {23928} 0.004210526 0.666666667  39.583333
## 826  {23928}             => {21336} 0.004210526 0.250000000  39.583333
## 827  {21336}             => {155}   0.004210526 0.666666667  28.787879
## 828  {155}               => {21336} 0.004210526 0.181818182  28.787879
## 829  {21336}             => {10702} 0.004210526 0.666666667  45.238095
## 830  {10702}             => {21336} 0.004210526 0.285714286  45.238095
## 831  {7096}              => {23628} 0.004210526 0.285714286  13.571429
## 832  {23628}             => {7096}  0.004210526 0.200000000  13.571429
## 833  {7096}              => {10702} 0.004210526 0.285714286  19.387755
## 834  {10702}             => {7096}  0.004210526 0.285714286  19.387755
## 835  {8637}              => {27791} 0.004210526 0.181818182   4.112554
## 836  {27791}             => {8637}  0.004210526 0.095238095   4.112554
## 837  {8637}              => {7868}  0.006315789 0.272727273   5.397727
## 838  {7868}              => {8637}  0.006315789 0.125000000   5.397727
## 839  {25651}             => {14261} 0.004210526 0.500000000  21.590909
## 840  {14261}             => {25651} 0.004210526 0.181818182  21.590909
## 841  {11176}             => {4949}  0.006315789 0.300000000  15.833333
## 842  {4949}              => {11176} 0.006315789 0.333333333  15.833333
## 843  {11176}             => {3627}  0.006315789 0.300000000  12.954545
## 844  {3627}              => {11176} 0.006315789 0.272727273  12.954545
## 845  {11176}             => {23628} 0.004210526 0.200000000   9.500000
## 846  {23628}             => {11176} 0.004210526 0.200000000   9.500000
## 847  {4807}              => {7061}  0.004210526 0.666666667  63.333333
## 848  {7061}              => {4807}  0.004210526 0.400000000  63.333333
## 849  {4807}              => {15584} 0.004210526 0.666666667  52.777778
## 850  {15584}             => {4807}  0.004210526 0.333333333  52.777778
## 851  {14065}             => {14917} 0.004210526 0.666666667  79.166667
## 852  {14917}             => {14065} 0.004210526 0.500000000  79.166667
## 853  {14065}             => {4411}  0.004210526 0.666666667  52.777778
## 854  {4411}              => {14065} 0.004210526 0.333333333  52.777778
## 855  {22556}             => {155}   0.004210526 0.500000000  21.590909
## 856  {155}               => {22556} 0.004210526 0.181818182  21.590909
## 857  {22556}             => {14020} 0.004210526 0.500000000  13.194444
## 858  {14020}             => {22556} 0.004210526 0.111111111  13.194444
## 859  {14917}             => {4411}  0.004210526 0.500000000  39.583333
## 860  {4411}              => {14917} 0.004210526 0.333333333  39.583333
## 861  {17959}             => {9111}  0.004210526 0.500000000  29.687500
## 862  {9111}              => {17959} 0.004210526 0.250000000  29.687500
## 863  {12285}             => {23628} 0.004210526 0.181818182   8.636364
## 864  {23628}             => {12285} 0.004210526 0.200000000   8.636364
## 865  {12285}             => {11679} 0.004210526 0.181818182   7.196970
## 866  {11679}             => {12285} 0.004210526 0.166666667   7.196970
## 867  {12285}             => {14020} 0.006315789 0.272727273   7.196970
## 868  {14020}             => {12285} 0.006315789 0.166666667   7.196970
## 869  {12285}             => {7868}  0.004210526 0.181818182   3.598485
## 870  {7868}              => {12285} 0.004210526 0.083333333   3.598485
## 871  {4571}              => {3228}  0.004210526 0.166666667   5.654762
## 872  {3228}              => {4571}  0.004210526 0.142857143   5.654762
## 873  {4571}              => {29099} 0.004210526 0.166666667   4.398148
## 874  {29099}             => {4571}  0.004210526 0.111111111   4.398148
## 875  {15315}             => {9111}  0.004210526 0.250000000  14.843750
## 876  {9111}              => {15315} 0.004210526 0.250000000  14.843750
## 877  {15315}             => {14020} 0.004210526 0.250000000   6.597222
## 878  {14020}             => {15315} 0.004210526 0.111111111   6.597222
## 879  {7061}              => {15584} 0.004210526 0.400000000  31.666667
## 880  {15584}             => {7061}  0.004210526 0.333333333  31.666667
## 881  {7061}              => {155}   0.004210526 0.400000000  17.272727
## 882  {155}               => {7061}  0.004210526 0.181818182  17.272727
## 883  {20979}             => {14261} 0.004210526 0.250000000  10.795455
## 884  {14261}             => {20979} 0.004210526 0.181818182  10.795455
## 885  {7105}              => {11080} 0.004210526 0.166666667   5.277778
## 886  {11080}             => {7105}  0.004210526 0.133333333   5.277778
## 887  {7105}              => {155}   0.004210526 0.166666667   7.196970
## 888  {155}               => {7105}  0.004210526 0.181818182   7.196970
## 889  {7105}              => {7868}  0.004210526 0.166666667   3.298611
## 890  {7868}              => {7105}  0.004210526 0.083333333   3.298611
## 891  {4949}              => {3627}  0.004210526 0.222222222   9.595960
## 892  {3627}              => {4949}  0.004210526 0.181818182   9.595960
## 893  {4949}              => {8689}  0.008421053 0.444444444  15.079365
## 894  {8689}              => {4949}  0.008421053 0.285714286  15.079365
## 895  {3228}              => {11679} 0.004210526 0.142857143   5.654762
## 896  {11679}             => {3228}  0.004210526 0.166666667   5.654762
## 897  {18805}             => {18024} 0.006315789 0.300000000  10.178571
## 898  {18024}             => {18805} 0.006315789 0.214285714  10.178571
## 899  {18805}             => {14261} 0.004210526 0.200000000   8.636364
## 900  {14261}             => {18805} 0.004210526 0.181818182   8.636364
## 901  {23628}             => {9111}  0.004210526 0.200000000  11.875000
## 902  {9111}              => {23628} 0.004210526 0.250000000  11.875000
## 903  {15584}             => {4411}  0.004210526 0.333333333  26.388889
## 904  {4411}              => {15584} 0.004210526 0.333333333  26.388889
## 905  {15584}             => {11679} 0.004210526 0.333333333  13.194444
## 906  {11679}             => {15584} 0.004210526 0.166666667  13.194444
## 907  {18024}             => {29099} 0.004210526 0.142857143   3.769841
## 908  {29099}             => {18024} 0.004210526 0.111111111   3.769841
## 909  {8689}              => {155}   0.004210526 0.142857143   6.168831
## 910  {155}               => {8689}  0.004210526 0.181818182   6.168831
## 911  {8689}              => {14020} 0.006315789 0.214285714   5.654762
## 912  {14020}             => {8689}  0.006315789 0.166666667   5.654762
## 913  {23928}             => {10702} 0.004210526 0.250000000  16.964286
## 914  {10702}             => {23928} 0.004210526 0.285714286  16.964286
## 915  {9111}              => {29099} 0.004210526 0.250000000   6.597222
## 916  {29099}             => {9111}  0.004210526 0.111111111   6.597222
## 917  {2729,3151}         => {14020} 0.004210526 1.000000000  26.388889
## 918  {14020,2729}        => {3151}  0.004210526 1.000000000  67.857143
## 919  {14020,3151}        => {2729}  0.004210526 0.500000000  79.166667
## 920  {12717,22043}       => {22359} 0.004210526 1.000000000  79.166667
## 921  {12717,22359}       => {22043} 0.004210526 1.000000000 118.750000
## 922  {22043,22359}       => {12717} 0.004210526 1.000000000 237.500000
## 923  {23019,7692}        => {27791} 0.004210526 1.000000000  22.619048
## 924  {27791,7692}        => {23019} 0.004210526 1.000000000 237.500000
## 925  {23019,27791}       => {7692}  0.004210526 1.000000000 237.500000
## 926  {21838,24172}       => {11080} 0.004210526 1.000000000  31.666667
## 927  {11080,24172}       => {21838} 0.004210526 1.000000000 118.750000
## 928  {11080,21838}       => {24172} 0.004210526 1.000000000 158.333333
## 929  {3913,530}          => {11679} 0.004210526 1.000000000  39.583333
## 930  {11679,3913}        => {530}   0.004210526 1.000000000 118.750000
## 931  {11679,530}         => {3913}  0.004210526 1.000000000 237.500000
## 932  {10999,16110}       => {16540} 0.004210526 1.000000000  52.777778
## 933  {10999,16540}       => {16110} 0.004210526 1.000000000  79.166667
## 934  {16110,16540}       => {10999} 0.004210526 1.000000000  79.166667
## 935  {10999,16110}       => {11679} 0.004210526 1.000000000  39.583333
## 936  {10999,11679}       => {16110} 0.004210526 1.000000000  79.166667
## 937  {11679,16110}       => {10999} 0.004210526 1.000000000  79.166667
## 938  {10999,16540}       => {11679} 0.004210526 1.000000000  39.583333
## 939  {10999,11679}       => {16540} 0.004210526 1.000000000  52.777778
## 940  {11679,16540}       => {10999} 0.004210526 1.000000000  79.166667
## 941  {22749,530}         => {12285} 0.004210526 0.666666667  28.787879
## 942  {12285,530}         => {22749} 0.004210526 1.000000000  79.166667
## 943  {12285,22749}       => {530}   0.004210526 1.000000000 118.750000
## 944  {22749,530}         => {23628} 0.004210526 0.666666667  31.666667
## 945  {23628,530}         => {22749} 0.004210526 1.000000000  79.166667
## 946  {22749,23628}       => {530}   0.004210526 1.000000000 118.750000
## 947  {12285,530}         => {23628} 0.004210526 1.000000000  47.500000
## 948  {23628,530}         => {12285} 0.004210526 1.000000000  43.181818
## 949  {12285,23628}       => {530}   0.004210526 1.000000000 118.750000
## 950  {16110,16540}       => {11679} 0.004210526 1.000000000  39.583333
## 951  {11679,16110}       => {16540} 0.004210526 1.000000000  52.777778
## 952  {11679,16540}       => {16110} 0.004210526 1.000000000  79.166667
## 953  {18515,8842}        => {10702} 0.004210526 1.000000000  67.857143
## 954  {10702,18515}       => {8842}  0.004210526 1.000000000 158.333333
## 955  {10702,8842}        => {18515} 0.004210526 1.000000000 237.500000
## 956  {12285,22749}       => {23628} 0.004210526 1.000000000  47.500000
## 957  {22749,23628}       => {12285} 0.004210526 1.000000000  43.181818
## 958  {12285,23628}       => {22749} 0.004210526 1.000000000  79.166667
## 959  {10325,21336}       => {23928} 0.004210526 1.000000000  59.375000
## 960  {10325,23928}       => {21336} 0.004210526 1.000000000 158.333333
## 961  {21336,23928}       => {10325} 0.004210526 1.000000000 237.500000
## 962  {10325,21336}       => {10702} 0.004210526 1.000000000  67.857143
## 963  {10325,10702}       => {21336} 0.004210526 1.000000000 158.333333
## 964  {10702,21336}       => {10325} 0.004210526 1.000000000 237.500000
## 965  {10325,23928}       => {10702} 0.004210526 1.000000000  67.857143
## 966  {10325,10702}       => {23928} 0.004210526 1.000000000  59.375000
## 967  {10702,23928}       => {10325} 0.004210526 1.000000000 237.500000
## 968  {19421,22313}       => {25651} 0.004210526 1.000000000 118.750000
## 969  {19421,25651}       => {22313} 0.004210526 1.000000000 158.333333
## 970  {22313,25651}       => {19421} 0.004210526 1.000000000 158.333333
## 971  {19421,22313}       => {14261} 0.004210526 1.000000000  43.181818
## 972  {14261,19421}       => {22313} 0.004210526 1.000000000 158.333333
## 973  {14261,22313}       => {19421} 0.004210526 1.000000000 158.333333
## 974  {19421,25651}       => {14261} 0.004210526 1.000000000  43.181818
## 975  {14261,19421}       => {25651} 0.004210526 1.000000000 118.750000
## 976  {14261,25651}       => {19421} 0.004210526 1.000000000 158.333333
## 977  {22313,25651}       => {14261} 0.004210526 1.000000000  43.181818
## 978  {14261,22313}       => {25651} 0.004210526 1.000000000 118.750000
## 979  {14261,25651}       => {22313} 0.004210526 1.000000000 158.333333
## 980  {1000,4807}         => {7061}  0.004210526 1.000000000  95.000000
## 981  {1000,7061}         => {4807}  0.004210526 1.000000000 158.333333
## 982  {4807,7061}         => {1000}  0.004210526 1.000000000 158.333333
## 983  {1000,4807}         => {15584} 0.004210526 1.000000000  79.166667
## 984  {1000,15584}        => {4807}  0.004210526 1.000000000 158.333333
## 985  {15584,4807}        => {1000}  0.004210526 1.000000000 158.333333
## 986  {1000,7061}         => {15584} 0.004210526 1.000000000  79.166667
## 987  {1000,15584}        => {7061}  0.004210526 1.000000000  95.000000
## 988  {15584,7061}        => {1000}  0.004210526 1.000000000 158.333333
## 989  {10014,26523}       => {4411}  0.004210526 1.000000000  79.166667
## 990  {26523,4411}        => {10014} 0.004210526 1.000000000  95.000000
## 991  {10014,4411}        => {26523} 0.004210526 1.000000000  95.000000
## 992  {21336,7061}        => {155}   0.004210526 1.000000000  43.181818
## 993  {155,21336}         => {7061}  0.004210526 1.000000000  95.000000
## 994  {155,7061}          => {21336} 0.004210526 1.000000000 158.333333
## 995  {21336,23928}       => {10702} 0.004210526 1.000000000  67.857143
## 996  {10702,21336}       => {23928} 0.004210526 1.000000000  59.375000
## 997  {10702,23928}       => {21336} 0.004210526 1.000000000 158.333333
## 998  {11176,4949}        => {3627}  0.004210526 0.666666667  28.787879
## 999  {11176,3627}        => {4949}  0.004210526 0.666666667  35.185185
## 1000 {3627,4949}         => {11176} 0.004210526 1.000000000  47.500000
## 1001 {4807,7061}         => {15584} 0.004210526 1.000000000  79.166667
## 1002 {15584,4807}        => {7061}  0.004210526 1.000000000  95.000000
## 1003 {15584,7061}        => {4807}  0.004210526 1.000000000 158.333333
## 1004 {14065,14917}       => {4411}  0.004210526 1.000000000  79.166667
## 1005 {14065,4411}        => {14917} 0.004210526 1.000000000 118.750000
## 1006 {14917,4411}        => {14065} 0.004210526 1.000000000 158.333333
## 1007 {10999,16110,16540} => {11679} 0.004210526 1.000000000  39.583333
## 1008 {10999,11679,16110} => {16540} 0.004210526 1.000000000  52.777778
## 1009 {10999,11679,16540} => {16110} 0.004210526 1.000000000  79.166667
## 1010 {11679,16110,16540} => {10999} 0.004210526 1.000000000  79.166667
## 1011 {12285,22749,530}   => {23628} 0.004210526 1.000000000  47.500000
## 1012 {22749,23628,530}   => {12285} 0.004210526 1.000000000  43.181818
## 1013 {12285,23628,530}   => {22749} 0.004210526 1.000000000  79.166667
## 1014 {12285,22749,23628} => {530}   0.004210526 1.000000000 118.750000
## 1015 {10325,21336,23928} => {10702} 0.004210526 1.000000000  67.857143
## 1016 {10325,10702,21336} => {23928} 0.004210526 1.000000000  59.375000
## 1017 {10325,10702,23928} => {21336} 0.004210526 1.000000000 158.333333
## 1018 {10702,21336,23928} => {10325} 0.004210526 1.000000000 237.500000
## 1019 {19421,22313,25651} => {14261} 0.004210526 1.000000000  43.181818
## 1020 {14261,19421,22313} => {25651} 0.004210526 1.000000000 118.750000
## 1021 {14261,19421,25651} => {22313} 0.004210526 1.000000000 158.333333
## 1022 {14261,22313,25651} => {19421} 0.004210526 1.000000000 158.333333
## 1023 {1000,4807,7061}    => {15584} 0.004210526 1.000000000  79.166667
## 1024 {1000,15584,4807}   => {7061}  0.004210526 1.000000000  95.000000
## 1025 {1000,15584,7061}   => {4807}  0.004210526 1.000000000 158.333333
## 1026 {15584,4807,7061}   => {1000}  0.004210526 1.000000000 158.333333
inspect(sort(rules, by="support")[1:3])
##     lhs    rhs     support    confidence lift
## 520 {}  => {7868}  0.05052632 0.05052632 1   
## 517 {}  => {27791} 0.04421053 0.04421053 1   
## 518 {}  => {14020} 0.03789474 0.03789474 1
inspect(sort(rules, by="support", decreasing=F)[1:3])
##   lhs    rhs     support     confidence  lift
## 1 {}  => {3658}  0.004210526 0.004210526 1   
## 2 {}  => {14294} 0.004210526 0.004210526 1   
## 3 {}  => {7963}  0.004210526 0.004210526 1

实例三、分析Titanic数据,其中不同船舱的生存率

#1、加载数据并查看
str(Titanic)
##  table [1:4, 1:2, 1:2, 1:2] 0 0 35 0 0 0 17 0 118 154 ...
##  - attr(*, "dimnames")=List of 4
##   ..$ Class   : chr [1:4] "1st" "2nd" "3rd" "Crew"
##   ..$ Sex     : chr [1:2] "Male" "Female"
##   ..$ Age     : chr [1:2] "Child" "Adult"
##   ..$ Survived: chr [1:2] "No" "Yes"
dim(Titanic)
## [1] 4 2 2 2
str(Titanic)
##  table [1:4, 1:2, 1:2, 1:2] 0 0 35 0 0 0 17 0 118 154 ...
##  - attr(*, "dimnames")=List of 4
##   ..$ Class   : chr [1:4] "1st" "2nd" "3rd" "Crew"
##   ..$ Sex     : chr [1:2] "Male" "Female"
##   ..$ Age     : chr [1:2] "Child" "Adult"
##   ..$ Survived: chr [1:2] "No" "Yes"
str(df)
## function (x, df1, df2, ncp, log = FALSE)

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