igraph 中的接近度归一化似乎不起作用
Closeness normalisation in igraph doesn't seem to work
我从一个包含（符号）边列表和权重的数据框构建了一个 igraph 图。这是数据框：
>dput(y)
structure(list(from = c("United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"Togo", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "Brunei", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "Bangladesh", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "Tunisia", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "Senegal",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "Gambia", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom"
), to = c("Antigua", "Argentina", "Australia", "Austria", "Bahamas",
"Bahrain", "Bangladesh", "Barbados", "Belgium", "Bermuda", "Bolivia",
"Botswana", "Brazil", "British Virgin", "Bulgaria", "Burkina Faso",
"Canada", "Cayman Islands", "Chile", "China", "Colombia", "Costa Rica",
"Croatia", "Cuba", "Cyprus", "Czech Republic", "Dem Rep Congo",
"Denmark", "Dominican Rep", "Ecuador", "Egypt", "Estonia", "Finland",
"France", "Gabon", "Georgia", "Germany", "Ghana", "Gibraltar",
"Greece", "Greenland", "Guernsey", "Guinea", "Guyana", "Honduras",
"Hong Kong", "Hungary", "Iceland", "India", "Indonesia", "Iran",
"Ireland-Rep", "Isle of Man", "Israel", "Italy", "Ivory Coast",
"Jamaica", "Japan", "Jersey", "Jordan", "Kazakhstan", "Kenya",
"Kyrgyzstan", "Lebanon", "Libya", "Liechtenstein", "Lithuania",
"Luxembourg", "Madagascar", "Madagascar", "Malaysia", "Malta",
"Mauritania", "Mauritius", "Mexico", "Monaco", "Montenegro",
"Morocco", "Mozambique", "Myanmar(Burma)", "Namibia", "Nepal",
"Neth Antilles", "Netherlands", "New Zealand", "Nigeria", "Norway",
"Oman", "Pakistan", "Panama", "Paraguay", "Peru", "Philippines",
"Poland", "Portugal", "Puerto Rico", "Rep of Congo", "Rep of Congo",
"Romania", "Russian Fed", "Rwanda", "Saudi Arabia", "Serbia & Mont.",
"Serbia & Mont.", "Sierra Leone", "Singapore", "Slovak Rep",
"Slovenia", "South Africa", "South Korea", "Spain", "Sri Lanka",
"Sweden", "Switzerland", "Taiwan", "Tajikistan", "Tanzania",
"Thailand", "Turkey", "Uganda", "Ukraine", "United Kingdom",
"United States", "Unknown", "US Virgin Is", "Utd Arab Em", "Uzbekistan",
"Venezuela", "Vietnam", "Zambia", "Zimbabwe"), weight = c(0.00652158317953266,
0.000647329216751068, 0.0000251029566387844, 0.000214174129564211,
0.0456767003151692, 0.00508385824169679, 0.00186393289841566,
0.158755357993332, 0.000182399538893966, 0.0000415260352876621,
0.00594332445796881, 0.01093302429318, 0.000114591772539915,
0.00429007790781481, 0.00284147415679254, 0.0500675912481851,
0.0000287088339723346, 0.00263403275683136, 0.000448611949766228,
0.000679452144147131, 0.000252040964722078, 0.0136804520021342,
0.00654146306362881, 0.526315789473684, 0.00191543727517555,
0.00017092079991618, 0.00132017906908893, 0.0000627870348540249,
0.240153698366955, 0.0132308384382318, 0.000733717703580983,
0.0114161767224157, 0.0001650156302805, 0.000012155463860949,
0.0154993102806925, 0.00647282707195195, 0.00000360412192179335,
0.152230172020094, 0.0041524790299809, 0.000592713769629939,
0.242130750605327, 0.00135643063417201, 0.5, 0.0434782608695652,
0.00117508813160987, 0.000221503566207416, 0.0011185457116076,
0.000215847012817643, 0.0000670498565971192, 0.000454026832077722,
0.305530094714329, 0.0000503965198179275, 0.000317324724102019,
0.00273860057510612, 0.0000367428222896657, 0.194287934719254,
0.0724270297675092, 0.000171929928925887, 0.00109404761514031,
0.0500025001250063, 0.0027947871629836, 0.056695770495521, 0.175469380593087,
0.0431034482758621, 1.96078431372549, 0.111831804965332, 0.00155982636012959,
0.000119064940161533, 0.0171291538198013, 1.5625, 0.00732745671304947,
0.00243336237145763, 0.00729394602479942, 0.023089355806973,
0.000311509885298945, 0.00462855820411942, 0.150715900527506,
0.0199992000319987, 0.137703112090333, 0.00384711562506011, 0.0333355557037136,
0.0842815002107038, 0.0445811600017832, 0.0000184857050227916,
0.000437414895464401, 0.0146017376067752, 0.000147070437768394,
0.135080372821829, 0.0272420180887, 0.000557344010558325, 0.0625,
0.000839938046169714, 0.00254634993468612, 0.000289772340360796,
0.000306490675634175, 0.0333333333333333, 0.0930232558139535,
0.0357142857142857, 0.00229049421993784, 0.00024170323435183,
0.198609731876862, 0.0213269636801809, 0.046189376443418, 0.0176056338028169,
0.035297024460838, 0.000462550522080774, 0.0252748641476052,
0.00447631581303324, 0.000064428161729891, 0.000223055060249402,
0.0000167409403597136, 0.0205846027171676, 0.0000149409029764804,
0.0000902779740069852, 0.00052983585155483, 0.228571428571429,
0.155787505842031, 0.00130985033650055, 0.0000850992563686581,
0.0333333333333333, 0.0053616715547239, 0.085397096498719, 0.00000198776814942642,
0.0568181818181818, 0.914076782449726, 0.00308342198171531, 0.338983050847458,
0.00303167187608951, 0.00502777847608034, 0.00731743011854237,
0.075993616536211)), row.names = c(20L, 51L, 113L, 142L, 158L,
167L, 176L, 183L, 218L, 239L, 250L, 266L, 304L, 320L, 361L, 367L,
436L, 454L, 478L, 524L, 548L, 565L, 581L, 585L, 595L, 626L, 631L,
661L, 669L, 682L, 704L, 737L, 773L, 820L, 826L, 837L, 888L, 899L,
906L, 926L, 929L, 948L, 953L, 957L, 964L, 1003L, 1035L, 1039L,
1077L, 1103L, 1110L, 1134L, 1144L, 1164L, 1206L, 1212L, 1221L,
1252L, 1263L, 1273L, 1294L, 1304L, 1317L, 1336L, 1341L, 1342L,
1360L, 1382L, 1398L, 1400L, 1436L, 1449L, 1458L, 1466L, 1498L,
1516L, 1527L, 1536L, 1546L, 1552L, 1561L, 1562L, 1569L, 1618L,
1642L, 1655L, 1699L, 1703L, 1715L, 1728L, 1743L, 1765L, 1784L,
1817L, 1839L, 1846L, 1856L, 1857L, 1892L, 1934L, 1938L, 1946L,
1977L, 1981L, 1986L, 2024L, 2046L, 2062L, 2097L, 2125L, 2168L,
2180L, 2229L, 2269L, 2291L, 2294L, 2302L, 2329L, 2377L, 2388L,
2416L, 2438L, 2557L, 2562L, 2578L, 2593L, 2605L, 2630L, 2647L,
2676L, 2684L), class = "data.frame")
我使用了下面的代码
g <- graph_from_data_frame(y, directed=TRUE, vertices=unique(c(y$from,y$to)))
closeness_score=as.data.frame(closeness(g, mode="out",normalized = T))
计算结果网络的接近中心性（模式“out”测量从顶点开始的路径）。所有国家的接近度结果值为
United Kingdom 13.173718
Togo 19.973000
Brunei 58.380000
Bangladesh 11.865000
Tunisia 10.750000
Senegal 21.650000
Gambia 6.222462
和 NaN 用于所有其他顶点。我无法解释这个结果，因为如果我不执行归一化，即
closeness_score=as.data.frame(closeness(g, mode="out",normalized = F))
我得到
United Kingdom 0.10455332
Togo 19.97300000
Brunei 58.38000000
Bangladesh 11.86500000
Tunisia 10.75000000
Senegal 21.65000000
Gambia 0.04899576
正如我们在 igraph R manual 中所读到的，“归一化是通过将原始接近度乘以 n-1 来执行的，其中 n 是图中顶点的数量”。那么，为什么多哥、文莱、孟加拉国、突尼斯和塞内加尔的亲密度没有变化？
手册有点过时了。我将更新它以发布 1.3.2。如有疑问，请检查 the igraph C library 的文档，如果您发现与 R 文档有任何不一致，请报告问题。
您的图表没有（强）连接，并且对于此类图表来说，紧密度没有多大意义。通常，顶点 v 的接近度定义为从 v 到所有其他顶点的平均距离的倒数。但是，如果无法从 v 到达其他一些顶点怎么办？ R/igraph 1.3 将只考虑到可达顶点的距离。相应地，归一化是通过可达顶点的数量来完成的，而不是n-1。如果没有顶点可达，它 returns NaN.
简要说明：
- 对于
normalized=T，它计算从 v 可达的所有顶点的平均距离的倒数。
- 对于
normalized=F，它计算从 v. 可达的所有顶点的距离总和的倒数
请注意，断开连接的图形的行为自 1.2 以来已发生变化，请参阅 the changelog。 1.2 版认为到不可达顶点的距离是 n，这完全是任意的，而不是数学上的 well-founded.
考虑是否：
- 您打算考虑此图中的边缘方向
- 谐波中心性更适合您的应用
我从一个包含（符号）边列表和权重的数据框构建了一个 igraph 图。这是数据框：
>dput(y)
structure(list(from = c("United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"Togo", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "Brunei", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "Bangladesh", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "Tunisia", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "Senegal",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "Gambia", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom",
"United Kingdom", "United Kingdom", "United Kingdom", "United Kingdom"
), to = c("Antigua", "Argentina", "Australia", "Austria", "Bahamas",
"Bahrain", "Bangladesh", "Barbados", "Belgium", "Bermuda", "Bolivia",
"Botswana", "Brazil", "British Virgin", "Bulgaria", "Burkina Faso",
"Canada", "Cayman Islands", "Chile", "China", "Colombia", "Costa Rica",
"Croatia", "Cuba", "Cyprus", "Czech Republic", "Dem Rep Congo",
"Denmark", "Dominican Rep", "Ecuador", "Egypt", "Estonia", "Finland",
"France", "Gabon", "Georgia", "Germany", "Ghana", "Gibraltar",
"Greece", "Greenland", "Guernsey", "Guinea", "Guyana", "Honduras",
"Hong Kong", "Hungary", "Iceland", "India", "Indonesia", "Iran",
"Ireland-Rep", "Isle of Man", "Israel", "Italy", "Ivory Coast",
"Jamaica", "Japan", "Jersey", "Jordan", "Kazakhstan", "Kenya",
"Kyrgyzstan", "Lebanon", "Libya", "Liechtenstein", "Lithuania",
"Luxembourg", "Madagascar", "Madagascar", "Malaysia", "Malta",
"Mauritania", "Mauritius", "Mexico", "Monaco", "Montenegro",
"Morocco", "Mozambique", "Myanmar(Burma)", "Namibia", "Nepal",
"Neth Antilles", "Netherlands", "New Zealand", "Nigeria", "Norway",
"Oman", "Pakistan", "Panama", "Paraguay", "Peru", "Philippines",
"Poland", "Portugal", "Puerto Rico", "Rep of Congo", "Rep of Congo",
"Romania", "Russian Fed", "Rwanda", "Saudi Arabia", "Serbia & Mont.",
"Serbia & Mont.", "Sierra Leone", "Singapore", "Slovak Rep",
"Slovenia", "South Africa", "South Korea", "Spain", "Sri Lanka",
"Sweden", "Switzerland", "Taiwan", "Tajikistan", "Tanzania",
"Thailand", "Turkey", "Uganda", "Ukraine", "United Kingdom",
"United States", "Unknown", "US Virgin Is", "Utd Arab Em", "Uzbekistan",
"Venezuela", "Vietnam", "Zambia", "Zimbabwe"), weight = c(0.00652158317953266,
0.000647329216751068, 0.0000251029566387844, 0.000214174129564211,
0.0456767003151692, 0.00508385824169679, 0.00186393289841566,
0.158755357993332, 0.000182399538893966, 0.0000415260352876621,
0.00594332445796881, 0.01093302429318, 0.000114591772539915,
0.00429007790781481, 0.00284147415679254, 0.0500675912481851,
0.0000287088339723346, 0.00263403275683136, 0.000448611949766228,
0.000679452144147131, 0.000252040964722078, 0.0136804520021342,
0.00654146306362881, 0.526315789473684, 0.00191543727517555,
0.00017092079991618, 0.00132017906908893, 0.0000627870348540249,
0.240153698366955, 0.0132308384382318, 0.000733717703580983,
0.0114161767224157, 0.0001650156302805, 0.000012155463860949,
0.0154993102806925, 0.00647282707195195, 0.00000360412192179335,
0.152230172020094, 0.0041524790299809, 0.000592713769629939,
0.242130750605327, 0.00135643063417201, 0.5, 0.0434782608695652,
0.00117508813160987, 0.000221503566207416, 0.0011185457116076,
0.000215847012817643, 0.0000670498565971192, 0.000454026832077722,
0.305530094714329, 0.0000503965198179275, 0.000317324724102019,
0.00273860057510612, 0.0000367428222896657, 0.194287934719254,
0.0724270297675092, 0.000171929928925887, 0.00109404761514031,
0.0500025001250063, 0.0027947871629836, 0.056695770495521, 0.175469380593087,
0.0431034482758621, 1.96078431372549, 0.111831804965332, 0.00155982636012959,
0.000119064940161533, 0.0171291538198013, 1.5625, 0.00732745671304947,
0.00243336237145763, 0.00729394602479942, 0.023089355806973,
0.000311509885298945, 0.00462855820411942, 0.150715900527506,
0.0199992000319987, 0.137703112090333, 0.00384711562506011, 0.0333355557037136,
0.0842815002107038, 0.0445811600017832, 0.0000184857050227916,
0.000437414895464401, 0.0146017376067752, 0.000147070437768394,
0.135080372821829, 0.0272420180887, 0.000557344010558325, 0.0625,
0.000839938046169714, 0.00254634993468612, 0.000289772340360796,
0.000306490675634175, 0.0333333333333333, 0.0930232558139535,
0.0357142857142857, 0.00229049421993784, 0.00024170323435183,
0.198609731876862, 0.0213269636801809, 0.046189376443418, 0.0176056338028169,
0.035297024460838, 0.000462550522080774, 0.0252748641476052,
0.00447631581303324, 0.000064428161729891, 0.000223055060249402,
0.0000167409403597136, 0.0205846027171676, 0.0000149409029764804,
0.0000902779740069852, 0.00052983585155483, 0.228571428571429,
0.155787505842031, 0.00130985033650055, 0.0000850992563686581,
0.0333333333333333, 0.0053616715547239, 0.085397096498719, 0.00000198776814942642,
0.0568181818181818, 0.914076782449726, 0.00308342198171531, 0.338983050847458,
0.00303167187608951, 0.00502777847608034, 0.00731743011854237,
0.075993616536211)), row.names = c(20L, 51L, 113L, 142L, 158L,
167L, 176L, 183L, 218L, 239L, 250L, 266L, 304L, 320L, 361L, 367L,
436L, 454L, 478L, 524L, 548L, 565L, 581L, 585L, 595L, 626L, 631L,
661L, 669L, 682L, 704L, 737L, 773L, 820L, 826L, 837L, 888L, 899L,
906L, 926L, 929L, 948L, 953L, 957L, 964L, 1003L, 1035L, 1039L,
1077L, 1103L, 1110L, 1134L, 1144L, 1164L, 1206L, 1212L, 1221L,
1252L, 1263L, 1273L, 1294L, 1304L, 1317L, 1336L, 1341L, 1342L,
1360L, 1382L, 1398L, 1400L, 1436L, 1449L, 1458L, 1466L, 1498L,
1516L, 1527L, 1536L, 1546L, 1552L, 1561L, 1562L, 1569L, 1618L,
1642L, 1655L, 1699L, 1703L, 1715L, 1728L, 1743L, 1765L, 1784L,
1817L, 1839L, 1846L, 1856L, 1857L, 1892L, 1934L, 1938L, 1946L,
1977L, 1981L, 1986L, 2024L, 2046L, 2062L, 2097L, 2125L, 2168L,
2180L, 2229L, 2269L, 2291L, 2294L, 2302L, 2329L, 2377L, 2388L,
2416L, 2438L, 2557L, 2562L, 2578L, 2593L, 2605L, 2630L, 2647L,
2676L, 2684L), class = "data.frame")
我使用了下面的代码
g <- graph_from_data_frame(y, directed=TRUE, vertices=unique(c(y$from,y$to)))
closeness_score=as.data.frame(closeness(g, mode="out",normalized = T))
计算结果网络的接近中心性（模式“out”测量从顶点开始的路径）。所有国家的接近度结果值为
United Kingdom 13.173718
Togo 19.973000
Brunei 58.380000
Bangladesh 11.865000
Tunisia 10.750000
Senegal 21.650000
Gambia 6.222462
和 NaN 用于所有其他顶点。我无法解释这个结果，因为如果我不执行归一化，即
closeness_score=as.data.frame(closeness(g, mode="out",normalized = F))
我得到
United Kingdom 0.10455332
Togo 19.97300000
Brunei 58.38000000
Bangladesh 11.86500000
Tunisia 10.75000000
Senegal 21.65000000
Gambia 0.04899576
正如我们在 igraph R manual 中所读到的，“归一化是通过将原始接近度乘以 n-1 来执行的，其中 n 是图中顶点的数量”。那么，为什么多哥、文莱、孟加拉国、突尼斯和塞内加尔的亲密度没有变化？
手册有点过时了。我将更新它以发布 1.3.2。如有疑问，请检查 the igraph C library 的文档，如果您发现与 R 文档有任何不一致，请报告问题。
您的图表没有（强）连接，并且对于此类图表来说，紧密度没有多大意义。通常，顶点 v 的接近度定义为从 v 到所有其他顶点的平均距离的倒数。但是，如果无法从 v 到达其他一些顶点怎么办？ R/igraph 1.3 将只考虑到可达顶点的距离。相应地，归一化是通过可达顶点的数量来完成的，而不是n-1。如果没有顶点可达，它 returns NaN.
简要说明：
- 对于
normalized=T，它计算从v可达的所有顶点的平均距离的倒数。 - 对于
normalized=F，它计算从v. 可达的所有顶点的距离总和的倒数
请注意，断开连接的图形的行为自 1.2 以来已发生变化，请参阅 the changelog。 1.2 版认为到不可达顶点的距离是 n，这完全是任意的，而不是数学上的 well-founded.
考虑是否：
- 您打算考虑此图中的边缘方向
- 谐波中心性更适合您的应用