在 TidyGraph 中计算 Everett-Valente 经纪分数
Computing the Everett-Valente Brokerage Score in TidyGraph
我想计算定向网络中每个节点的 Everett-Valente 经纪分数（Everett 和 Valente 2016）。该分数基于中介中心性。本质上，这控制了网络规模。代理控制 information/resource 流的能力受网络大小 and/or 连接冗余的调节。对于无向图，Everett - Valente Brokerage Score 计算如下：
- 计算节点介数中心性。
- 将每个节点的计算介数中心性加倍，并将 (n - 1) 添加到每个非悬垂条目。
- 将每个非零分数除以节点的度数。
我计划使用 if_else 语句来处理非挂件和零分，例如
g <- g %>%
activate(nodes) %>%
mutate(betweenness = centrality_betweenness(),
ev_brokerage = if_else(..if_else(..)..))
我不知道如何执行ev_brokerage（条件语句）。为了将此扩展到定向案例，Everett 和 Valente (2016) 提供了以下规则：
对于电动车内经纪业务：
- 计算 v 的节点介数中心性
- 如果节点介数中心性 = 0 添加 j，其中 j = 可以到达 v 的顶点数。
- 将每个非零和除以v的入度
对于 EV 外经纪业务：
- 计算 v 的节点介数中心性
- 如果节点介数中心性 = 0 添加 k，其中 k = v 可以到达的顶点数。
- 将每个非零和除以v的出度
v 的 EV 经纪 = in-EV 和 out-EV 的平均值。
如果有人可以帮助我处理 mutate() 语句，我将不胜感激。我想知道如何在定向情况下计算出 j 和 k，并在无向情况下计算出非悬垂节点。
如果您只是将它变成一个计算 igraph 对象分数的独立函数，那么推理（和概括）起来会简单得多。然后它可以适应 tidygraph 友好的东西。
suppressPackageStartupMessages(library(tidygraph))
if_else <- dplyr::if_else
case_when <- dplyr::case_when
map2_dbl <- purrr::map2_dbl
使用无向图非常简单，因为您不需要嵌套任何控制流。
create_notable("Zachary") %>%
mutate(pendant = centrality_degree() == 1, # is a node a pendant?
btwn = centrality_betweenness()) %>% # raw betweenness
mutate(ev_step1 = if_else(pendant, # if it's a pendant...
btwn * 2, # double betweenness...
btwn * 2 + (graph_order() - 1)), # else double it AND subtract n (nodes) - 1
ev_brok = if_else(ev_step1 == 0, # if it's 0...
ev_step1, # leave it as is...
ev_step1 / centrality_degree()) # else divide it by raw degree
) %>%
select(ev_brok, btwn, pendant)
#> # A tbl_graph: 34 nodes and 78 edges
#> #
#> # An undirected simple graph with 1 component
#> #
#> # Node Data: 34 x 3 (active)
#> ev_brok btwn pendant
#> <dbl> <dbl> <lgl>
#> 1 30.9 231. FALSE
#> 2 10.00 28.5 FALSE
#> 3 18.5 75.9 FALSE
#> 4 7.60 6.29 FALSE
#> 5 11.2 0.333 FALSE
#> 6 16.2 15.8 FALSE
#> # ... with 28 more rows
#> #
#> # Edge Data: 78 x 2
#> from to
#> <int> <int>
#> 1 1 2
#> 2 1 3
#> 3 1 4
#> # ... with 75 more rows
这是一个有向图示例...
(g <- matrix(c(1, 2,
1, 3,
3, 4,
4, 1,
2, 5,
5, 6, # 6 is pendant with in-tie
7, 2, # 7 is pendant with out-ie
4, 8, # 8 is pendant with in-tie
9, 10,
10, 11,
11, 12, # 12 is a pendant with in-tie
11, 13,
9, 13),
ncol = 2, byrow = TRUE) %>%
igraph::graph_from_edgelist()) %>% plot()
与其将 ifelse() 彼此嵌套，不如将它们用 dplyr::case_when() 包裹起来（但它仍然应该放在可以测试和验证的适当函数中）。
(
res <- g %>%
as_tbl_graph() %>%
mutate(btwn = centrality_betweenness(),
in_reach = local_size(order = graph_order(), mode = "in") - 1, # reach being max. ego graph order - 1 for ego
out_reach = local_size(order = graph_order(), mode = "out") - 1,
in_deg = centrality_degree(mode = "in"),
out_deg = centrality_degree(mode = "out")) %>%
mutate(ev_in = case_when(
btwn == 0 ~ if_else(btwn + in_reach == 0, # if btwn is 0 and if btwn + in_reach is 0
btwn + in_reach, # then btwn + in_reach (0)
(btwn + in_reach) / in_deg), # else add btwn and in_reach, then divide by in_deg
btwn != 0 ~ btwn / in_deg
)) %>%
mutate(ev_out = case_when(
btwn == 0 ~ if_else(btwn + out_reach == 0,
btwn + out_reach,
(btwn + out_reach) / out_deg),
btwn != 0 ~ btwn / out_deg
)) %>%
mutate(ev_brok = map2_dbl(ev_in, ev_out, ~ mean(c(.x, .y)))) %>%
select(ev_brok, starts_with("ev_"), btwn, everything())
)
#> # A tbl_graph: 13 nodes and 13 edges
#> #
#> # A directed simple graph with 2 components
#> #
#> # Node Data: 13 x 8 (active)
#> ev_brok ev_in ev_out btwn in_reach out_reach in_deg out_deg
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 5.25 7 3.5 7 2 6 1 2
#> 2 6 4 8 8 4 2 2 1
#> 3 2 2 2 2 2 6 1 1
#> 4 4.5 6 3 6 2 6 1 2
#> 5 5 5 5 5 5 1 1 1
#> 6 3 6 0 0 6 0 1 0
#> # ... with 7 more rows
#> #
#> # Edge Data: 13 x 2
#> from to
#> <int> <int>
#> 1 1 2
#> 2 1 3
#> 3 3 4
#> # ... with 10 more rows
这里是完整的 table 检查数学：
res %>% as_tibble()
#> # A tibble: 13 x 8
#> ev_brok ev_in ev_out btwn in_reach out_reach in_deg out_deg
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 5.25 7 3.5 7 2 6 1 2
#> 2 6 4 8 8 4 2 2 1
#> 3 2 2 2 2 2 6 1 1
#> 4 4.5 6 3 6 2 6 1 2
#> 5 5 5 5 5 5 1 1 1
#> 6 3 6 0 0 6 0 1 0
#> 7 1.5 0 3 0 0 3 0 1
#> 8 1.5 3 0 0 3 0 1 0
#> 9 1 0 2 0 0 4 0 2
#> 10 2 2 2 2 1 3 1 1
#> 11 2.25 3 1.5 3 2 2 1 2
#> 12 1.5 3 0 0 3 0 1 0
#> 13 0.75 1.5 0 0 3 0 2 0
在对照 Everett 和 Valente (2016) 中提出的 campnet 示例进行检查后，定向网络的 EV 经纪分数可以计算如下：
g <- g %>%
activate(nodes) %>%
# compute in-degree, out-degree, and betweenness centrality
mutate(betweenness = centrality_betweenness(),
in_degree = centrality_degree(mode = "in"),
out_degree = centrality_degree(mode = "out"),
in_reach = local_size(order = graph_order(), mode = "in") - 1,
out_reach = local_size(order = graph_order(), mode = "out") - 1) %>%
# compute everett-valente brokerage score
mutate(ev_in = if_else(betweenness != 0, betweenness + in_reach, betweenness),
ev_in = if_else(ev_in != 0, ev_in / in_degree, ev_in),
ev_out = if_else(betweenness != 0, betweenness + out_reach, betweenness),
ev_out = if_else(ev_out != 0, ev_out / out_degree, ev_out),
ev_brokerage = (ev_in + ev_out) / 2)
使用 Granovetter (1973) 在 Everett 和 Valente (2016) 中提出的假设无向网络，EV 经纪分数可以计算如下：
edgelist <- data.frame(from = c(1,1,1,2,2,2,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,8,8,8,9,
9,10,10,10,11,11,11,11,11,12,12,12,13,13,13,13,14,14,
14,14,15,15,15,16,16,17,17,17,18,18,18,18,19,19,20,20,
20,20,20,21,21,22,22,22,23,23,23,24,24,24,25,25,25,25),
to = c(2,3,24,1,3,4,1,2,4,5,2,3,5,6,3,4,6,5,5,7,6,8,9,10,11,
14,8,10,9,8,11,10,8,12,14,13,11,14,13,11,12,14,15,8,11,
12,13,13,16,17,15,17,15,16,18,17,19,20,21,18,20,19,18,
21,25,22,18,20,20,25,23,24,25,22,1,25,23,24,23,22,20))
g <- igraph::graph_from_edgelist(as.matrix(edgelist), directed = F) %>% simplify()
g <- as_tbl_graph(g) %>%
activate(nodes) %>%
# compute brokerage
mutate(betweenness = centrality_betweenness(),
degree = centrality_degree(),
ev_condition = if_else(betweenness != 0, betweenness * 2 + graph_order() - 1, betweenness),
ev_brokerage = if_else(ev_condition != 0, ev_condition / degree, ev_condition))
data <- g %>% as.tibble()
我没有按照 Everett 和 Valente (2016) 规范化 EV 经纪评分。
我想计算定向网络中每个节点的 Everett-Valente 经纪分数（Everett 和 Valente 2016）。该分数基于中介中心性。本质上，这控制了网络规模。代理控制 information/resource 流的能力受网络大小 and/or 连接冗余的调节。对于无向图，Everett - Valente Brokerage Score 计算如下：
- 计算节点介数中心性。
- 将每个节点的计算介数中心性加倍，并将 (n - 1) 添加到每个非悬垂条目。
- 将每个非零分数除以节点的度数。
我计划使用 if_else 语句来处理非挂件和零分，例如
g <- g %>%
activate(nodes) %>%
mutate(betweenness = centrality_betweenness(),
ev_brokerage = if_else(..if_else(..)..))
我不知道如何执行ev_brokerage（条件语句）。为了将此扩展到定向案例，Everett 和 Valente (2016) 提供了以下规则：
对于电动车内经纪业务：
- 计算 v 的节点介数中心性
- 如果节点介数中心性 = 0 添加 j，其中 j = 可以到达 v 的顶点数。
- 将每个非零和除以v的入度
对于 EV 外经纪业务：
- 计算 v 的节点介数中心性
- 如果节点介数中心性 = 0 添加 k，其中 k = v 可以到达的顶点数。
- 将每个非零和除以v的出度
v 的 EV 经纪 = in-EV 和 out-EV 的平均值。
如果有人可以帮助我处理 mutate() 语句，我将不胜感激。我想知道如何在定向情况下计算出 j 和 k，并在无向情况下计算出非悬垂节点。
如果您只是将它变成一个计算 igraph 对象分数的独立函数，那么推理（和概括）起来会简单得多。然后它可以适应 tidygraph 友好的东西。
suppressPackageStartupMessages(library(tidygraph))
if_else <- dplyr::if_else
case_when <- dplyr::case_when
map2_dbl <- purrr::map2_dbl
使用无向图非常简单，因为您不需要嵌套任何控制流。
create_notable("Zachary") %>%
mutate(pendant = centrality_degree() == 1, # is a node a pendant?
btwn = centrality_betweenness()) %>% # raw betweenness
mutate(ev_step1 = if_else(pendant, # if it's a pendant...
btwn * 2, # double betweenness...
btwn * 2 + (graph_order() - 1)), # else double it AND subtract n (nodes) - 1
ev_brok = if_else(ev_step1 == 0, # if it's 0...
ev_step1, # leave it as is...
ev_step1 / centrality_degree()) # else divide it by raw degree
) %>%
select(ev_brok, btwn, pendant)
#> # A tbl_graph: 34 nodes and 78 edges
#> #
#> # An undirected simple graph with 1 component
#> #
#> # Node Data: 34 x 3 (active)
#> ev_brok btwn pendant
#> <dbl> <dbl> <lgl>
#> 1 30.9 231. FALSE
#> 2 10.00 28.5 FALSE
#> 3 18.5 75.9 FALSE
#> 4 7.60 6.29 FALSE
#> 5 11.2 0.333 FALSE
#> 6 16.2 15.8 FALSE
#> # ... with 28 more rows
#> #
#> # Edge Data: 78 x 2
#> from to
#> <int> <int>
#> 1 1 2
#> 2 1 3
#> 3 1 4
#> # ... with 75 more rows
这是一个有向图示例...
(g <- matrix(c(1, 2,
1, 3,
3, 4,
4, 1,
2, 5,
5, 6, # 6 is pendant with in-tie
7, 2, # 7 is pendant with out-ie
4, 8, # 8 is pendant with in-tie
9, 10,
10, 11,
11, 12, # 12 is a pendant with in-tie
11, 13,
9, 13),
ncol = 2, byrow = TRUE) %>%
igraph::graph_from_edgelist()) %>% plot()
与其将 ifelse() 彼此嵌套，不如将它们用 dplyr::case_when() 包裹起来（但它仍然应该放在可以测试和验证的适当函数中）。
(
res <- g %>%
as_tbl_graph() %>%
mutate(btwn = centrality_betweenness(),
in_reach = local_size(order = graph_order(), mode = "in") - 1, # reach being max. ego graph order - 1 for ego
out_reach = local_size(order = graph_order(), mode = "out") - 1,
in_deg = centrality_degree(mode = "in"),
out_deg = centrality_degree(mode = "out")) %>%
mutate(ev_in = case_when(
btwn == 0 ~ if_else(btwn + in_reach == 0, # if btwn is 0 and if btwn + in_reach is 0
btwn + in_reach, # then btwn + in_reach (0)
(btwn + in_reach) / in_deg), # else add btwn and in_reach, then divide by in_deg
btwn != 0 ~ btwn / in_deg
)) %>%
mutate(ev_out = case_when(
btwn == 0 ~ if_else(btwn + out_reach == 0,
btwn + out_reach,
(btwn + out_reach) / out_deg),
btwn != 0 ~ btwn / out_deg
)) %>%
mutate(ev_brok = map2_dbl(ev_in, ev_out, ~ mean(c(.x, .y)))) %>%
select(ev_brok, starts_with("ev_"), btwn, everything())
)
#> # A tbl_graph: 13 nodes and 13 edges
#> #
#> # A directed simple graph with 2 components
#> #
#> # Node Data: 13 x 8 (active)
#> ev_brok ev_in ev_out btwn in_reach out_reach in_deg out_deg
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 5.25 7 3.5 7 2 6 1 2
#> 2 6 4 8 8 4 2 2 1
#> 3 2 2 2 2 2 6 1 1
#> 4 4.5 6 3 6 2 6 1 2
#> 5 5 5 5 5 5 1 1 1
#> 6 3 6 0 0 6 0 1 0
#> # ... with 7 more rows
#> #
#> # Edge Data: 13 x 2
#> from to
#> <int> <int>
#> 1 1 2
#> 2 1 3
#> 3 3 4
#> # ... with 10 more rows
这里是完整的 table 检查数学：
res %>% as_tibble()
#> # A tibble: 13 x 8
#> ev_brok ev_in ev_out btwn in_reach out_reach in_deg out_deg
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 5.25 7 3.5 7 2 6 1 2
#> 2 6 4 8 8 4 2 2 1
#> 3 2 2 2 2 2 6 1 1
#> 4 4.5 6 3 6 2 6 1 2
#> 5 5 5 5 5 5 1 1 1
#> 6 3 6 0 0 6 0 1 0
#> 7 1.5 0 3 0 0 3 0 1
#> 8 1.5 3 0 0 3 0 1 0
#> 9 1 0 2 0 0 4 0 2
#> 10 2 2 2 2 1 3 1 1
#> 11 2.25 3 1.5 3 2 2 1 2
#> 12 1.5 3 0 0 3 0 1 0
#> 13 0.75 1.5 0 0 3 0 2 0
在对照 Everett 和 Valente (2016) 中提出的 campnet 示例进行检查后，定向网络的 EV 经纪分数可以计算如下：
g <- g %>%
activate(nodes) %>%
# compute in-degree, out-degree, and betweenness centrality
mutate(betweenness = centrality_betweenness(),
in_degree = centrality_degree(mode = "in"),
out_degree = centrality_degree(mode = "out"),
in_reach = local_size(order = graph_order(), mode = "in") - 1,
out_reach = local_size(order = graph_order(), mode = "out") - 1) %>%
# compute everett-valente brokerage score
mutate(ev_in = if_else(betweenness != 0, betweenness + in_reach, betweenness),
ev_in = if_else(ev_in != 0, ev_in / in_degree, ev_in),
ev_out = if_else(betweenness != 0, betweenness + out_reach, betweenness),
ev_out = if_else(ev_out != 0, ev_out / out_degree, ev_out),
ev_brokerage = (ev_in + ev_out) / 2)
使用 Granovetter (1973) 在 Everett 和 Valente (2016) 中提出的假设无向网络，EV 经纪分数可以计算如下：
edgelist <- data.frame(from = c(1,1,1,2,2,2,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,8,8,8,9,
9,10,10,10,11,11,11,11,11,12,12,12,13,13,13,13,14,14,
14,14,15,15,15,16,16,17,17,17,18,18,18,18,19,19,20,20,
20,20,20,21,21,22,22,22,23,23,23,24,24,24,25,25,25,25),
to = c(2,3,24,1,3,4,1,2,4,5,2,3,5,6,3,4,6,5,5,7,6,8,9,10,11,
14,8,10,9,8,11,10,8,12,14,13,11,14,13,11,12,14,15,8,11,
12,13,13,16,17,15,17,15,16,18,17,19,20,21,18,20,19,18,
21,25,22,18,20,20,25,23,24,25,22,1,25,23,24,23,22,20))
g <- igraph::graph_from_edgelist(as.matrix(edgelist), directed = F) %>% simplify()
g <- as_tbl_graph(g) %>%
activate(nodes) %>%
# compute brokerage
mutate(betweenness = centrality_betweenness(),
degree = centrality_degree(),
ev_condition = if_else(betweenness != 0, betweenness * 2 + graph_order() - 1, betweenness),
ev_brokerage = if_else(ev_condition != 0, ev_condition / degree, ev_condition))
data <- g %>% as.tibble()
我没有按照 Everett 和 Valente (2016) 规范化 EV 经纪评分。