由tidygraph计算的无向网络图显示了更多的度中心性

Question

我有一个包含26个节点的清理后的数据集。我使用tidygraph将这26个节点放在一个无向网络图中，其中我使用centrality_degree()函数来计算中心度。然而，当我绘制结果网络时，我可能的最高中心度是40，这应该是不可能的。当我将图形更改为directed时，这一点就被更正了。

我有点困惑，因为我过去用过的其他方法，我手动计算中心度，我从来没有遇到过这个问题。

这是正常行为，还是我做错了什么？

可重现的例子：

library(tidygraph)
library(ggraph)
library(tidyverse)

nodes <- structure(list(id = 1:26, label = c("a", "b", "c", "d", "e", 
    "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", 
    "s", "t", "u", "v", "w", "x", "y", "z")), row.names = c(NA, -26L
    ), class = "data.frame")
    edges <- structure(list(from = c(21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 
    21L, 21L, 21L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
    11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 12L, 12L, 
    12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 
    12L, 12L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 
    13L, 13L, 13L, 13L, 13L, 13L, 13L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
    3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 18L, 
    18L, 18L, 18L, 18L, 18L, 18L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
    16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 24L, 
    24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 
    24L, 24L, 24L, 24L, 24L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
    5L, 5L, 5L, 5L, 5L, 5L, 5L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
    7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 14L, 14L, 14L, 14L, 
    14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
    10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
    6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
    6L, 6L, 6L, 6L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 
    25L, 25L, 25L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 
    9L, 9L, 9L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 
    22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 15L, 15L, 15L, 
    15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 
    15L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 
    20L, 20L, 20L, 20L, 20L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
    8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 17L, 17L, 17L, 17L, 17L), 
        to = c(1L, 12L, 3L, 16L, 24L, 4L, 10L, 6L, 22L, 2L, 8L, 1L, 
        12L, 13L, 3L, 18L, 16L, 24L, 5L, 7L, 14L, 4L, 10L, 6L, 9L, 
        22L, 15L, 2L, 20L, 8L, 21L, 12L, 13L, 3L, 16L, 24L, 5L, 7L, 
        14L, 4L, 10L, 6L, 22L, 15L, 2L, 8L, 17L, 21L, 1L, 13L, 3L, 
        16L, 5L, 7L, 14L, 10L, 6L, 9L, 22L, 15L, 2L, 20L, 8L, 17L, 
        21L, 1L, 3L, 18L, 16L, 5L, 7L, 14L, 4L, 10L, 6L, 25L, 9L, 
        22L, 15L, 20L, 8L, 17L, 21L, 11L, 1L, 12L, 13L, 18L, 16L, 
        24L, 5L, 7L, 14L, 4L, 10L, 6L, 25L, 9L, 22L, 15L, 20L, 8L, 
        17L, 1L, 3L, 10L, 6L, 22L, 20L, 8L, 21L, 11L, 1L, 13L, 3L, 
        18L, 24L, 7L, 4L, 10L, 6L, 25L, 9L, 22L, 15L, 2L, 20L, 8L, 
        17L, 21L, 11L, 1L, 12L, 13L, 18L, 16L, 5L, 7L, 14L, 10L, 
        6L, 25L, 9L, 22L, 15L, 20L, 8L, 17L, 1L, 3L, 18L, 16L, 7L, 
        14L, 4L, 10L, 6L, 9L, 22L, 15L, 2L, 20L, 8L, 17L, 21L, 11L, 
        1L, 12L, 13L, 3L, 18L, 16L, 24L, 14L, 4L, 10L, 6L, 25L, 9L, 
        22L, 15L, 2L, 20L, 8L, 11L, 1L, 3L, 18L, 16L, 7L, 10L, 6L, 
        9L, 22L, 15L, 2L, 20L, 8L, 17L, 21L, 11L, 1L, 12L, 13L, 3L, 
        18L, 16L, 24L, 5L, 7L, 14L, 10L, 6L, 25L, 9L, 22L, 15L, 2L, 
        20L, 8L, 17L, 21L, 11L, 1L, 12L, 13L, 3L, 18L, 16L, 24L, 
        5L, 7L, 14L, 4L, 6L, 25L, 9L, 22L, 15L, 2L, 20L, 8L, 17L, 
        21L, 11L, 1L, 12L, 13L, 3L, 18L, 24L, 5L, 7L, 14L, 4L, 10L, 
        25L, 9L, 22L, 15L, 2L, 20L, 8L, 21L, 1L, 13L, 3L, 18L, 5L, 
        10L, 6L, 22L, 2L, 20L, 8L, 21L, 1L, 13L, 3L, 18L, 16L, 24L, 
        4L, 10L, 6L, 22L, 15L, 2L, 20L, 8L, 11L, 1L, 12L, 13L, 3L, 
        16L, 24L, 5L, 7L, 14L, 4L, 10L, 6L, 25L, 9L, 15L, 2L, 20L, 
        8L, 17L, 21L, 1L, 12L, 3L, 18L, 16L, 24L, 7L, 10L, 6L, 25L, 
        9L, 22L, 2L, 20L, 8L, 17L, 21L, 11L, 1L, 12L, 13L, 3L, 18L, 
        16L, 24L, 5L, 7L, 14L, 4L, 6L, 25L, 9L, 22L, 15L, 20L, 8L, 
        17L, 21L, 11L, 1L, 3L, 16L, 24L, 7L, 10L, 6L, 22L, 2L, 8L, 
        21L, 11L, 1L, 12L, 13L, 3L, 18L, 16L, 24L, 14L, 4L, 10L, 
        6L, 25L, 9L, 22L, 2L, 20L, 7L, 6L, 25L, 22L, 8L), weight = c(3L, 
        1L, 3L, 2L, 1L, 1L, 5L, 1L, 8L, 2L, 1L, 2L, 3L, 2L, 5L, 1L, 
        4L, 1L, 4L, 4L, 4L, 1L, 5L, 13L, 3L, 7L, 3L, 2L, 3L, 8L, 
        1L, 1L, 1L, 15L, 10L, 7L, 2L, 4L, 2L, 5L, 19L, 23L, 6L, 2L, 
        11L, 7L, 1L, 1L, 2L, 3L, 3L, 5L, 4L, 5L, 4L, 4L, 21L, 2L, 
        9L, 8L, 1L, 1L, 12L, 1L, 2L, 1L, 3L, 1L, 6L, 6L, 5L, 6L, 
        1L, 6L, 22L, 2L, 2L, 9L, 8L, 3L, 13L, 1L, 5L, 6L, 4L, 10L, 
        13L, 3L, 41L, 46L, 11L, 39L, 9L, 55L, 2L, 108L, 2L, 8L, 31L, 
        30L, 13L, 39L, 2L, 2L, 1L, 3L, 4L, 8L, 5L, 1L, 8L, 1L, 6L, 
        1L, 8L, 2L, 3L, 23L, 2L, 12L, 96L, 1L, 3L, 21L, 1L, 6L, 12L, 
        38L, 4L, 5L, 4L, 4L, 8L, 8L, 3L, 29L, 3L, 11L, 3L, 3L, 63L, 
        2L, 5L, 18L, 19L, 4L, 25L, 1L, 2L, 3L, 1L, 7L, 6L, 7L, 1L, 
        3L, 17L, 1L, 3L, 6L, 1L, 4L, 11L, 1L, 5L, 1L, 5L, 1L, 1L, 
        15L, 4L, 7L, 3L, 1L, 4L, 12L, 8L, 1L, 9L, 32L, 3L, 7L, 5L, 
        35L, 1L, 1L, 3L, 1L, 6L, 4L, 4L, 12L, 2L, 5L, 4L, 2L, 2L, 
        9L, 1L, 2L, 3L, 4L, 9L, 13L, 2L, 1L, 25L, 25L, 10L, 14L, 
        10L, 4L, 59L, 4L, 5L, 21L, 19L, 1L, 8L, 27L, 3L, 5L, 8L, 
        8L, 11L, 12L, 111L, 5L, 50L, 45L, 15L, 32L, 10L, 49L, 109L, 
        1L, 8L, 28L, 39L, 53L, 13L, 48L, 5L, 13L, 2L, 20L, 3L, 3L, 
        27L, 10L, 8L, 1L, 58L, 1L, 7L, 32L, 13L, 21L, 110L, 1L, 17L, 
        27L, 124L, 1L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 7L, 1L, 1L, 1L, 
        2L, 2L, 1L, 5L, 2L, 2L, 2L, 1L, 3L, 3L, 14L, 2L, 2L, 4L, 
        1L, 3L, 14L, 5L, 8L, 44L, 16L, 14L, 4L, 12L, 4L, 19L, 41L, 
        47L, 2L, 1L, 11L, 24L, 2L, 18L, 1L, 7L, 5L, 1L, 7L, 3L, 27L, 
        3L, 15L, 7L, 54L, 1L, 4L, 17L, 5L, 6L, 27L, 1L, 1L, 2L, 3L, 
        4L, 10L, 56L, 3L, 25L, 25L, 7L, 16L, 5L, 29L, 59L, 3L, 3L, 
        20L, 17L, 5L, 31L, 3L, 6L, 1L, 4L, 7L, 1L, 3L, 1L, 6L, 5L, 
        13L, 1L, 2L, 9L, 1L, 15L, 2L, 1L, 16L, 4L, 4L, 3L, 1L, 6L, 
        17L, 10L, 1L, 13L, 63L, 11L, 12L, 1L, 5L, 1L, 2L, 3L)), row.names = c(NA, 
    -383L), class = c("tbl_df", "tbl", "data.frame"))

routes_tidy <- tbl_graph(nodes=nodes, edges=edges, directed=FALSE) %>% mutate(neighbors = centrality_degree())

# Filtering out 3 nodes out of the graph as they have no connections and zoom the figure way out
ggraph(routes_tidy, layout="graphopt") +
  geom_node_point(aes(size=neighbors, filter=(label!="z" & label!="s" & label!="w"))) + 
  geom_edge_link(aes(width=weight, alpha=weight)) +
  scale_edge_width(range=c(0.2, 2)) +
  geom_node_text(aes(label=label, fontface="bold", size=neighbors, filter=(label!="z" & label!="s" & label!="w")), repel=TRUE) +
  labs(edge_width="N") +
  theme_graph()

Answer 1

我是tidygraph的新手，偶然发现了这个问题，感到困惑，觉得这是一种很好的了解东西的方式。所以，我不知道这是一个bug还是一个特性，但这种行为是因为你有双重边缘而触发的：

# Given your edges
edges %>%
  filter((from == 1 & to == 2) | from == 2 & to == 1)
# A tibble: 2 x 3
   from    to weight
  <int> <int>  <int>
1     1     2     11
2     2     1      3

在度数中心性的计算中，这些连接被算作2个连接。消除这些双边的一种方法是将网络转换为简单网络：

routes_simple <-
  routes_tidy %>%
  morph(to_simple) %>%
  crystallise() %>%
  pull(graph) %>%
  getElement(1) %>%
  activate(nodes) %>%
  mutate(neighbors = centrality_degree()) 

现在最高温度是22度(也可能是最高温度，大概是25度)。