网络分析

图论基本知识

网络图有两个主要特征: nodes and edges，

nodes:
edges:

当然还包括其它的概念，比如

adjacency matrix:
edge list:
Node list:
Weighted network graph:
Directed and undirected network graph:

有向图 !图片

无向图 !图片

先介绍tidygraph宏包

tidygraph: A tidy API for graph manipulation

Tidy Network Anaylsis

在 tidygraph 框架, 网络数据可以分解成两个tidy数据框:
一个是 node data
一个是 edge data

tidygraph 宏包提供了node数据框和edge数据框相互切换的方案，并且可以使用dplyr的语法操控
tidygraph 提供了常用的网络结构的algorithms，比如，计算网络拓扑结构中节点的重要性、中心度等。

Create network objects

创建网络对象主要有两个函数:

tbl_graph(). Creates a network object from nodes and edges data
as_tbl_graph(). Converts network data and objects to a tbl_graph network.

案例: 欧盟总统之间通话以及次数。

R

library("navdata") # devtools::install_github("kassambara/navdata")
data("phone.call2")

R

node_list <- phone.call2$nodes
node_list

R

edge_list <- phone.call2$edges
edge_list

Use `tbl_graph`

Create a tbl_graph network object using the phone call data:

R

phone.net <- tbl_graph(nodes = node_list, edges = edge_list, directed = TRUE)

Visualize the network graph

R

ggraph(phone.net, layout = "graphopt") +
  geom_edge_link(width = 1, colour = "lightgray") +
  geom_node_point(size = 4, colour = "red") +
  geom_node_text(aes(label = label), repel = TRUE) +
  theme_graph()

Use `as_tbl_graph`

mtcars data set: R 的内置数据集，记录了32种不同品牌的轿车的的11个属性

1、we create a correlation matrix network graph

R

library(corrr)
res.cor <- datasets::mtcars[, c(1, 3:6)] %>% # (1)
  t() %>%
  corrr::correlate() %>% # (2)
  corrr::shave(upper = TRUE) %>% # (3)
  corrr::stretch(na.rm = TRUE) %>% # (4)
  dplyr::filter(r &gt;= 0.998) # (5)
res.cor

2、Create the correlation network graph:

R

set.seed(1)
cor.graph <- as_tbl_graph(res.cor, directed = FALSE)

R

ggraph(cor.graph) +
  geom_edge_link() +
  geom_node_point() +
  geom_node_text(
    aes(label = name),
    size = 3, repel = TRUE
  ) +
  theme_graph()

Print out a network object

R

cor.graph

extract the current active data

R

cor.graph %>%
  activate(edges) %>%
  arrange(desc(r))

Note that, to extract the current active data as a tibble, you can use the function as_tibble(cor.graph).

Network graph manipulation

Car groups info (Number of cylinders)

R

# Car groups info
cars.group <- tibble(
  name = rownames(datasets::mtcars),
  cyl = as.factor(datasets::mtcars$cyl)
)
cars.group

Modify the nodes data:

R

# Modify the nodes data
cor.graph <- cor.graph %>%
  activate(nodes) %>%
  left_join(cars.group, by = "name") %>%
  rename(label = name)
cor.graph

Modify the edge data.

R

# Modify the edge data.
cor.graph <- cor.graph %>%
  activate(edges) %>%
  rename(weight = r)
cor.graph

Display the final modified graphs object:

R

cor.graph

Visualize the correlation network

R

set.seed(1)
ggraph(cor.graph) +
  geom_edge_link(aes(width = weight), alpha = 0.2) +
  scale_edge_width(range = c(0.2, 1)) +
  geom_node_point(aes(color = cyl), size = 2) +
  geom_node_text(aes(label = label), size = 3, repel = TRUE) +
  theme_graph()

Network analysis

Centrality

Centrality is an important concept when analyzing network graph.

The tidygraph package contains more than 10 centrality measures, prefixed with the term centrality_ :

R

# centrality_alpha()
# centrality_power()
# centrality_authority()
# centrality_betweenness()
# centrality_closeness()
# centrality_hub()
# centrality_degree()
# centrality_pagerank()
# centrality_eigen()
# centrality_subgraph
# centrality_edge_betweenness()

example:

use the phone call network graph ( 欧盟总统之间通话以及次数)
compute nodes centrality

R

set.seed(123)
phone.net %>%
  activate(nodes) %>%
  mutate(centrality = centrality_authority())

R

set.seed(123)
phone.net %>%
  activate(nodes) %>%
  mutate(centrality = centrality_authority()) %>%
  ggraph(layout = "graphopt") +
  geom_edge_link(width = 1, colour = "lightgray") +
  geom_node_point(aes(size = centrality, colour = centrality)) +
  geom_node_text(aes(label = label), repel = TRUE) +
  scale_color_gradient(low = "yellow", high = "red") +
  theme_graph()

Clustering

Clustering is a common operation in network analysis and it consists of grouping nodes based on the graph topology.

Many clustering algorithms from are available in the tidygraph package and prefixed with the term group_. These include:
Infomap community finding. It groups nodes by minimizing the expected description length of a random walker trajectory. R function: group_infomap()
Community structure detection based on edge betweenness. It groups densely connected nodes. R function: group_edge_betweenness()