01-degree-assortativity.Rmd

# 度度匹配性

*分析空手道俱乐部网络和经济物理学家网络的度度匹配性。*

## 空手道俱乐部网络

```{r karate}
karate_edge_list <- read_tsv("datasets/空手道俱乐部.txt", col_names = FALSE) %>%
  as.matrix()
karate_graph <- graph_from_edgelist(karate_edge_list, directed = FALSE)
# calculate assortativity using Pearson correlation coefficient
assortativity_pearson <- get.edgelist(karate_graph) %>%
  as_tibble(.name_repair = ~ c("V1", "V2")) %>%
  mutate(
    dgr1 = degree(karate_graph, V1),
    dgr2 = degree(karate_graph, V2)
  ) %>%
  summarise(r = cor(dgr1, dgr2)) %>%
  pull(r)
# calculate assortativity using Newman's method
assortativity_newman <- assortativity_degree(karate_graph)
```

我们首先采用老师在课上提出的简单方法，即取出所有边两侧顶点的度值，然后计算皮尔逊相关值，得到的同配性（或度相关）系数为`r round(assortativity_pearson, 3)`。

而采用基于Newman的计算公式的来自`igraph`包的`assortativity_degree`函数算出来的度相关系数则为`r round(assortativity_newman, 3)`。

可以看到这两个值之间差异不大，且都为负值，说明空手道网络是异配的，即度值较大的节点更多与度值较小的节点连接。

## 经济物理学家网络

```{r author}
papers_authors <- read_tsv(
  "datasets/经济物理学家合作网络/paperID_authorID.txt",
  col_names = c("paper_id", "author_id")
) %>%
  # index of 0 is not supported in R
  mutate_all(~ . + 1)
num_authors <- n_distinct(papers_authors$author_id)
author_matrix <- matrix(0, num_authors, num_authors)
# get the number of cooperation papers for each pair of authors
papers <- unique(papers_authors$paper_id)
authors_coop <- tibble()
for (paper in papers) {
  paper_authors <- filter(papers_authors, paper_id == paper)
  if (nrow(paper_authors) <= 1)
    next
  paper_coop <- expand_grid(
    author1 = paper_authors$author_id,
    author2 = paper_authors$author_id
  ) %>%
    filter(author1 != author2) %>%
    add_column(n = 1)
  authors_coop <- bind_rows(authors_coop, paper_coop)
}
authors_coop <- authors_coop %>%
  group_by(author1, author2) %>%
  summarise(n = sum(n)) %>%
  ungroup()
# construct a non-weighted adjacency matrix
author_matrix[as.matrix(select(authors_coop, starts_with("author")))] <- 1
author_graph_raw <- graph_from_adjacency_matrix(author_matrix, "undirected")
# find the largest connected components
author_graph <- decompose(author_graph_raw) %>%
  enframe(name = "id", value = "graph") %>%
  mutate(num_vertices = map_dbl(graph, vcount)) %>%
  filter(num_vertices == max(num_vertices)) %>%
  pluck("graph", 1)
# calculate assortativity using Pearson correlation coefficient
assortativity_pearson <- get.edgelist(author_graph) %>%
  as_tibble(.name_repair = ~ c("V1", "V2")) %>%
  mutate(
    dgr1 = degree(author_graph, V1),
    dgr2 = degree(author_graph, V2)
  ) %>%
  summarise(r = cor(dgr1, dgr2)) %>%
  pull(r)
# calculate assortativity using Newman's method
assortativity_newman <- assortativity_degree(author_graph)
```

和空手道网络相同，我们首先采用老师在课上提出的计算皮尔逊相关方法，得到的度相关系数为`r round(assortativity_pearson, 3)`。

而采用基于Newman的计算公式的来自`igraph`包的`assortativity_degree`函数算出来的度相关系数则为`r round(assortativity_newman, 3)`。

可以看出来对于经济物理学家网络似乎这两个值的差异相对较大，不过度相关系数的绝对值都比较小，说明经济物理学家网络的度匹配性应该是中立的。