# tets


```{r}
#| label: fig-moved-accounts
#| fig-height: 4
#| eval: false
moved_accounts <- arrow::read_feather("data/scratch/moved_accounts.feather")
popular_servers <- arrow::read_feather("data/scratch/popular_servers.feather")
server_movement_data <- left_join(
  (moved_accounts %>% group_by(server) %>% summarize(out_count = sum(count)) %>% select(server, out_count)),
  (moved_accounts %>% group_by(moved_server) %>% summarize(in_count = sum(count)) %>% select(moved_server, in_count) %>% rename(server=moved_server)),
  by="server"
) %>% replace_na(list(out_count = 0, in_count = 0)) %>%
  mutate(diff = in_count - out_count) %>%
  arrange(diff) %>%
  left_join(., popular_servers, by="server") %>%
  rename(user_count = count) %>% arrange(desc(user_count))
server_movement_data %>%
  ggplot(aes(x=user_count, y=diff)) +
  geom_point() + scale_x_log10() + theme_bw_small_labels()
```

If there was no relationship, we would expect these jumps to be random with respect to server size.

```{r}
popular_servers <-
  arrow::read_feather("data/scratch/popular_servers.feather")
moved_accounts <-
  arrow::read_feather("data/scratch/moved_accounts.feather") %>%
  # Remove loops
  filter(server != moved_server)
activity <-
  arrow::read_feather("data/scratch/activity.feather",
                      col_select = c("server", "logins")) %>%
  arrange(desc(logins))
popular_and_large_servers <-
  popular_servers %>% filter(count >= 1) %>%
  mutate(count = log10(count))
jm <- arrow::read_feather("data/scratch/joinmastodon.feather")
ma <- moved_accounts %>%
  filter(server %in% popular_and_large_servers$server) %>%
  filter(moved_server %in% popular_and_large_servers$server)
# Construct network
edgeNet <- network(ma, matrix.type = "edgelist")
edgeNet %v% "user_count" <-
  left_join((as_tibble(edgeNet %v% 'vertex.names') %>% rename(server = value)),
            popular_and_large_servers,
            by = "server") %>%
  select(count) %>%
  unlist()
edgeNet %v% "in_jm" <-
  as_tibble(edgeNet %v% 'vertex.names') %>%
  mutate(in_jm = value %in% jm$domain) %>%
  select(in_jm) %>% unlist()
```

We construct an exponential family random graph model (ERGM) where nodes represent servers and weighted directed edges represent the number of accounts that moved between servers.

$$
  \begin{aligned}
\text{Sum}_{i,j} = & \beta_1 (log10(\text{user count}_j) - log10(\text{user count}_i)) + \\
& \beta_2 \\
& \beta_3 \\
& \beta_4 \\
\end{aligned}
$$
  
  ```{r}
#| label: ergm-model
#| cache: true
m1 <-
  ergm(
    edgeNet ~ sum +
      diff("user_count", pow = 1, form = "sum") +
      nodecov("user_count", form = "sum") +
      nodematch("in_jm", diff = TRUE, form = "sum"),
    response = "count",
    reference =  ~ Binomial(3),
    control=control.ergm(parallel=4, parallel.type="PSOCK")
  )

save(m1, file = "data/scratch/ergm-model.rda")
```


```{r}
#| label: tag-ergm-result
#| output: asis
ergm_model <- load("data/scratch/ergm-model.rda")

modelsummary(
  m1,
  escape = FALSE,
  coef_rename = c(
    "sum" = "$\\beta_0$ Intercept",
    "diff.sum.t-h.user_count" = "$\\beta_1$ User Count Difference",
    "nodecov.sum.user_count" = "$\\beta_2$ User Count (Node Covariate)",
    "nodematch.sum.in_jm.TRUE" = "$\\beta_3$ In JoinMastodon (Both True)",
    "nodematch.sum.in_jm.FALSE" = "$\\beta_4$ In JoinMastodon (Both False)"
  ),
)
```

We find a strong preference for accounts to move from large servers to smaller servers. 

```{python}
#| eval: false
#| include: false
import random

def simulate_account_moves(origin: str, servers: dict, n: int):
  server_list = list(set(servers.keys()) - {origin})
weights = [servers[x] for x in server_list]
return pl.DataFrame({
  "simulation": list(range(n)),
  "server": [origin] * n,
  "moved_server": random.choices(server_list, weights=weights, k=n)
})

simulations = pl.concat([simulate_account_moves(row["server"], {x["server"]: x["count"] for x in popular_servers.iter_rows(named=True)}, 1000) for row in maccounts.iter_rows(named=True)])
m_counts = maccounts.join(popular_servers, how="inner", on="server").rename({"count": "origin_count"}).join(popular_servers.rename({"server": "moved_server"}), how="inner", on="moved_server").rename({"count": "target_count"})
sim_counts = simulations.join(popular_servers, how="inner", on="server").rename({"count": "origin_count"}).join(popular_servers.rename({"server": "moved_server"}), how="inner", on="moved_server").rename({"count": "target_count"})
```