Data Exploration and Visualization

In this part we will visualize the network and look for temporal and structural patterns.

We will use the inferences we make to create the Shiny App.

For the purposes of this this investigation, we will focus on the network of the SouthSeafood Express Corp.

1 Setup

1.1 Loading Packages

We will use the following packages.

  • knitr - For better table displays

  • tidyverse - Data science tools

  • tidygraph - For graph manipulations

  • igraph - Contains functions for network analysis

  • ggraph - For plotting network data

  • ggiraph - Interactive plots

  • DT - interactive tables

  • ggtext - Tools for text formatting

  • scales - Extends functions to operate on ggplot2 scales. Useful for wrapping text and formatting numbers in axes.

pacman::p_load(knitr, tidyverse, tidygraph, igraph, ggraph, ggiraph, DT, ggtext, scales)

1.2 Loading the data

We will load the supernetwork data from the RDS we prepared during data preparation.

supernetwork <- readRDS("data/rds/supernetwork.rds")

2 Extracting the subnetwork

2.1 Extracting connected network

We will use the extract_subnetwork function to extract the subnetwork within distance = 3 of SouthSeafood Express Corp.

sec_network <- supernetwork %>% extract_subnetwork("SouthSeafood Express Corp", distance = 3)

Let us check the node and edge counts to confirm if this is a smaller graph.

vcount(sec_network)
[1] 12
ecount(sec_network)
[1] 16

2.2 Most active years

The edges of the subnetwork contains relationship from all-time.

We will prioritize our investigation by activity. In order to do this, we need to identify the years with the most number of transactions for the network.

Code 
sec_edges <- sec_network %>% as_data_frame(what="edges")

start_df <- sec_edges %>%
  mutate(year = lubridate::year(start_date)) %>%
  group_by(year) %>% summarize(count = n())

end_df <- sec_edges %>%
  mutate(year = lubridate::year(end_date)) %>%
  group_by(year) %>% summarize(count = n())

txns_per_year <- start_df %>% rbind(end_df) %>%
  group_by(year) %>% summarize(count = sum(count)) %>%
  filter(!is.na(year))
  
ggplot(txns_per_year, aes(x = year, y = count, fill = year)) +
  geom_bar(stat = "identity",
           width = 0.75,
           fill = ifelse(txns_per_year$year == 2035, "blue", "grey50")) +
  geom_text(
    aes(label = count), nudge_y = 0.35, size = 4.5,
    family = "Roboto Condensed", fontface = "bold") +
  scale_x_continuous(n.breaks = 8) +
  scale_y_continuous(breaks = breaks_pretty()) +
  labs(x = "Year", y = "Number of transactions") +
  ggtitle(
    "Yearly Network Transactions",
    "2035 is the the most active year for SouthSeafood Express Corp's network"
  ) +
  theme_minimal() +
  theme(
    text = element_text(family = "Roboto Condensed"),
    panel.grid.minor = element_blank(),
    axis.line = element_line(),
    axis.ticks = element_line(),
    plot.title = element_text(face = "bold"),
  )

2035 is the year that has the most transactions. Let examine this year more closely.

Double counting

Take note that an edge may be counted twice as there are a maximum of 2 events per edge. One for starting the relationship and another for ending the relationship.

We will use an interactive datatable to investigate the transactions for this year.

sec_network %>%
  as_data_frame(what="edges") %>%
  filter((year(start_date) == 2035) | (year(end_date) == 2035)) %>%
  select(from, to, subtype, start_date, end_date) %>%
  arrange(start_date) %>%
  datatable()
Findings

2035 is a suspicious year for this network as there our many Shareholdership transactions that happened.

The most notable are in rows 4 and 8, which indicate a change in Shareholdership of SouthSeafood Express Corp from AguaLeska Transit N.V. to Tainamarine Fishing Co.

The first in this series of events is Liam Conti giving up the shareholdership of AguaLeska Transit N.V.

This is very suspicious as this can indicate that Liam Conti wants to distance himself from SouthSeafood Express Corp after the company was caught illegal fishing.

3 Visualizing the Network

While were able to derive some insights from the table, it can only give us a hint as to the time period that we should look at more closely.

To better see patterns in the network, we need to visualize it.

3.1 Plotting Function

We will use the function plot_fishing_relationships() to visualize the business relationships within the network:

Show MAPPINGS 
MAPPINGS = list(
  # Available shapes: https://www.datanovia.com/en/blog/ggplot-point-shapes-best-tips/
  node_supertype_to_shape = c(
    "Person" = 24, # Triangle
    "Organization" = 21 # Circle
  ),
  # Color schemes
  # Colorblind pallettes from https://davidmathlogic.com/colorblind
  node_subtype_to_color = c(
    "Person" = "#44AA99",
    "CEO" = "#117733",
    "Company" = "#DDCC77",
    "FishingCompany" = "#88CCEE",
    "LogisticsCompany" = "#332288",
    "FinancialCompany" = "#AA4499",
    "NGO" = "#CC6677",
    "NewsCompany" = "#882255"
  ),
  
  edge_relationship_subtype_to_color = c(
    "WorksFor" = "#D81B60",
    "Shareholdership" = "#FFC107",
    "BeneficialOwnership" = "#004D40",
    "FamilyRelationship" = "#1E88E5"
  ),
  edge_power_subtype_to_color = c(
    "WorksFor" = "#D81B60",
    "HasShareholder" = "#FFC107",
    "OwnedBy" = "#004D40",
    "FamilyRelationship" = "#1E88E5"
  )
)
Show COMMON_THEME 
COMMON_THEME = theme(
  text = element_text(family = "Roboto Condensed", color = "grey50"),
  plot.title = element_text(size = 12, margin = margin(b = 6), color = "grey25"),
  plot.subtitle = element_markdown(size = 8, margin = margin(b = 6), color = "grey50"),
  plot.margin = margin(2, 0, 0, 0, unit = "pt"),
  
  # Legend styles
  legend.position = "right",
  legend.location = "plot",
  legend.justification = "top",
  legend.direction = "vertical",
  legend.title = element_markdown(
    color = "grey25",
    face = "bold",
    size = unit(8, "pt")
  ),
  legend.text = element_text(size = unit(6, "pt"), vjust = 0.5),
  legend.box.spacing = unit(4, "pt"),
  legend.margin = margin(r = 6),
  legend.spacing.x = unit(2, "pt"),
  legend.spacing.y = unit(8, "pt"),
  legend.key.size = unit(12, "pt"),
  
  panel.border = element_rect(
    color = "grey50",
    fill = NA,
    linewidth = 0.5
  )
)
Show code for plot_fishing_relationships() 
plot_fishing_relationships <- function(graph,
                                       # Name of nodes to emphasize
                                       emphasize_nodes = c(),
                                       # Layout options
                                       layout = "nicely",
                                       title = NULL,
                                       subtitle = NULL) {
  set.seed(4231)
  
  if(vcount(graph) == 0) {
    return(NULL)
  }
  
  nodes <- as_data_frame(graph, what = "vertices")
  
  g <- ggraph(graph, layout = layout) +
    # Render nodes
    geom_point_interactive(
      aes(
        x = x,
        y = y,
        # Replace ' as it causes tooltips to not render correctly in JS
        data_id = sub("'", "&#39;", name),
        tooltip = sprintf("%s<br/>(%s)", sub("'", "&#39;", name), subtype),
        fill = subtype,
        # To show people as triangle, organizations as circle
        # See scale_shape_manual code below
        shape = supertype,
      ),
      alpha = nodes$included,
      size = 7.5,
      # Thicken border if emphasized
      color = ifelse(nodes$name %in% emphasize_nodes, "black", "grey50"),
      stroke = ifelse(nodes$name %in% emphasize_nodes, 1, 0.5),
    ) +
    geom_node_text(
      aes(label = alias),
      family = "Roboto Condensed",
      size = 2,
      color = "white",
      fontface = ifelse(nodes$name %in% emphasize_nodes, "bold", "plain"),
      alpha = nodes$included,
    ) +
    
    # Render edges. Use geom_edge fan so edges along the same path don't overlap
    geom_edge_fan(
      aes(
        color = subtype,
        filter = ifelse(included == 1, TRUE, FALSE)
      ),
      strength = 0.5,
      arrow = arrow(type = "closed", length = unit(2, "pt")),
      end_cap = circle(3.2, "mm"),
      start_cap = circle(3.2, "mm"),
      alpha = 0.8
    ) +
    scale_shape_manual(values = MAPPINGS$node_supertype_to_shape) +
    scale_fill_manual(values = MAPPINGS$node_subtype_to_color) +
    scale_edge_color_manual(values = MAPPINGS$edge_relationship_subtype_to_color) +
    
    # Change legend names
    labs(shape = "Node Supertypes",
         fill = "Node Subtypes",
         edge_color = "Edge Subtypes") +
    
    # Make sure the plot is not clipped
    scale_x_continuous(expand = expansion(mult = c(0.10, 0.10))) +
    scale_y_continuous(expand = expansion(mult = c(0.10, 0.10))) +
    
    # Style legend keys
    guides(
      shape = guide_legend(
        override.aes = list(size = 3, fill = "blue"),
        order = 1
      ),
      fill = guide_legend(
        override.aes = list(
          size = 4,
          shape = 22,
          color = NA
        ),
        order = 2,
      ),
      edge_color = guide_legend(order = 3),
    ) +
    ggtitle(title, subtitle) +
    
    # Style graph
    unset_graph_style() +
    theme_graph(base_family = "Roboto Condensed",
                plot_margin = margin(0)) +
    COMMON_THEME
  
  girafe(
    ggobj = g,
    width_svg = 6,
    height_svg = 6 * 0.618,
    options = list(
      opts_tooltip(
        css = paste0(
          "background-color:black;color:white;",
          "font-family:Roboto Condensed;font-size:10pt;",
          "padding:4px;text-align:center;"
        ),
      ),
      opts_sizing(rescale = TRUE),
      opts_selection(type = "none"),
      opts_zoom(min = 1, max = 5)
    )
  )
}

3.2 Plotting the Network (distance = 3)

With the above function, we can plot the state of the network before and after 2035.

Code 
sec_network %>%
  extract_network_snapshot("2034-12-31") %>%
  plot_fishing_relationships(
    emphasize_nodes = c("SouthSeafood Express Corp", "Liam Conti"),
    title = "SouthSeafood Express Corp's Network (distance = 3) on Dec 31, 2034",
    subtitle = "**Liam Conti** is the person ultimately in control of the company via **AguaLeska Transit N.V.**"
  )
Code 
sec_network %>%
  extract_network_snapshot("2036-01-01") %>%
  plot_fishing_relationships(
    emphasize_nodes = c("SouthSeafood Express Corp", "Liam Conti"),
    title = "SouthSeafood Express Corp's Network (distance = 3) on Jan 1, 2036",
    subtitle = "Liam Conti **distanced** himself from the company while still maintaining some form of control through a series of companies."
  )
Findings

The visualization confirms our initial inference that Liam Conti distanced himself from SouthSeafood Express Corp after the discovery of illegal fishing.

It also reveals another beneficiary of this action, Fintan Park, who is also a beneficial owner of StitchtingMarine Shipping Company, which is the company who eventually holds the power over SouthSeafood Express Corp.

3.3 Plotting the Network (all connected nodes)

It is also important to look at the wider network if there are other suspicious changes and additional information related to Liam Conti’s actions.

Code 
supernetwork %>%
  extract_subnetwork("SouthSeafood Express Corp") %>%
  extract_network_snapshot("2034-12-31") %>%
  plot_fishing_relationships(
    emphasize_nodes = c(
      "SouthSeafood Express Corp",
      "Liam Conti",
      "Nadia Conti",
      "Lena Conti-Park",
      "Fintan Park",
      "Nathan Conti",
      "Lemuel Conti",
      "Fabio Conti",
      "Samuel Conti"
      ),
    title = "SouthSeafood Express Corp's Full Network on Dec 31, 2034",
    subtitle = "Members of the **Conti Clan** are related to all fishing businesses in the network."
  )
Code 
supernetwork %>%
  extract_subnetwork("SouthSeafood Express Corp") %>%
  extract_network_snapshot("2036-01-01") %>%
  plot_fishing_relationships(
    emphasize_nodes = c(
      "SouthSeafood Express Corp",
      "Liam Conti",
      "Nadia Conti",
      "Lena Conti-Park",
      "Fintan Park",
      "Nathan Conti",
      "Lemuel Conti",
      "Fabio Conti",
      "Samuel Conti",
      "The News Buoy"
      ),
    title = "SouthSeafood Express Corp's Full Network on Jan 1, 2036",
    subtitle = "The Conti Clan obtained control of a news company, **The News Buoy** in 2035."
  )
Findings

Looking at the wider network reveals that all the fishing companies in the network are under a control of a group of people, the Conti Clan. Although not formally related as family members in the graph, their family names indicate the relationship. Some influential people like Fintan Park are also part of the clan by marriage (e.g., to Lena-Conti Park).

Another suspicious event in 2035 is the clan’s acquisition of shareholdership in a news company, The News Buoy through Samuel Conti. This could be an effort to influence the narrative of SouthSeafood and the whole Conti Clan’s fishing activities.

4 Visualizing Influence

4.1 Calculating measures of centrality

To visualize influence, we first need to calculate the measures of centrality for each state of the network from before and after 2035.

sec_network_full <- supernetwork %>%
  extract_subnetwork("SouthSeafood Express Corp") %>%
  convert_graph_to_power_flow()
nodes_influence_before <- sec_network_full %>%
  extract_network_snapshot('2034-12-31', delete = TRUE) %>%
  mutate(
    pagerank = centrality_pagerank(weights = E(.)$weight),
    betweenness = centrality_betweenness(weights = E(.)$weight, normalized = TRUE)
  ) %>%
  as_data_frame(what="vertices")

# Generate the graph for plotting
sec_influence_before <- sec_network_full %>%
  extract_network_snapshot('2034-12-31') %>%
  left_join(nodes_influence_before)

nodes_influence_before %>% arrange(name) %>% select(-name) %>% kable()
alias supertype subtype product_services included pagerank betweenness
4. SeaCargo Ges.m.b.H. 4SGm Organization LogisticsCompany Tuna, sword fish, bass, trout, and salmon, as well as offers shellfish, mollusks, crustaceans, sea vegetables, shrimp, lobster, squid, oysters, crabs, and clams, and other related seafood products TRUE 0.0398513 0.0019231
9. RiverLine CJSC 9RC Organization Company Unknown TRUE 0.0143016 0.0012821
AguaLeska Transit N.V. ATNV Organization FishingCompany Fish and seafood products TRUE 0.0200629 0.0032051
ArawakFish Cargo Ges.m.b.H. ACGm Organization Company Fish and seafood products TRUE 0.0219065 0.0038462
BaringoAmerica Marine Ges.m.b.H. BMGm Organization FishingCompany Seafood TRUE 0.0108448 0.0000000
Dry CreekRybachit Marine A/S DCMA Organization FishingCompany Fish, crustaceans and other seafood TRUE 0.0325836 0.0044872
Dry CreekWorldLogistics Ltd. Liability Co DCLL Organization LogisticsCompany Fish and seafood products TRUE 0.0108448 0.0000000
Eun-Ji Park EJP Person Person NA TRUE 0.0108448 0.0000000
Fabio Conti FC Person Person NA TRUE 0.0714647 0.0000000
Fintan Park FP Person Person NA TRUE 0.0435924 0.0000000
FlounderLeska Marine BV FMB Organization FishingCompany Albacore, Alfonsino, Barramundi, Bass, Black Cod, Blue Cod, Bluenose, Caviar, Flounder, Groper, Gurnard, John Dory, Kingfish, Ling Kingclip, Lobster, Mahi, Ocean Trout, Opah Moonfish, Tuna TRUE 0.0108448 0.0000000
GvardeyskAmerica Shipping Plc GSP Organization Company Shipping services TRUE 0.0589632 0.0192308
Harvey Janus HJ Person Person NA TRUE 0.0166061 0.0000000
HomabayMarine Carriers N.V. HCNV Organization Company Fish, crustaceans and other seafood TRUE 0.0161452 0.0025641
James Bell JB Person Person NA TRUE 0.0200629 0.0000000
KambalaSea Freight Inc KFI Organization Company Fish and seafood products TRUE 0.0219065 0.0025641
KisumuSeafoodBrothers Ltd KL Organization FishingCompany Fresh and frozen seafood TRUE 0.0357336 0.0057692
Lemuel Conti LC Person Person NA TRUE 0.0963356 0.0000000
Lena Conti-Park LCP Person Person NA TRUE 0.0108448 0.0000000
Liam Conti LC Person Person NA TRUE 0.0299945 0.0000000
Maacama Ocean Worldwide LLC MOWL Organization FishingCompany Fish and seafood products TRUE 0.0108448 0.0000000
Nadia Conti NC Person Person NA TRUE 0.0108448 0.0000000
NamRiver Transit A/S NTAS Organization LogisticsCompany Fish and seafood products TRUE 0.0609635 0.0179487
Nathan Conti NC Person Person NA TRUE 0.0530417 0.0000000
NyanzaRiver Worldwide AS NWA Organization FishingCompany Fish and seafood products TRUE 0.0343217 0.0006410
Oka Charter Boat Transport OJSC OCBT Organization Company Sea and coastal water transportation and other related shipping activities TRUE 0.0108448 0.0000000
Oka Seafood Shipping Ges.m.b.H. OSSG Organization FishingCompany Fish and fish products (fresh and frozen seafood and other aquatic products, and canned and cured fish and seafood) TRUE 0.0163756 0.0019231
OranjestadCreek Express Sagl OES Organization Company Fish and seafood products TRUE 0.0292810 0.0051282
Rafael Sanchez RS Person Person NA TRUE 0.0155335 0.0000000
RechFish Freight Plc RFP Organization LogisticsCompany Freight trucking and other related transportation services TRUE 0.0108448 0.0000000
SamakaDredgeTransport OJSC SO Organization Company Sea and coastal water transportation and other related shipping activities TRUE 0.0108448 0.0000000
Samuel Conti SC Person Person NA TRUE 0.0108448 0.0000000
Sanaa El-Amin SEA Person Person NA TRUE 0.0108448 0.0000000
SavanetaCreek Solutions NV SSN Organization LogisticsCompany Shipping, freight trucking and other related transportation services TRUE 0.0202260 0.0038462
ScaniaSeafood Holdings Ltd. Liability Co SHLL Organization FishingCompany Marine fishing TRUE 0.0108448 0.0000000
SouthLeska Worldwide AS SWA Organization FishingCompany Fish and seafood products TRUE 0.0251699 0.0006410
SouthSeafood Express Corp SEC Organization FishingCompany Fishing and other related activities TRUE 0.0108448 0.0000000
StichtingMarine Shipping Company SSC Organization FishingCompany Fish and seafood products TRUE 0.0212151 0.0064103
SumacAmerica Transport GmbH & Co. KG STGC Organization LogisticsCompany Sea and coastal water transportation and other related shipping activities TRUE 0.0108448 0.0000000
The News Buoy TNB Organization NewsCompany Publication of daily newspaper, website, and other news sources TRUE 0.0108448 0.0000000
WestRiver Shipping KgaA WSK Organization Company Fish and seafood products TRUE 0.0108448 0.0000000 
nodes_influence_after <- sec_network_full %>%
  extract_network_snapshot('2036-01-01', delete = TRUE) %>%
  mutate(
    pagerank = centrality_pagerank(weights = E(.)$weight),
    betweenness = centrality_betweenness(weights = E(.)$weight, normalized = TRUE)
  ) %>%
  as_data_frame(what="vertices")

# Generate the graph for plotting
sec_influence_after <- sec_network_full %>%
  extract_network_snapshot('2036-01-01') %>%
  left_join(nodes_influence_after)

nodes_influence_after %>% arrange(name) %>% select(-name) %>% kable()
alias supertype subtype product_services included pagerank betweenness
4. SeaCargo Ges.m.b.H. 4SGm Organization LogisticsCompany Tuna, sword fish, bass, trout, and salmon, as well as offers shellfish, mollusks, crustaceans, sea vegetables, shrimp, lobster, squid, oysters, crabs, and clams, and other related seafood products TRUE 0.0347480 0.0016611
9. RiverLine CJSC 9RC Organization Company Unknown TRUE 0.0125506 0.0011074
ArawakFish Cargo Ges.m.b.H. ACGm Organization Company Fish and seafood products TRUE 0.0192244 0.0033223
BaringoAmerica Marine Ges.m.b.H. BMGm Organization FishingCompany Seafood TRUE 0.0095170 0.0000000
Dry CreekRybachit Marine A/S DCMA Organization FishingCompany Fish, crustaceans and other seafood TRUE 0.0278910 0.0038760
Dry CreekWorldLogistics Ltd. Liability Co DCLL Organization LogisticsCompany Fish and seafood products TRUE 0.0095170 0.0000000
Elise Hauser EH Person Person NA TRUE 0.0095170 0.0000000
Eun-Ji Park EJP Person Person NA TRUE 0.0095170 0.0000000
Fabio Conti FC Person Person NA TRUE 0.0638108 0.0000000
Fintan Park FP Person Person NA TRUE 0.0454812 0.0000000
FlounderLeska Marine BV FMB Organization FishingCompany Albacore, Alfonsino, Barramundi, Bass, Black Cod, Blue Cod, Bluenose, Caviar, Flounder, Groper, Gurnard, John Dory, Kingfish, Ling Kingclip, Lobster, Mahi, Ocean Trout, Opah Moonfish, Tuna TRUE 0.0095170 0.0000000
GvardeyskAmerica Shipping Plc GSP Organization Company Shipping services TRUE 0.0517440 0.0166113
Harvey Janus HJ Person Person NA TRUE 0.0154003 0.0000000
HomabayMarine Carriers N.V. HCNV Organization Company Fish, crustaceans and other seafood TRUE 0.0133411 0.0022148
James Bell JB Person Person NA TRUE 0.0145729 0.0000000
KambalaSea Freight Inc KFI Organization Company Fish and seafood products TRUE 0.0192244 0.0022148
KisumuSeafoodBrothers Ltd KL Organization FishingCompany Fresh and frozen seafood TRUE 0.0313586 0.0049834
Lemuel Conti LC Person Person NA TRUE 0.0839766 0.0000000
Lena Conti-Park LCP Person Person NA TRUE 0.0095170 0.0000000
Liam Conti LC Person Person NA TRUE 0.0309248 0.0000000
Maacama Ocean Worldwide LLC MOWL Organization FishingCompany Fish and seafood products TRUE 0.0095170 0.0000000
Nadia Conti NC Person Person NA TRUE 0.0095170 0.0000000
NamRiver Transit A/S NTAS Organization LogisticsCompany Fish and seafood products TRUE 0.0534994 0.0155039
Namorna Transit Ltd NTL Organization Company Seafood products TRUE 0.0372032 0.0110742
Nathan Conti NC Person Person NA TRUE 0.0476434 0.0000000
NyanzaRiver Worldwide AS NWA Organization FishingCompany Fish and seafood products TRUE 0.0314088 0.0011074
Oka Charter Boat Transport OJSC OCBT Organization Company Sea and coastal water transportation and other related shipping activities TRUE 0.0095170 0.0000000
Oka Seafood Shipping Ges.m.b.H. OSSG Organization FishingCompany Fish and fish products (fresh and frozen seafood and other aquatic products, and canned and cured fish and seafood) TRUE 0.0143707 0.0016611
OranjestadCreek Express Sagl OES Organization Company Fish and seafood products TRUE 0.0256959 0.0044297
Rafael Sanchez RS Person Person NA TRUE 0.0143648 0.0000000
RechFish Freight Plc RFP Organization LogisticsCompany Freight trucking and other related transportation services TRUE 0.0095170 0.0000000
SamakaDredgeTransport OJSC SO Organization Company Sea and coastal water transportation and other related shipping activities TRUE 0.0095170 0.0000000
Samuel Conti SC Person Person NA TRUE 0.0125506 0.0022148
Sanaa El-Amin SEA Person Person NA TRUE 0.0095170 0.0000000
SavanetaCreek Solutions NV SSN Organization LogisticsCompany Shipping, freight trucking and other related transportation services TRUE 0.0209122 0.0049834
ScaniaSeafood Holdings Ltd. Liability Co SHLL Organization FishingCompany Marine fishing TRUE 0.0095170 0.0000000
SouthLeska Worldwide AS SWA Organization FishingCompany Fish and seafood products TRUE 0.0233775 0.0011074
SouthSeafood Express Corp SEC Organization FishingCompany Fishing and other related activities TRUE 0.0095170 0.0000000
StichtingMarine Shipping Company SSC Organization FishingCompany Fish and seafood products TRUE 0.0427576 0.0132890
SumacAmerica Transport GmbH & Co. KG STGC Organization LogisticsCompany Sea and coastal water transportation and other related shipping activities TRUE 0.0095170 0.0000000
Tainamarine Fishing Co TFC Organization FishingCompany Fish and seafood products TRUE 0.0176065 0.0038760
The News Buoy TNB Organization NewsCompany Publication of daily newspaper, website, and other news sources TRUE 0.0095170 0.0000000
V. Miesel Shipping VMS Organization Company Seafood products TRUE 0.0325720 0.0099668
WestRiver Shipping KgaA WSK Organization Company Fish and seafood products TRUE 0.0095170 0.0000000

4.2 Plotting function

We will use the function plot_centrality() to visualize the influence within the network:

Show code for plot_centrality() 
plot_centrality <- function(graph,
                            # Column containing centrality measure, can be
                            # pagerank: for most powerful nodes
                            # betweeness: for power brokers
                            centrality_col,
                            # Name of nodes to emphasize
                            emphasize_nodes = c(),
                            # Layout options
                            layout = "nicely",
                            title = NULL,
                            subtitle = NULL) {
  set.seed(4231)
  
  if (!(centrality_col %in% c("pagerank", "betweenness"))) {
    stop("Only pagerank and betweenness centralities are relevant in our analysis")
  }
  
  nodes <- as_data_frame(graph, what = "vertices")
  
  edges <- as_data_frame(graph, what = "edges")
  max_weight <- edges$weight %>% max()
  min_weight <- edges$weight %>% min()
  
  g <- ggraph(graph, layout = layout) +
    # Render nodes
    geom_point_interactive(
      aes(
        x = x,
        y = y,
        data_id = sub("'", "&#39;", name),
        tooltip = sprintf(
          "%s (%s)<br/>Score: %0.5f",
          sub("'", "&#39;", name),
          subtype, 
          .data[[centrality_col]]
        ),
        # To show people as triangle, organizations as circle
        # See scale_shape_manual code below
        shape = supertype,
        # Get centrality measures from a column
        fill = .data[[centrality_col]],
        size = .data[[centrality_col]],
      ),
      alpha = nodes$included,
      # Thicken border if emphasized
      color = ifelse(nodes$name %in% emphasize_nodes, "black", "grey50"),
      stroke = ifelse(nodes$name %in% emphasize_nodes, 1, 0.5),
    ) +
    geom_node_label(
      aes(label = alias),
      family = "Roboto Condensed",
      size = 2,
      color = alpha("black", nodes$included),
      fontface = ifelse(nodes$name %in% emphasize_nodes, "bold", "plain"),
      alpha = nodes$included
    ) +
    
    # Render edges. Use geom_edge fan so edges along the same path don't overlap
    geom_edge_fan(
      aes(
        color = subtype,
        edge_width = weight,
        filter = ifelse(included == 1, TRUE, FALSE)
      ),
      strength = 0.5,
      arrow = arrow(type = "closed", length = unit(2, "pt")),
      end_cap = circle(1.6, "mm"),
      start_cap = circle(1.6, "mm"),
      alpha = 0.8
    ) +
    scale_shape_manual(values = MAPPINGS$node_supertype_to_shape) +
    scale_edge_color_manual(values = MAPPINGS$edge_power_subtype_to_color) +
    
    # Centrality visualization
    scale_fill_gradient(
      high = ifelse(centrality_col == "pagerank", "blue", "orange"),
      low = "white"
    ) +
    scale_size_continuous(range = c(3, 12), guide = FALSE) +
    
    # Make sure edge widths are consistent across diff graphs
    scale_edge_width(
      range = c(min_weight * 0.2, max_weight * 0.2),
      guide = "none"
    ) +
    
    # Change legend names
    labs(
      fill = ifelse(
        centrality_col == "pagerank",
        "PageRank Score",
        "Betweenness Score"
      ),
      shape = "Node Supertypes",
      edge_color = "Edge Subtypes"
    ) +
    
    # Make sure the plot is not clipped
    scale_x_continuous(expand = expansion(mult = c(0.10, 0.10))) +
    scale_y_continuous(expand = expansion(mult = c(0.10, 0.10))) +
    
    # Style legend keys
    guides(
      shape = guide_legend(
        override.aes = list(
          size = 3,
          fill = "blue"
        ),
        order = 1
      ),
      edge_color = guide_legend(order = 2),
      fill = guide_colorbar(order = 3)
    ) +
    ggtitle(title, subtitle) +
    
    # Style graph
    unset_graph_style() +
    theme_graph(base_family = "Roboto Condensed",
                plot_margin = margin(0)) +
    
    COMMON_THEME
  
  girafe(
    ggobj = g,
    width_svg = 6,
    height_svg = 6 * 0.618,
    options = list(
      opts_tooltip(
        css = paste0(
          "background-color:black;color:white;",
          "font-family:Roboto Condensed;font-size:10pt;",
          "padding:4px;text-align:center;"
        ),
      ),
      opts_sizing(rescale = TRUE),
      opts_selection(type = "none"),
      opts_zoom(min = 1, max = 5)
    )
  )
}

4.3 Visualizing Power Holders

We will use the plotting function to plot the power holders.

Code 
sec_influence_before %>%
  plot_centrality(
    centrality_col = "pagerank",
    emphasize_nodes = "SouthSeafood Express Corp",
    title = "SouthSeafood Express Corp's Full Network on Dec 31, 2034",
    subtitle = "**Lemuel Conti** and other members of the Conti clan hold the most power in the network."
  )

Nodes List

Code 
sec_influence_before %>%
  as_data_frame(what = "vertices") %>%
  filter(included == 1) %>%
  arrange(-pagerank) %>%
  select(name, subtype, pagerank) %>%
  mutate(pagerank = round(pagerank, 3)) %>%
  datatable(rownames = FALSE)
Code 
sec_influence_after %>%
  plot_centrality(
    centrality_col = "pagerank",
    emphasize_nodes = "SouthSeafood Express Corp",
    title = "SouthSeafood Express Corp's Full Network on Jan 1, 2036",
    subtitle = "There is little no no change in influence as power holders of the Conti Clan members."
  )

Nodes List

Code 
sec_influence_after %>%
  as_data_frame(what = "vertices") %>%
  filter(included == 1) %>%
  arrange(-pagerank) %>%
  select(name, subtype, pagerank) %>%
  mutate(pagerank = round(pagerank, 3)) %>%
  datatable(rownames = FALSE)
Findings

The actions of the Conti Clan to distance themselves from SouthSeafood Express Corp has little to no impact to their power over the system.

Liam Conti’s power wasn’t impacted much even when his company, AguaLeska Transit N.V., closed as a result of this series of events. Have a business network like the Conti Clan’s lead to cooperation to maintain control, which can make it more difficult to crack down on illegal fishing in this network.

4.4 Visualizing Power Brokers

We will use the plotting function to plot the power brokers.

Code 
sec_influence_before %>%
  plot_centrality(
    centrality_col = "betweenness",
    emphasize_nodes = "SouthSeafood Express Corp",
    title = "SouthSeafood Express Corp's Full Network on Dec 31, 2034",
    subtitle = "Companies controlled by the Conti Clan are the power brokers in the network."
  )

Nodes List

Code 
sec_influence_before %>%
  as_data_frame(what = "vertices") %>%
  filter(included == 1) %>%
  arrange(-betweenness) %>%
  select(name, subtype, betweenness) %>%
  mutate(betweenness = round(betweenness, 3)) %>%
  datatable(rownames = FALSE)
Code 
sec_influence_after %>%
  plot_centrality(
    centrality_col = "betweenness",
    emphasize_nodes = "SouthSeafood Express Corp",
    title = "SouthSeafood Express Corp's Full Network on Jan 1, 2036",
    subtitle = "**StichtingMarine Shipping Company**'s influence increased as provides the only connection of the Contis to SouthSeafood Express Corp."
  )

Nodes List

Code 
sec_influence_after %>%
  as_data_frame(what = "vertices") %>%
  filter(included == 1) %>%
  arrange(-betweenness) %>%
  select(name, subtype, betweenness) %>%
  mutate(betweenness = round(betweenness, 3)) %>%
  datatable(rownames = FALSE)
Findings

The influence of StichtingMarine Shipping Company as a power broker increased after “hiding” SouthSeafood Express Corp behind a series of companies. This is because StichtingMarine Shipping Company is the only connection of the Conti Clan to SouthSeafood Express Corp.