# How To Use This Package

#### Mauricio Vargas

#### 2024-12-12

This example is inspired after the visualizations from Hausmann et al. (2014) with some ggplot additions. The original vignette was largely improved from what I learned in Network Analysis taught at ICPSR 2023 by Dr. Sarah Shugars.

# World Trade and Per-Capita GDP

    library(economiccomplexity)

    # partial view of trade matrix
    head(world_trade_avg_1998_to_2000)

    ##   country product value
    ## 1     afg    0011 30068
    ## 2     afg    0012 16366
    ## 3     afg    0111 19273
    ## 4     afg    0112   893
    ## 5     afg    0113   350
    ## 6     afg    0116  1561

    # partial view of gdp vector
    head(world_gdp_avg_1998_to_2000)

    ##   country value
    ## 1     abw 19185
    ## 2     ago  1540
    ## 3     alb  1433
    ## 4     and 27765
    ## 5     arb  3312
    ## 6     are 43082

# Balassa Index

You can obtain Balassa Index with `balassa_index()`.

    bi <- balassa_index(world_trade_avg_1998_to_2000)

    # partial view of index
    n <- seq_len(5)
    bi[n, n]

    ##     0011 0012 0013 0014 0015
    ## afg    0    0    0    0    0
    ## ago    0    0    0    0    0
    ## aia    0    0    0    0    0
    ## alb    0    0    0    0    0
    ## and    1    0    0    0    1

Another possibility is to obtain Balassa Index without discretization.

    bi_dec <- balassa_index(world_trade_avg_1998_to_2000, discrete = FALSE)

    # partial view of index
    bi_dec[n, n]

    ##          0011        0012        0013       0014        0015
    ## afg 0.2312238 0.285438688 0.000000000 0.00000000 0.000000000
    ## ago 0.1777917 0.087436319 0.002076625 0.00139056 0.001106041
    ## aia 0.0000000 0.002581853 0.000000000 0.00000000 0.000000000
    ## alb 0.0000000 0.000000000 0.000000000 0.01582754 0.073011368
    ## and 2.4825815 0.550954168 0.000000000 0.48208017 3.815013019

# Complexity Measures

You can compute complexity indexes (e.g. such as the Economic Complexity Index and Product Complexity Index) by using `complexity_measures()`. The calculations methods are fitness (default), reflections, eigenvalues. See (Mariani et al. 2015) for the methodological details.

The eigenvalues also calls the reflections methods in order to correct the index sign in some special cases when the correlation between the output from both methods is negative.

## Complexity-Fitness

    com_fit <- complexity_measures(bi)

    # partial view of indexes
    com_fit$complexity_index_country[n]

    ##        afg        ago        aia        alb        and
    ## 0.78605655 0.03999516 1.05645538 1.24261128 1.37321261

    com_fit$complexity_index_product[n]

    ##      0011      0012      0013      0014      0015
    ## 0.7538883 0.7491391 2.3018690 0.9903918 1.3120378

## Reflections

    com_ref <- complexity_measures(bi, method = "reflections")

    # partial view of indexes
    com_ref$complexity_index_country[n]

    ##        afg        ago        aia        alb        and
    ## -0.5788151 -1.7710696  1.4074821 -0.1754989  1.0738736

    com_ref$complexity_index_product[n]

    ##        0011        0012        0013        0014        0015
    ## -0.66255100 -1.62169896 -0.07449482  0.20554725  0.15848849

## Eigenvalues

    com_eig <- complexity_measures(bi, method = "eigenvalues")

    # partial view of indexes
    com_eig$complexity_index_country[n]

    ##        afg        ago        aia        alb        and
    ## -0.5764283 -1.7770752  1.4090414 -0.1732606  1.0772452

    com_eig$complexity_index_product[n]

    ##        0011        0012        0013        0014        0015
    ## -0.66657613 -1.62657599 -0.08149436  0.19917280  0.14935653

# Proximity

Proximity matrices are used to create projections e.g. (country-country and product-product networks) for bipartite networks. Using `proximity()` is straightforward.

    pro <- proximity(bi)

    # partial view of proximity matrices
    pro$proximity_country[n, n]

    ##            afg         ago         aia        alb         and
    ## afg 1.00000000 0.015873016 0.181818182 0.19689119 0.192513369
    ## ago 0.01587302 1.000000000 0.006993007 0.01554404 0.005347594
    ## aia 0.18181818 0.006993007 1.000000000 0.16580311 0.251336898
    ## alb 0.19689119 0.015544041 0.165803109 1.00000000 0.310880829
    ## and 0.19251337 0.005347594 0.251336898 0.31088083 1.000000000

    pro$proximity_product[n, n]

    ##           0011      0012      0013      0014      0015
    ## 0011 1.0000000 0.3658537 0.1707317 0.2439024 0.2682927
    ## 0012 0.3658537 1.0000000 0.2500000 0.2250000 0.2500000
    ## 0013 0.1707317 0.2500000 1.0000000 0.2500000 0.1200000
    ## 0014 0.2439024 0.2250000 0.2500000 1.0000000 0.2250000
    ## 0015 0.2682927 0.2500000 0.1200000 0.2250000 1.0000000

# Projections

The `projections()` function is designed to use `igraph` for the internal computations and also to pass proximity-based networks to `igraph`, `ggraph` or export to Cytoscape by saving the output as csv/tsv.

    library(igraph)

    net <- projections(pro$proximity_country, pro$proximity_product)

    # partial view of projections
    E(net$network_country)[n]

    ## + 5/484 edges from bfc823a (vertex names):
    ## [1] zaf--zwe tza--zmb tza--uga tuv--wlf tuv--umi

    E(net$network_product)[n]

    ## + 5/1505 edges from 2aa2eae (vertex names):
    ## [1] 8981--8982 8946--9510 8922--8932 8921--8922 8852--8959

We can also use `igraph` to see how many edges are in the networks nd also the networks’ density, diameter and transitivity.

    ecount(net$network_country)

    ## [1] 484

    ecount(net$network_product)

    ## [1] 1505

    edge_density(net$network_country, loops = FALSE)

    ## [1] 0.01903638

    edge_density(net$network_product, loops = FALSE)

    ## [1] 0.00489081

    diameter(net$network_country, directed = FALSE, unconnected = FALSE)

    ## [1] 7.845477

    diameter(net$network_product, directed = FALSE, unconnected = FALSE)

    ## [1] 12.78569

    transitivity(net$network_country, type = "global")

    ## [1] 0.6151159

    transitivity(net$network_product, type = "global")

    ## [1] 0.4457284

# Centrality measures

We calculate the degree centrality of every node in the network and plot a histogram of these values. The drawback is that the network was trimmed until obtaining an average of 4 links per edge (or arcs per node), therefore the computation and histograms reflect a biased distribution.

    deg_country <- degree(net$network_country)
    deg_product <- degree(net$network_product)

    # country with the highest degree centrality
    deg_country[which.max(deg_country)]

    ## svn
    ##  25

    # product with the highest degree centrality
    deg_product[which.max(deg_product)]

    ## 8421
    ##   33

In the same way, we can compute the betweenness, cloness and eigenvector centrality of the networks.

    bet_country <- betweenness(net$network_country)
    bet_product <- betweenness(net$network_product)

    clo_country <- closeness(net$network_country)
    clo_product <- closeness(net$network_product)

    eig_country <- eigen_centrality(net$network_country)$vector
    eig_product <- eigen_centrality(net$network_product)$vector

    # country with the highest betweenness centrality
    bet_country[which.max(bet_country)]

    ##   ken
    ## 16718

    # product with the highest betweenness centrality
    bet_product[which.max(bet_product)]

    ##    7412
    ## 53858.5

    # country with the highest closeness centrality
    clo_country[which.max(clo_country)]

    ##         ken
    ## 0.002555277

    # product with the highest closeness centrality
    clo_product[which.max(clo_product)]

    ##         7412
    ## 0.0005298341

    # country with the highest eigenvector centrality
    eig_country[which.max(eig_country)]

    ## cze
    ##   1

    # product with the highest eigenvector centrality
    eig_product[which.max(eig_product)]

    ## 8434
    ##    1

Following the analysis, we can verify that the largest connected component is the same as the original networks in this case.

    # sub-networks of the largest connected component

    lcc_countries <- induced_subgraph(
      net$network_country,
      which(components(net$network_country)$membership ==
        which.max(components(net$network_country)$csize))
    )

    lcc_products <- induced_subgraph(
      net$network_product,
      which(components(net$network_product)$membership ==
        which.max(components(net$network_product)$csize))
    )

    # is this the same as the original networks?

    ecount(lcc_countries) == ecount(net$network_country)

    ## [1] TRUE

    vcount(lcc_countries) == vcount(net$network_product)

    ## [1] FALSE

    deg2_countries <- degree(lcc_countries)
    deg2_products <- degree(lcc_products)

    bet2_countries <- betweenness(lcc_countries)
    bet2_products <- betweenness(lcc_products)

    clo2_countries <- closeness(lcc_countries)
    clo2_products <- closeness(lcc_products)

    eig2_countries <- eigen_centrality(lcc_countries)$vector
    eig2_products <- eigen_centrality(lcc_products)$vector

    all.equal(
      deg_country[which.max(deg_country)],
      deg2_countries[which.max(deg2_countries)]
    )

    ## [1] TRUE

    all.equal(
      deg_product[which.max(deg_product)],
      deg2_products[which.max(deg2_products)]
    )

    ## [1] TRUE

    all.equal(
      bet_country[which.max(bet_country)],
      bet2_countries[which.max(bet2_countries)]
    )

    ## [1] TRUE

    all.equal(
      bet_product[which.max(bet_product)],
      bet2_products[which.max(bet2_products)]
    )

    ## [1] TRUE

    all.equal(
      clo_country[which.max(clo_country)],
      clo2_countries[which.max(clo2_countries)]
    )

    ## [1] TRUE

    all.equal(
      clo_product[which.max(clo_product)],
      clo2_products[which.max(clo2_products)]
    )

    ## [1] TRUE

    all.equal(
      eig_country[which.max(eig_country)],
      eig2_countries[which.max(eig2_countries)]
    )

    ## [1] TRUE

    all.equal(
      eig_product[which.max(eig_product)],
      eig2_products[which.max(eig2_products)]
    )

    ## [1] TRUE

# K-core and backbone

We can identify the k-core of the networks for an arbitray value “k”.

    k <- 4

    # identify the core of the network
    core_country <- coreness(net$network_country, mode = "all")
    core_product <- coreness(net$network_product, mode = "all")

    # identify the nodes in the core
    kcore_country <- induced_subgraph(
      net$network_country,
      which(core_country >= k)
    )

    kcore_product <- induced_subgraph(
      net$network_product,
      which(core_product >= k)
    )

    V(kcore_country)$name

    ##  [1] "aut" "bel" "bgr" "bih" "blr" "che" "chn" "cze" "deu" "dnk" "esp" "est"
    ## [13] "fin" "fra" "gbr" "grc" "hkg" "hrv" "hun" "ind" "ita" "jpn" "ken" "lbn"
    ## [25] "ltu" "mkd" "nld" "pak" "pol" "prt" "rom" "scg" "svk" "svn" "swe" "tur"
    ## [37] "ukr" "usa"

    V(kcore_product)$name

    ##   [1] "0142" "0223" "0240" "0252" "0484" "0565" "0583" "0586" "0620" "0730"
    ##  [11] "0980" "5332" "5334" "5335" "5417" "5419" "5542" "5543" "5821" "5825"
    ##  [21] "5989" "6123" "6210" "6289" "6343" "6354" "6359" "6416" "6417" "6418"
    ##  [31] "6421" "6422" "6424" "6428" "6518" "6546" "6575" "6581" "6583" "6584"
    ##  [41] "6589" "6618" "6631" "6632" "6633" "6635" "6648" "6794" "6911" "6912"
    ##  [51] "6921" "6924" "6940" "6954" "6973" "6975" "6991" "6996" "6997" "6998"
    ##  [61] "7139" "7211" "7212" "7213" "7219" "7259" "7269" "7281" "7368" "7369"
    ##  [71] "7371" "7372" "7412" "7413" "7416" "7423" "7429" "7432" "7436" "7439"
    ##  [81] "7449" "7452" "7492" "7493" "7499" "7711" "7732" "7742" "7757" "7758"
    ##  [91] "7783" "7810" "7821" "7849" "7868" "7919" "8121" "8122" "8211" "8212"
    ## [101] "8219" "8421" "8422" "8423" "8424" "8429" "8431" "8432" "8433" "8434"
    ## [111] "8435" "8439" "8441" "8442" "8443" "8451" "8452" "8459" "8461" "8462"
    ## [121] "8463" "8464" "8465" "8472" "8510" "8720" "8742" "8922" "8931" "8932"
    ## [131] "8939" "8997"

We can also identify the backbone of the networks.

    # identify the backbone of the network
    bbn_country <- delete_vertices(net$network_country, which(core_country < k))
    bbn_product <- delete_vertices(net$network_product, which(core_product < k))

    bbn_country

    ## IGRAPH 733b7e6 UNW- 38 283 --
    ## + attr: name (v/c), weight (e/n)
    ## + edges from 733b7e6 (vertex names):
    ##  [1] swe--usa svn--usa svn--tur svn--swe svk--usa svk--swe svk--svn scg--ukr
    ##  [9] scg--tur scg--svn scg--svk rom--ukr rom--tur rom--svn rom--svk rom--scg
    ## [17] prt--tur prt--svn prt--svk prt--scg prt--rom pol--usa pol--tur pol--swe
    ## [25] pol--svn pol--svk pol--scg pol--rom pol--prt pak--tur nld--usa nld--swe
    ## [33] nld--svk mkd--tur mkd--scg mkd--rom mkd--prt mkd--pak ltu--ukr lbn--tur
    ## [41] lbn--mkd ken--tur ken--scg ken--lbn jpn--usa jpn--swe jpn--svn ita--usa
    ## [49] ita--tur ita--swe ita--svn ita--svk ita--prt ita--pol ita--nld ita--jpn
    ## [57] ind--tur ind--scg ind--rom ind--pak ind--ken ind--ita hun--usa hun--tur
    ## + ... omitted several edges

    bbn_product

    ## IGRAPH dd6e1b9 UNW- 132 709 --
    ## + attr: name (v/c), weight (e/n)
    ## + edges from dd6e1b9 (vertex names):
    ##  [1] 8922--8932 8720--8939 8720--8742 8472--8997 8465--8510 8465--8472
    ##  [7] 8464--8472 8464--8465 8463--8510 8463--8472 8463--8465 8463--8464
    ## [13] 8462--8472 8462--8465 8462--8464 8462--8463 8461--8472 8461--8465
    ## [19] 8461--8463 8459--8472 8459--8465 8459--8464 8459--8463 8459--8462
    ## [25] 8452--8472 8452--8465 8452--8464 8452--8463 8452--8462 8452--8461
    ## [31] 8452--8459 8451--8997 8451--8472 8451--8465 8451--8464 8451--8463
    ## [37] 8451--8462 8451--8459 8451--8452 8443--8997 8443--8472 8443--8465
    ## [43] 8443--8464 8443--8463 8443--8462 8443--8459 8443--8452 8443--8451
    ## + ... omitted several edges

# Community detection

We can identify the communities of the networks with a fast greedy algorithm.

    com_country <- cluster_fast_greedy(net$network_country)
    com_product <- cluster_fast_greedy(net$network_product)

    all.equal(vcount(net$network_country), length(com_country$membership))

    ## [1] TRUE

    all.equal(vcount(net$network_product), length(com_product$membership))

    ## [1] TRUE

    # number of communities
    length(unique(com_country$membership))

    ## [1] 12

    length(unique(com_product$membership))

    ## [1] 41

# Complexity Outlook

Both the Complexity Outlook Index and Complexity Outlook Gain are obtained after the `complexity_outlook()` function.

    co <- complexity_outlook(
      economiccomplexity_output$balassa_index,
      economiccomplexity_output$proximity$proximity_product,
      economiccomplexity_output$complexity_measures$complexity_index_product
    )

    # partial view of complexity outlook
    co$complexity_outlook_index[n]

    ##        afg        ago        aia        alb        and
    ## 103.948610   9.962401 122.311158 152.107317 151.295380

    co$complexity_outlook_gain[n, n]

    ##          0011      0012      0013      0014      0015
    ## afg 0.8615531 0.7613878 0.7537907 1.0961458 0.8143851
    ## ago 0.9681802 0.8436855 0.8219918 1.2151040 0.8883146
    ## aia 0.8339114 0.7475080 0.7247198 1.0425043 0.7671877
    ## alb 0.7979779 0.7199705 0.7132042 1.0170093 0.7636545
    ## and 0.0000000 0.7118512 0.6829531 0.9987236 0.0000000

# Productivy Levels

The `productivity_levels()` dataset follows the definitions from Hausmann et al. (2014) and Hausmann, Hwang, and Rodrik (2005).

I don’t have a per-capita GDP dataset for the Galactic Federation, so I’ll create simulated data for the example.

    pl <- productivity_levels(
      world_trade_avg_1998_to_2000,
      world_gdp_avg_1998_to_2000
    )

    # partial view of productivity levels
    pl$productivity_level_country[n]

    ##       ago       alb       and       are       arg
    ##  8223.607  6343.341 13783.485 10207.679  9269.670

    pl$productivity_level_product[n]

    ##      0011      0012      0013      0014      0015
    ##  7915.893  3986.371 11375.710  6273.428 17628.950

# Integration with `ggplot2`

We can plot the distributions for the centrality measures.

    library(ggplot2)

    deg_country <- data.frame(
      country = names(deg_country),
      deg = deg_country
    )

    deg_product <- data.frame(
      product = names(deg_product),
      deg = deg_product
    )

    ggplot(deg_country) +
      geom_histogram(aes(x = deg), bins = 20, fill = "#002948") +
      theme_minimal(base_size = 13) +
      labs(title = "Degree Centrality Distribution for Countries")

    ggplot(deg_product) +
      geom_histogram(aes(x = deg), bins = 20, fill = "#002948") +
      theme_minimal(base_size = 13) +
      labs(title = "Degree Centrality Distribution for Products")

    bet_country <- data.frame(
      country = names(bet_country),
      bet = bet_country
    )

    bet_product <- data.frame(
      product = names(bet_product),
      bet = bet_product
    )

    clo_country <- data.frame(
      country = names(clo_country),
      clo = clo_country
    )

    clo_product <- data.frame(
      product = names(clo_product),
      clo = clo_product
    )

    eig_country <- data.frame(
      country = names(eig_country),
      eig = eig_country
    )

    eig_product <- data.frame(
      product = names(eig_product),
      eig = eig_product
    )

    ggplot(bet_country) +
      geom_histogram(aes(x = bet), bins = 20, fill = "#002948") +
      theme_minimal(base_size = 13) +
      labs(title = "Betweenness Centrality Distribution for Countries")

    ggplot(bet_product) +
      geom_histogram(aes(x = bet), bins = 20, fill = "#002948") +
      theme_minimal(base_size = 13) +
      labs(title = "Betweenness Centrality Distribution for Products")

    ggplot(clo_country) +
      geom_histogram(aes(x = clo), bins = 20, fill = "#002948") +
      theme_minimal(base_size = 13) +
      labs(title = "Closeness Centrality Distribution for Countries")

    ggplot(clo_product) +
      geom_histogram(aes(x = clo), bins = 20, fill = "#002948") +
      theme_minimal(base_size = 13) +
      labs(title = "Closeness Centrality Distribution for Products")

    ggplot(eig_country) +
      geom_histogram(aes(x = eig), bins = 20, fill = "#002948") +
      theme_minimal(base_size = 13) +
      labs(title = "Eigenvector Centrality Distribution for Countries")

    ggplot(eig_product) +
      geom_histogram(aes(x = eig), bins = 20, fill = "#002948") +
      theme_minimal(base_size = 13) +
      labs(title = "Eigenvector Centrality Distribution for Products")

# Integration with `ggraph`

We start by plotting the network of countries. Each node will be sized by its total exports.

    set.seed(200100)

    library(ggraph)

    aggregated_countries <- aggregate(
      world_trade_avg_1998_to_2000$value,
      by = list(country = world_trade_avg_1998_to_2000$country),
      FUN = sum
    )

    aggregated_countries <- setNames(
      aggregated_countries$x,
      aggregated_countries$country
    )

    V(net$network_country)$size <- aggregated_countries[
      match(V(net$network_country)$name,
      names(aggregated_countries))
    ]

    ggraph(net$network_country, layout = "kk") +
      # geom_edge_link(aes(edge_width = weight), edge_colour = "#a8a8a8") +
      geom_edge_link(edge_colour = "#a8a8a8") +
      geom_node_point(aes(size = size), color = "#002948") +
      geom_node_text(aes(label = name), size = 2, vjust = 2.2) +
      ggtitle("Proximity Based Network Projection for Countries") +
      theme_void()

Now we can highlight the countries with the highest centralities from the previous part.

    # Paint svn, ken and cze in yellow and the rest of the world in blue

    V(net$network_country)$color <- rep(
      "Rest of the World",
      length(V(net$network_country)$size)
    )
    V(net$network_country)$color[match(
      c("svn", "ken", "cze"),
      V(net$network_country)$name
    )] <- "Slovakia, Kenia and Czech Republic"

    ggraph(net$network_country, layout = "kk") +
      geom_edge_link(edge_colour = "#a8a8a8") +
      geom_node_point(aes(size = size, color = color)) +
      geom_node_text(aes(label = name), size = 2, vjust = 2.2) +
      ggtitle("Proximity Based Network Projection for Countries") +
      theme_void() +
      scale_colour_manual(values = c(
        "Slovakia, Kenia and Czech Republic" = "#fac704",
        "Rest of the World" = "#002948"
      ))

We can also plot the network of products. Each node will be sized by its total exports. Because the product names are large, we display the product codes instead. You can read about the codes here and if you need the codes in R, you can use the `tradestatistics` package, which can be installed from CRAN.

    set.seed(200100)

    aggregated_products <- aggregate(
      world_trade_avg_1998_to_2000$value,
      by = list(country = world_trade_avg_1998_to_2000$product),
      FUN = sum
    )

    aggregated_products <- setNames(
      aggregated_products$x,
      aggregated_products$country
    )

    V(net$network_product)$size <- aggregated_products[
      match(V(net$network_product)$name,
      names(aggregated_products))
    ]

    ggraph(net$network_product, layout = "kk") +
      geom_edge_link(edge_colour = "#a8a8a8") +
      geom_node_point(aes(size = size), color = "#002948") +
      geom_node_text(aes(label = name), size = 2, vjust = 2.2) +
      ggtitle("Proximity Based Network Projection for Products") +
      theme_void()

Now we can highlight the products with the highest centralities from the previous part.

    # Paint 8421, 7412 and 8434 in yellow and the rest of the products in blue

    V(net$network_product)$color <- rep(
      "Rest of the Products",
      length(V(net$network_product)$size)
    )
    V(net$network_product)$color[match(
      c("8421", "7412", "8434"),
      V(net$network_product)$name
    )] <- "8421, 7412 and 8434"

    ggraph(net$network_product, layout = "kk") +
      geom_edge_link(edge_colour = "#a8a8a8") +
      geom_node_point(aes(size = size, color = color)) +
      geom_node_text(aes(label = name), size = 2, vjust = 2.2) +
      ggtitle("Proximity Based Network Projection for Products") +
      theme_void() +
      scale_colour_manual(values = c(
        "8421, 7412 and 8434" = "#fac704",
        "Rest of the Products" = "#002948"
      ))

The communities detected in the previous part can be used to improve the plots.

    # Paint by community
    # for each vertex, replace X with the community number

    set.seed(200100)

    V(net$network_country)$color2 <- rep(NA, length(V(net$network_country)$size))

    for (i in seq_along(V(net$network_country)$color2)) {
      com_i <- as.character(com_country$membership[i])

      # if len(com$membership[i]) = 1, append a 0
      if (nchar(com_i) == 1) {
        com_i <- paste0("0", com_i)
      }

      V(net$network_country)$color2[i] <- paste0("Community ", com_i)
    }

    my_colors <- c(
      "#74c0e2", "#406662", "#549e95", "#8abdb6", "#bcd8af",
      "#a8c380", "#ede788", "#d6c650", "#dc8e7a", "#d05555",
      "#bf3251", "#872a41"
    )

    ggraph(net$network_country, layout = "kk") +
      geom_edge_link(edge_colour = "#a8a8a8") +
      geom_node_point(aes(size = size, color = color2)) +
      geom_node_text(aes(label = name), size = 2, vjust = 2.2) +
      ggtitle("Proximity Based Network Projection for Countries") +
      theme_void() +
      scale_colour_manual(values = my_colors)

For products, the challenge is to obtain 41 distinguisable colors.

    # Paint by community
    # for each vertex, replace X with the community number

    set.seed(200100)

    V(net$network_product)$color2 <- rep(NA, length(V(net$network_product)$size))

    for (i in seq_along(V(net$network_product)$color2)) {
      com_i <- as.character(com_product$membership[i])

      # if len(com$membership[i]) = 1, append a 0
      if (nchar(com_i) == 1) {
        com_i <- paste0("0", com_i)
      }

      V(net$network_product)$color2[i] <- paste0("Community ", com_i)
    }

    my_colors_2 <- c(
      "#74c0e2", "#406662", "#549e95", "#8abdb6", "#bcd8af",
      "#a8c380", "#ede788", "#d6c650", "#dc8e7a", "#d05555",
      "#bf3251", "#872a41", "#74c0e2", "#406662", "#549e95",
      "#8abdb6", "#bcd8af", "#a8c380", "#ede788", "#d6c650",
      "#dc8e7a", "#d05555", "#bf3251", "#872a41", "#74c0e2",
      "#406662", "#549e95", "#8abdb6", "#bcd8af", "#a8c380",
      "#ede788", "#d6c650", "#dc8e7a", "#d05555", "#bf3251",
      "#872a41", "#74c0e2", "#406662", "#549e95", "#8abdb6",
      "#bcd8af"
    )

    ggraph(net$network_product, layout = "kk") +
      geom_edge_link(edge_colour = "#a8a8a8") +
      geom_node_point(aes(size = size, color = color2)) +
      geom_node_text(aes(label = name), size = 2, vjust = 2.2) +
      ggtitle("Proximity Based Network Projection for Products") +
      theme_void() +
      scale_colour_manual(values = my_colors_2)

We can try to obtain clusters in a different way, by pre-specifying the number of communities. Because this has some arbitrary element, we can specify a number equal to the sections in the Harmonised System, which is 21 plus the unspecified products.

    set.seed(200100)

    my_colors_3 <- c(
      "#74c0e2", "#406662", "#549e95", "#8abdb6", "#bcd8af",
      "#a8c380", "#ede788", "#d6c650", "#dc8e7a", "#d05555",
      "#bf3251", "#872a41", "#993f7b", "#7454a6", "#a17cb0",
      "#d1a1bc", "#a1aafb", "#5c57d9", "#1c26b3", "#4d6fd0",
      "#7485aa", "#d3d3d3"
    )

    com_product <- cluster_fluid_communities(
      net$network_product,
      no.of.communities = 22
    )

    V(net$network_product)$color2 <- rep(NA, length(V(net$network_product)$size))

    for (i in seq_along(V(net$network_product)$color2)) {
      com_i <- as.character(com_product$membership[i])

      # if len(com$membership[i]) = 1, append a 0
      if (nchar(com_i) == 1) {
        com_i <- paste0("0", com_i)
      }

      V(net$network_product)$color2[i] <- paste0("Community ", com_i)
    }

    ggraph(net$network_product, layout = "kk") +
      geom_edge_link(edge_colour = "#a8a8a8") +
      geom_node_point(aes(size = size, color = color2)) +
      geom_node_text(aes(label = name), size = 2, vjust = 2.2) +
      ggtitle("Proximity Based Network Projection for Products") +
      theme_void() +
      scale_colour_manual(values = my_colors_3)

# References

Hausmann, Ricardo, César Hidalgo, Sebastián Bustos, Michele Coscia, Alexander Simoes, and Muhammed Yildirim. 2014. The Atlas of Economic Complexity: Mapping Paths to Prosperity. MIT Press. https://doi.org/10.7551/mitpress/9647.001.0001.

Hausmann, Ricardo, Jason Hwang, and Dani Rodrik. 2005. “What You Export Matters.” Working Paper 11905. Working Paper Series. National Bureau of Economic Research. https://doi.org/10.3386/w11905.

Mariani, Manuel, Alexandre Vidmer, Matsúš Medo, and Yi-Cheng Zhang. 2015. “Measuring Economic Complexity of Countries and Products: Which Metric to Use?” The European Physical Journal B 88 (11): 293. https://doi.org/10.1140/epjb/e2015-60298-7.