Exploration of project memberships

Author

Romain Frelat

Published

August 13, 2026

The objective is to explore the relation among members of FRB-MTE-OFB projects.

Based on project membership, we:

cluster projects based on shared members
identify members that link multiple projects (i.e. hubs)

This document is mostly an exploration of network analysis methodology and interactive visualization.

The raw data is not available on Github to safeguard privacy.

General overview

Code

library(igraph) # network analysis
library(visNetwork) # interactive network
library(plotly) # interactive plot

# load membership list
mem <- read.csv(
  here::here("data", "derived-data", "mte_members.csv")
)

# load informations on projects
meta <- readxl::read_xlsx(
  here::here("data", "raw-data", "mte", "Projets_FRB-MTECT-OFB.xlsx")
)

# create a last+first name column
mem$name <- paste(mem$lastname, mem$firstname)

# number of members per group and position
table(mem$group, mem$function_in_group)

             
              Associate Member PI Post-doc
  Acoucene            0     10  2        1
  Beyonds             0     10  2        1
  Carapat             1      4  2        0
  Comepi              0      8  1        1
  Desybel             1      8  1        0
  Discar              0     10  2        1
  Dragon              0      9  2        1
  Ebenn               0      5  1        1
  Elan                0      6  1        0
  Fellow              0     10  2        1
  Fragshifts          0      8  2        1
  Funbiodiv           0     10  2        1
  Funindic            0      5  1        1
  Impacts             0     10  2        1
  Indicators          0     10  2        1
  Interface           0      5  1        0
  Landbio             0      8  1        0
  Landworm            0      7  3        1
  Motiver             0     10  2        1
  Pppirec             1      1  2        0
  Rodexpo             1      6  2        0
  Solaire-pb          0      7  1        1
  Spatman             0      8  2        1
  Tres-pratic         0      8  1        1

Code

# number of members per type of group
n_mem <- data.frame(table(mem$group))
n_mem$Type <- meta$Type[match(n_mem$Var1, meta$Acronyme)]
tapply(n_mem$Freq, n_mem$Type, summary)

$`REVUE SYSTEMATIQUE`
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    7.0     8.5     9.5     9.0    10.0    10.0 

$SYNERGIE
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   4.00    7.00    8.00    8.30    9.75   13.00 

$SYNTHESE
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  11.00   12.25   13.00   12.50   13.00   13.00

Code

# list all group per name
infoV <- tapply(mem$group, mem$name, paste, collapse = "<br>")

nproj <- table(table(mem$name))

Among the 24 projects of the programs, there are 223 different researchers. Most of the researcher are member of a single project (N=204), but 17 researchers are attached to 2 projects; and 2 researchers works on 3 projects.

Project network

Based on the number of shared members, we can build a network of projects.

Code

group_mem <- table(mem$group, mem$name)
member_overlap <- tcrossprod(group_mem)
# or Jaccard to account for different group size
# proxy::simil(group_mem, method = "Jaccard", diag = TRUE, upper = TRUE)

diag(member_overlap) <- 0

netMEM <- igraph::graph_from_adjacency_matrix(
  member_overlap,
  mode = "undirected",
  weighted = TRUE
)

# modularity (optimal because the graph is tiny)
modMEM <- cluster_walktrap(netMEM) # same as cluster_optimal

# set color per group
cluMEM <- membership(modMEM)
nclu <- table(cluMEM)
cclu <- colorspace::qualitative_hcl(n = length(nclu), palette = "Dark 3")
cclu[nclu == 1] <- "#808080" # grey
colMEM <- cclu[cluMEM]
simclu <- ifelse(cluMEM <= (sum(nclu > 1)), cluMEM, "isolated")

The network has 24 nodes, 19 edges, a connectance of 0.069 and a modularity of 0.69

Project network with modules

Code

V(netMEM)$type <- as.factor(meta$Type[match(V(netMEM)$name, meta$Acronyme)])
V(netMEM)$year <- meta$Year[match(V(netMEM)$name, meta$Acronyme)]
V(netMEM)$group <- simclu
V(netMEM)$color <- colMEM
E(netMEM)$width <- E(netMEM)$weight
V(netMEM)$title <- paste(
  V(netMEM)$name,
  V(netMEM)$type,
  V(netMEM)$year,
  sep = "<br>"
)
visNetwork::visIgraph(netMEM, randomSeed = 54, layout = "layout_nicely") |>
  visOptions(
    highlightNearest = TRUE,
    selectedBy = list(variable = "group", multiple = T)
  ) |>
  visPhysics(stabilization = FALSE)

Code

# layout_nicely, layout_with_fr, layout_with_kk

Code

# identify cliques
for (i in sort(unique(simclu))) {
  print(paste(
    i,
    paste(V(netMEM)$name[simclu == i], collapse = ", "),
    sep = ": "
  ))
}

[1] "1: Comepi, Fellow, Funbiodiv, Motiver"
[1] "2: Acoucene, Indicators, Interface, Landbio"
[1] "3: Dragon, Funindic, Impacts, Landworm, Pppirec, Tres-pratic"
[1] "4: Desybel, Ebenn, Solaire-pb"
[1] "5: Beyonds, Elan"
[1] "isolated: Carapat, Discar, Fragshifts, Rodexpo, Spatman"

Project network with year and type

Code

# color by typexnod
typshp <- c("triangle", "square", "dot")[V(netMEM)$type]
V(netMEM)$shape <- typshp

# x-axis by year
vyr <- V(netMEM)$year
xnod <- (vyr - min(vyr)) / (max(vyr) - min(vyr)) * 2 - 1

# take the membership as y-axis
ymod <- as.numeric(as.factor(simclu))
ynod <- ymod / max(ymod)
# layout_nicely(netMEM)[, 2]
# sqrt(membership(modMEM)) / max(sqrt(membership(modMEM)))
# or take the first MDS dimension
# ynod <- layout_with_mds(netMEM)[, 1]

# coordinates
coo <- cbind(jitter(xnod, 1.5), jitter(ynod, 3))

# plot(netMEM, layout = coo)
laby <- sort(unique(vyr))
seqy <- (laby - min(laby)) / (max(laby) - min(laby)) * 2 - 1

visNetwork::visIgraph(
  netMEM,
  layout = 'layout.norm',
  layoutMatrix = coo,
  randomSeed = 54,
  type = "full"
) |>
  visLegend(
    addNodes = list(
      list(
        label = "Revue",
        shape = "triangle",
        color = "grey"
      ),
      list(
        label = "Synergie",
        shape = "square",
        color = "grey"
      ),
      list(
        label = "Synthese",
        shape = "dot",
        color = "grey"
      )
    ),
    useGroups = FALSE
  ) |>
  visOptions(
    highlightNearest = TRUE,
    selectedBy = list(variable = "type", multiple = T)
  )

Centrality

There are a lot of different measures of centrality. Here we use betweenness (number of shortest paths going through a vertex) and the Google page rank.

Code

centP <- data.frame(
  "betweenness" = betweenness(netMEM),
  "pagerank" = page_rank(netMEM)$vector,
  "degree" = degree(netMEM),
  "lab" = V(netMEM)$title,
  "color" = colMEM
)

plot_ly(centP) |>
  add_markers(
    x = ~betweenness,
    y = ~pagerank,
    size = ~degree,
    marker = list(color = ~color, line = list(color = ~color)),
    text = ~lab,
    hoverinfo = "text"
  ) |>
  layout(title = "Project centrality") |>
  config(
    modeBarButtons = list(list("toImage")),
    displaylogo = FALSE
  )

Code

info <- apply(centP[, 1:3], 2, round, 3)
score <- apply(scale(sqrt(info)), 1, mean)
DT::datatable(info[order(score, decreasing = TRUE), ])

Researcher network

Based on project membership, we can build two member networks:

where all group members are linked among them
where group members are linked only to the PI+postdoc

Code

pw <- c()
pw_pi <- c()
for (i in sort(unique(mem$group))) {
  ni <- mem$name[mem$group == i]
  pwi <- expand.grid(ni, ni) #or combn(ni, 2) for undirected
  combn(ni, 2)
  #remove identity / loop
  pwi <- pwi[pwi$Var1 != pwi$Var2, ]
  pw <- rbind(pw, pwi)

  # considering the central role of PI
  pi <- mem$name[
    mem$function_in_group %in% c("PI", "Post-doc") & mem$group == i
  ]
  pwi2 <- expand.grid(ni, pi)
  pwi2 <- pwi2[as.character(pwi2$Var1) != as.character(pwi2$Var2), ]
  pw_pi <- rbind(pw_pi, pwi2)
}

# add weight based on how many times
netRES <- igraph::graph_from_data_frame(pw, directed = FALSE)
modRES <- cluster_walktrap(netRES)
# plot(
#   netRES,
#   layout = layout_with_mds(netRES),
#   vertex.label = NA
# )

netRES_PI <- igraph::graph_from_data_frame(pw_pi, directed = FALSE)
modRES_PI <- cluster_walktrap(netRES_PI)
# plot(
#   netRES_PI,
#   layout = layout_with_mds(netRES_PI),
#   vertex.label = NA
# )

A. all members

The network linking all group members between them has 223 nodes, 2406 edges, a connectance of 0.097 and a modularity of 0.86.

Code

V(netRES)$title <- paste(
  V(netRES)$name,
  infoV[match(V(netRES)$name, names(infoV))],
  sep = "<br>"
)

modcol <- rainbow(max(membership(modRES)))[membership(modRES)]
V(netRES)$color <- modcol
visNetwork::visIgraph(netRES)

B. PI connected

The network linking all group members to the PI+Postdoc has 223 nodes, 559 edges, a connectance of 0.023 and a modularity of 0.89.

Code

V(netRES_PI)$title <- paste(
  V(netRES_PI)$name,
  infoV[match(V(netRES_PI)$name, names(infoV))],
  sep = "<br>"
)

modcol <- rainbow(max(membership(modRES_PI)))[membership(modRES_PI)]
V(netRES_PI)$color <- modcol
visNetwork::visIgraph(netRES_PI)

Centrality

We calculate centrality on the network with all members connected.

Code

centR <- data.frame(
  "betweenness" = betweenness(netRES),
  "degree" = degree(netRES),
  "pagerank" = page_rank(netRES)$vector,
  "lab" = V(netRES)$title
)

plot_ly(centR) |>
  add_markers(
    x = ~betweenness,
    y = ~pagerank,
    size = ~degree,
    text = ~lab,
    hoverinfo = "text"
  ) |>
  layout(title = "Researcher centrality") |>
  config(
    modeBarButtons = list(list("toImage")),
    displaylogo = FALSE
  )

Code

info <- apply(centR[, -4], 2, round, 3)
score <- apply(scale(sqrt(info)), 1, mean)
DT::datatable(info[order(score, decreasing = TRUE)[1:20], ])

Bipartite network

Code

netBI <- graph_from_data_frame(
  mem[, c("name", "group")]
)
V(netBI)$type <- V(netBI)$name %in% meta$Acronyme


V(netBI)$color <- ifelse(
  V(netBI)$type,
  V(netMEM)$color[match(V(netBI)$name, V(netMEM)$name)],
  "lightblue"
)
V(netBI)$shape <- ifelse(V(netBI)$type, "square", "dot")
# V(netBI)$size <- ifelse(V(netBI)$type, 3, 1)

extra <- ifelse(
  V(netBI)$type,
  paste(
    meta$Type[match(V(netBI)$name, meta$Acronyme)],
    meta$Year[match(V(netBI)$name, meta$Acronyme)],
    sep = "<br>"
  ),
  infoV[match(V(netBI)$name, names(infoV))]
)
V(netBI)$title <- paste(
  V(netBI)$name,
  extra,
  sep = "<br>"
)

# V(netBI)$size <- 1
modBI <- cluster_walktrap(netBI)

showBI <- delete_vertices(netBI, degree(netBI) == 1)
# plot(netBI, layout = layout_as_bipartite(netBI))
visNetwork::visIgraph(showBI)

The bipartite network has 247 nodes, 244 edges, and a connectance of 0.004.

Conclusion

We identified 5 sub-groups of projects based on shared members and a handful of researchers working on multiple FRB-MTE-OFB projects.

Yet, the membership is only a rough proxy of research collaboration. To better understand the research being produced, we need to investigate the bibliographic references produced and cited by each of the projects.